Modern physics predicts with extraordinary precision, but leaves its underlying physical picture spare. Particles are catalogued by their properties, fields by equations, forces by formalisms, and cosmology by large-scale parameters. These descriptions work, yet they leave open a question: could the same phenomena also admit a more concrete mechanism-based ontology?
The Inter-Rung Coupling Hypothesis (IRCH) explores one such possibility. It begins from two foundational commitments: waves require a supporting medium, and any force appearing to act at a distance must be mediated through such a medium. It then adopts a scale-recursive hypothesis: nature is organized as a hierarchy in which the persistent large-scale structure of one level becomes the medium of the next, and neighbouring levels are dynamically coupled.
From these premises, an observationally constrained deductive narrative unfolds in which the familiar forces and the observed matter/antimatter asymmetry are developed as candidate consequences of inter-rung coupling. Cosmologically, observable redshift and the cosmic microwave background are read as related consequences of inter-rung coupling, reflecting different aspects of how matter and light interact with their medium. The picture is not a finished theory. Its purpose is to test whether a small set of physical commitments, followed consistently, can generate a coherent story linking microphysics and cosmology while remaining constrained enough to invite future formal development.
Modern physics has a story for everything but few of those stories share a mechanism. Gravity is the geometry of spacetime. Forces are gauge symmetries acting on quantum fields. Particles are catalogued by their quantum numbers. Cosmology is parameterized by Hubble flow, dark matter, and dark energy. Each of these descriptions works extraordinarily well within its own domain, but they sit in parallel: they don't reduce to a common picture, and they don't share a mechanical account of why the phenomena look the way they do. The 19th-century impulse to ground physical law in mechanical pictures of an underlying medium was abandoned because it could not be made rigorous. But the desire behind it remains unmet: an ontology that explains as well as predicts.
This paper develops the Inter-Rung Coupling Hypothesis (IRCH): a sustained attempt to recover that mechanical picture under modern constraints. The central move is recursive. Matter is taken to be waves in a medium. That medium is the persistent large-scale organization of a finer-grained rung's matter. That finer-grained matter is itself waves in a still-deeper medium. The hierarchy is unbounded inward, with neighbouring rungs dynamically coupled. Once the recursion is on the table, a single mechanism recurs at every rung interface: a localized compression at one rung perturbs the medium one rung inward, and waves propagating through the perturbed inner medium guide localization at the original rung. We call this phase-delay oscillator coupling (PDOC). What we observe at our rung as gravity is one application of PDOC; the attractive balance within the strong nuclear force is another, one rung deeper.
The promise of a scale-recursive ontology is unification. The risk is unfalsifiable speculation, because the inner rungs are by construction inaccessible to direct observation. Emergent Rung Model Space (ERMS) [1] disciplines such constructions by spelling out architectural rules under which they can remain scientifically constrained. IRCH is a provisional implementation of those rules. It is a concrete physical narrative that respects ERMS's commitments and tests whether the framework can be realized in a coherent picture. The paper is qualitative throughout. Its goal is not to derive anything quantitatively. Instead, it makes the construction's internal dependencies and open derivational targets visible, so that the framework can be evaluated, refined, or falsified rather than endlessly adjusted.
The paper follows that arc from premises outward. Orientation (Part Ⅰ) sets out the conceptual lineage and the ERMS architecture. Foundations (Part Ⅱ) develops PDOC and applies it to gravity, confinement, particles, and the wider subatomic zoo. Bookkeeping (Part Ⅲ) asks whether the same ontology can carry baryogenesis, planetary evolution, medium emergence, AGN behaviour, cosmological redshift, and the CMB. Compatibility (Part Ⅳ) then considers relativity and quantum behaviour, not to replace their formalisms, but to ask what they look like when read through the same recursive-medium picture.
The ideas in this paper are part of an evolving story. They did not arrive as a finished proposal, and this section sketches their lineage so that the rest of the paper can be read in the right spirit: as an iterative conceptual exercise, not a closed theoretical construction.
Several distinct lines of thought fed into this picture.
The first was Tom Van Flandern's Meta Model [2], which proposed that physical phenomena arise from the interaction of two distinct substrates. One, which Van Flandern called elysium, was a light-carrying medium composed of small constituents called elysons; light was a disturbance in that medium, and its local density varied with gravitational potential. The other was a continuous isotropic flux of gravitons: ultra-small, ultra-fast particles whose partial absorption by matter produced gravity via Le Sage-style shadowing. Van Flandern further argued that an asymmetry in how matter interacts with this graviton flux could account for charge polarity, electrostatic repulsion and attraction, and the compaction of elysium into the dense envelopes that constitute the observable structure of particles and nuclei. In his picture, protons acted as absorbers while electrons acted as net emitters. The Meta Model treated both substrates as real, mechanically intelligible entities, and sought to recover familiar physics from their coupled dynamics.
IRCH does not inherit those details wholesale. It does not treat the gravitational carrier as a stream of particulate gravitons, and it does not assign charge polarity to protons and electrons acting as graviton absorbers or emitters. The influence is instead architectural and methodological: Van Flandern's insistence that physical theories should attempt mechanistic explanation, develop consequences deductively from explicit premises, and risk a priori predictions rather than only fitting known data shaped the style of inquiry pursued here.
The second influence was the broader family of Le Sage-style accounts of gravitation [3], in which gravity is interpreted as a pressure effect produced by a pervasive high-speed background flux partially obstructed by matter. These approaches have a long history and have persistently been set aside because of the so-called overheating problem, but they supply a concrete mechanical picture of gravity as a mediated interaction rather than an abstract geometric feature.
The third, encountered later, was the elastic-ether tradition. I first came across it through a podcast interview with Chantal Roth [4], in which she described space as a kind of solid: a real elastic medium in which matter and light are both waves. My initial reaction was to reject the idea. "How could empty space be a solid?" But the more I considered it, the more a different question took its place. If we are ourselves standing-wave structures in such a medium, how would we tell, from the inside, that the medium was solid? The tradition is much older than any specific modern presentation. It includes nineteenth-century work by MacCullagh [5] and Kelvin [6], among others. But it was the insistence on a genuinely solid substrate that made me take the family of ideas seriously. If light is a wave of a real medium, then that medium must support what light does; and because electromagnetic waves are transverse, the medium must admit elastic deformations (shear and torsion), not only compression.
Those influences supplied ingredients, but not yet a stable architecture. My first attempt to build on them was the Two-Medium Model (2MM) [7]. It specified two interacting media, a Light-Carrying Medium and a Gravity-Carrying Medium, and used them to develop an ontology of matter, forces, and cosmology. 2MMTwo-Medium "Model" was a misnomer. It was not a model in the quantitative sense, but a conceptual framework: a narrative ontology organized around two interacting media. was explicitly qualitative and intentionally did not attempt a formal dynamical specification. It went through many iterations. Each revision exposed problems in the earlier ones: ontological commitments made loosely and later found to overreach; mechanisms assigned to the wrong medium; architectural assumptions left implicit that turned out to matter once they were made explicit. None of these problems made the broader picture obviously wrong. What they did make clear was that a single paper trying both to name specific media and to constrain the rules governing how any such media could behave was bound to conflate two very different kinds of claim.
A more concrete problem forced the issue. 2MM had assigned both gravity and particle stability to the same Gravity-Carrying Medium, and a closer look made it clear that those two roles could not be played by the same flux. The natural fix was to introduce a third medium, with a still-deeper flux, dedicated to stability. But that move felt ad hoc, and it sharpened a more general concern. 2MM's gravitons were already at a scale we cannot directly observe: only their aggregate effect, gravity, is. A third medium would have sat at an even finer scale, even further from any direct empirical reach. Adding inaccessible-scale media on demand was exactly the kind of move that could turn the sketch into untestable conjecture.
That prompted a step back. Rather than continue to patch 2MM, I asked a more general question: what kinds of physical descriptions that invoke scales we cannot directly observe can remain scientifically constrained, rather than becoming repositories for unchecked speculation? The result was Emergent Rung Model Space (ERMS) [1]. ERMS is not a theory of physics; it is a framework: a set of architectural rules whose satisfaction is sufficient to keep a scale-recursive description scientifically accessible. ERMS does not claim to characterize the full space of admissible descriptions. It singles out a subspace within which any specific proposal can be evaluated, and if necessary falsified, rather than endlessly adjusted.
What this paper sketches is the picture I now call the Inter-Rung Coupling Hypothesis (IRCH): a revision of 2MM under ERMS's constraints, retaining several of its core commitments while replacing others outright. Three of 2MM's commitments carry forward mostly unchanged: matter as a chiral standing-wave structure, ongoing baryogenesis, and multiple co-existing media at distinct scales. The non-expansion treatment of cosmology is also retained: rung invariance forbids cosmological-scale evolution of the LCM. Observable redshift is developed instead as path-integrated phase-lock through a statistically stationary but locally dynamic medium, while the cosmic microwave background is treated as a candidate outward thermalized emission from the LCM reservoir. The medium hierarchy is made explicitly infinite, with each rung's matter dynamics depending on at least the two rungs immediately deeper. Gravity is no longer Le Sage-style shadowing but a wave-mechanical response of phase-locked oscillators to compression-induced phase landscapes in the surrounding medium. Vocabulary has been aligned with ERMS's framework throughout.
IRCH is offered as a high-level conceptual hypothesis, not a quantitative predictive model. In ERMS's own terms, it is a provisional implementation: a diagnostic construction meant to test whether the framework's commitments can be realized in a concrete physical narrative, and to expose where that attempt remains incomplete. This sketch is offered in that spirit.
This section sets up the framework and vocabulary the rest of the paper depends on. It begins with a quick introduction to Emergent Rung Model Space (ERMS): the architectural rules IRCH inherits, including the integer-indexed hierarchy of rungs, the recursive identification of each rung's medium with the scaffolding of the rung immediately inward, and the requirement that adjacent rungs couple dynamically. It then layers on the working vocabulary IRCH uses throughout: the Light-Carrying Medium, the role-named fluxes, and the Two Roles per Flux observation that directly motivates the mechanisms developed in the following sections.
Emergent Rung Model Space [1] treats physical reality as an open, integer-indexed hierarchy of rungs. Each rung corresponds to a non-overlapping interval of scale, and the rungs tile scale without gaps. No rung is singled out as fundamental. The observable rung is the rung whose dynamics we can directly measure.
concept Rung_{n} [Rung] The rung indexed by integer \(n\). The observable rung is labelled \(Rung_{0}\). Rungs further inward (smaller scales) are \(Rung_{-1}\), \(Rung_{-2}\), and so on. Rungs further outward (larger scales) are \(Rung_{+1}\), \(Rung_{+2}\), and so on.
In this paper, the observable rung is taken to span at least the range from the smallest subatomic particles we can directly detect (its inner bound) out to at least the cosmic web (its outer bound). Phenomena that sit cleanly inside this window are treated as intra-rung physics; phenomena that depend on structure inward of or outward of the detection range are handled through inter-rung coupling.
Because many arguments in ERMS are about a rung's neighbours rather than absolute indices, the framework introduces short aliases relative to a reference rung. For this paper the reference rung is always the observable one.
Each rung is described through four aspect symbols.
concept Rung_{n}^{med} [Medium] The medium of the rung is its structural support for propagation, interaction, and localization at that scale.
concept Rung_{n}^{flux} [Flux] Freely propagating modes supported by the medium.
concept Rung_{n}^{rest} [Rest] Localized modes supported by the medium.
concept Rung_{n}^{scaf} [Medium] The scaffolding of the rung is the large-scale organization that emerges from sustained collective behaviour of rest and flux near the upper end of the rung scale.
These symbols form a descriptive vocabulary. ERMS now adds three structural commitments.
Rung invariance. Every rung has the same structural and dynamical organization when described in its own native units. Native units include the rung's own characteristic length, time, and energy scales. Rung invariance is therefore form-invariance, not equality of dimensionful quantities when translated into DYN units. What looks like "radiation" or "particles" at \(Rung_{0}\) has structural counterparts at every other rung; the observable rung is not special at the framework level. In principle any rung can serve as the reference rung (\(DYN_{n}\) for an arbitrary integer \(n\)); in this paper the reference is usually the observable one, so we write \(DYN_{0}\), or simply \(DYN\) when the subscript is understood to be zero.
Recursive medium emergence. No rung's medium is taken as primitive. As a structural postulate of ERMS, the medium of any rung is identified with the scaffolding of the rung one step inward: \(DYN^{med} \equiv SUB^{scaf}\), \(SUB^{med} \equiv SUB2^{scaf}\), etc. This postulate is assumed here at the framework level; the paper's later sections motivate it by asking whether the observable rung can be read as a concrete instance of that recursive pattern. A direct consequence of recursive medium emergence is that media are not static substrates. Each rung's medium is the persistent organisation of the inner rung's matter, treated here as statistically stationary rather than frozen. The cosmological sections develop what that stationarity requires.
Mandatory inter-rung coupling. Adjacent rungs must interact through coupling between their respective flux and rest modes. Rungs are forbidden from being dynamically isolated: without such coupling, inaccessible rungs would be outside the domain of testable science.
Taken together, rung invariance, recursive medium emergence, and mandatory inter-rung coupling are the architectural devices by which ERMS attempts to define a class of scale-recursive descriptions that are in principle disprovable. They prevent inaccessible scales from becoming repositories of free parameters and force any candidate medium to answer to observable physics.
This paper's role, in ERMS's own terms, is that of a provisional implementation: a diagnostic construction meant to probe the internal coherence and failure modes of ERMS by trying to realize its commitments with concrete intra-rung and inter-rung processes. Provisional implementations are not candidate theories of nature; their value lies partly in what they illuminate when they fail.
IRCH now introduces a small role-based vocabulary for the concepts used most often in the sections that follow. These names do not replace ERMS's structural terms; they mark the pieces of that structure that are important from the observable rung.
Light is a subset of \(DYN^{flux}\); matter is a subset of \(DYN^{rest}\). The LCM is the only medium given a local name because its structural state is central throughout the paper: compression, gradients, and standing-wave configurations. The name also preserves the historical link to Tom Van Flandern's elysium in the Meta Model.
The other recurring terms are role-named fluxes: selected portions of neighbouring-rung wave energy, named for their observable role rather than for the whole rung they belong to.
concept g_{flux} [Flux] The gravity-relevant subset of \(SUB^{flux}\) whose coupling to compression-modified regions of the LCM produces gravity.
concept s_{flux} [Flux] Short for "stabilizing" flux. It is the particle-confining subset of \(SUB2^{flux}\) whose coupling to LCM compression confines high-frequency LCM oscillations into stable particles.
When the paper refers to the underlying media rather than to these role-selected fluxes, it uses the ERMS aliases directly: \(SUB^{med}\), \(SUB2^{med}\), and \(SUP^{med}\). There are no additional medium acronyms beyond LCM.
These labels are relational. They describe the observable role a flux plays for DYN, not what it is intrinsically. Just as \(DYN^{flux}\) may contain light-like and gravitational-wave-like partitions, \(SUB^{flux}\) should have its own internal partitions. \(g_{flux}\) is therefore not all of SUB flux, nor simply "SUB light"; it is the portion of SUB's light-like flux that lands on DYN as the gravity-mediating band. More specifically, it is the matter-resonant portion of \(SUB^{flux}\): the long-wavelength tail whose modes overlap the structures of phase-locked matter at DYN. Matter couples coherently to this resonant subset; the shorter-wavelength bulk of \(SUB^{flux}\) passes through DYN-scale matter without coupling, its sub-matter-scale features averaging out. Shift the reference rung inward, and \(s_{flux}\) plays the same 1-out gravitational role for SUB that \(g_{flux}\) plays for DYN.
Before developing this vocabulary further, one consequence of rung invariance is worth making explicit, because the sections that follow rely on it.
Each flux plays two roles at outer scales:
The strength asymmetry reflects what each role can detect: the 2-out role couples sharply to compact, compression-rich structures (\(s_{flux}\) is significant at the scale of a nucleus), while the 1-out role registers significantly only across extended aggregations (\(g_{flux}\) is negligible per particle but substantial at planet- and star-scale matter). This pattern is universal across rungs.
Each flux's effective range as an "agent of force" is itself narrower than a single rung. Its window straddles the boundary between the two outer rungs that host its roles: beginning partway through the 1-out rung and extending only into the early portion of the 2-out rung. This is what gives different observable forces their characteristic strengths and ranges. The concrete identifications at DYN (gravity, the strong nuclear force, particle confinement) are taken up in the sections that follow, where the underlying mechanism is also developed: phase-delay oscillator coupling (PDOC).
This section develops a single mechanism that recurs throughout the rest of the paper: how a localized compression structure at one rung produces a force on a test particle at that same rung, mediated by a flux propagating through a deeper rung. The wave-mechanical part of the mechanism is familiar: refractive phase delay through a medium with non-uniform impedance, the resulting anisotropic phase landscape at points inside such a medium, and the directional response of a driven phase-locked oscillator. What IRCH adds is the recursive rung setting that lets a compression at one rung perturb the medium one rung inward. We develop the mechanism here in rung-neutral language so that the concrete identifications at DYN (taken up in the following sections) can invoke it cleanly without each one re-deriving the same wave-mechanical bones.
Throughout this section we use neutral labels.
The mechanism is always across a single rung boundary: the flux that produces a force on \(Rung^{rest}_{n}\) lives exactly one rung inward, in \(Rung^{med}_{n-1}\). We call this coupling phase-delay oscillator coupling (PDOC) and avoid attaching it to any specific named forceThe named forces are special cases identified in the following sections. We use the abbreviation PDOC throughout the rest of the paper.
The mechanism rests on five assumptions, each combining ordinary wave-mechanical behaviour with the rung framework introduced in the previous section.
The mechanism that follows is what these five assumptions, taken together, imply.Some of the assumptions, particularly the fifth, are themselves motivated in later sections by what PDOC implies, which makes the overall reasoning circular. The structural defense of this kind of circularity is given in Appendix B.
Suppose \(Rung^{rest}_{n}\) aggregates somewhere; call this aggregation a source. By assumption 2, the source perturbs \(Rung^{med}_{n}\) locally: a compression halo extends around it, with density and impedance elevated near the source and falling off to ambient values at distance.
By assumption 3, \(Rung^{med}_{n} \equiv Rung^{scaf}_{n-1}\). Perturbing the scaffolding is perturbing how \(Rung^{rest}_{n-1}\) is organized at large scales: where the scaffolding compresses, the inner rung's rest is locally aggregated; where the scaffolding decompresses, it is sparser. The reorganization of \(Rung^{rest}_{n-1}\) has the same spatial profile as the original compression at \(Rung_{n}\).
But aggregated \(Rung^{rest}_{n-1}\) perturbs its own medium (assumption 2 applied at \(Rung_{n-1}\)). So the reorganization of \(Rung^{rest}_{n-1}\) in turn perturbs \(Rung^{med}_{n-1}\), with a profile that traces the original source at \(Rung_{n}\). This is the perturbation that \(Rung^{flux}_{n-1}\) will register.
The cascade is a single step:
\(Rung^{med}_{n}\) perturbed → \(Rung^{rest}_{n-1}\) reorganized → \(Rung^{med}_{n-1}\) perturbed.
Compression at \(Rung_{n}\) reaches \(Rung^{med}_{n-1}\) through this one step, leaving the inner medium perturbed in a spatial profile that traces the original source. There is some attenuation across the step (each transfer introduces inefficiencies and dilutes the perturbation against the inner rung's ambient state), but the directional profile remains anchored on the source. The cascade has a direction: inward. Outward effects are a different topic and are not invoked here.
\(Rung^{flux}_{n-1}\) propagates through \(Rung^{med}_{n-1}\). By assumption 4, where that medium is perturbed (compressed or impedance-shifted), the flux's local phase velocity is reduced, and a wave traversing such a region accumulates phase delay relative to one traversing unperturbed medium.
For the cascade-perturbed medium near our source: paths through different parts of the perturbation accumulate different amounts of phase delay. A path passing close to the source (where the cascade-perturbation is strongest) accumulates more delay; a path passing far from the source accumulates less.
At any test point in \(Rung^{med}_{n-1}\), \(Rung^{flux}_{n-1}\) arrives from many directions. The phase delays along paths from different directions are generally unequal, depending on each path's traversal of the cascade-perturbed region. Locally, this defines a phase landscape: a directionally-resolved pattern of phase delay at the test point.
The phase landscape has a gradient. Near a localized source, phase delay is greater along paths arriving from directions that pass closer to the source than along paths arriving from directions that miss it. The gradient at the test point points roughly towards the source: the side of the test point facing the source registers more phase delay than the side facing away.
This is standard refractive optics, applied to a flux passing through a medium perturbed by the cascade rather than by a direct material gradient. The mechanism that produces optical lensing through any non-uniform refractive medium is the same mechanism here: phase delay accumulating along paths through impedance gradients. What is rung-specific is only how the impedance gradient got there: through one cascade step from \(Rung_{n}\) to \(Rung_{n-1}\), rather than by direct material variation in a single medium.
A test instance of \(Rung^{rest}_{n}\) is, by assumption 5, a phase-locked standing wave with a definite eigenfrequency. It does not couple coherently to all of \(Rung^{flux}_{n-1}\): most of that flux runs at frequencies far above the test particle's eigenfrequency and averages out at the test particle's coherence timescale, contributing no directional driving. Only the matter-resonant subset of \(Rung^{flux}_{n-1}\) couples coherently to the test particle's wave structure. This is the band whose frequency content overlaps the test particle's eigenfrequency.
For that resonant subset, the phase landscape developed in the previous section applies: at the test particle's location, more phase delay arrives from the direction of the source than from the opposite direction. The test particle's response to this landscape follows from its wave structure (assumption 5) under standard wave mechanics. A phase-locked standing wave can be decomposed into counter-propagating travelling-wave components; each component is subject to refraction in a phase-velocity gradient, with wavefronts bending towards regions of lower phase velocity (greater phase delay). When both component travelling waves of a standing wave experience the same gradient, the standing wave's centroid drifts in the direction the wavefronts are bent towards. This is textbook geometrical optics applied to a standing-wave structure rather than to a free wave packet.
It follows that the test particle's centre of mass accelerates towards the direction of greater phase delay: towards the source.
The strength of the response depends on three structural quantities:
PDOC's wave-mechanical core has two pieces, and both have direct classical demonstrations. The first is a stationary medium perturbation creating a steady anisotropic phase landscape. The second is a phase-locked oscillator drifting in response to the gradient of that landscape.
Nearby classical analogies for the first piece are easy to find. A ripple tank with a glass plate submerged under part of the bath shows the basic wave-mechanical move directly: where the water is shallower, surface waves slow down, their wavelength shortens, and wavefronts crossing the boundary refract. Optical techniques show related behaviour in transparent media. Schlieren and shadowgraph imaging [8] visualize refractive-index gradients in heated air, gas plumes, and shock waves; Mach-Zehnder interferometry measures optical-path phase shifts through fringe displacement; and Shack-Hartmann wavefront sensors sample local wavefront slopes in real time, as in adaptive optics for atmospheric distortion of starlight. These are not demonstrations of PDOC itself. They are nearby demonstrations of the ordinary wave-mechanical ingredient PDOC borrows: a stationary perturbation of a wave-supporting medium can produce a stable, mappable wavefront or phase-gradient landscape for waves passing through it. The recursive-rung cascade that creates the perturbation in IRCH is a separate claim.
The second piece also has a nearby classical analogy, though an even looser one. In the bouncing-droplet hydrodynamic system [9], a small droplet bouncing on a vertically vibrated fluid bath phase-locks to the bath's vibration and moves through the wave field it helps sustain. Submerged topography that varies the local depth modifies the surface-wave dispersion relation and produces an anisotropic wave environment at the droplet's location [10]; the droplet's motion responds to that wave environment without direct contact with the obstacle. This is not a demonstration of IRCH rest, PDOC, or assumption 5 in full. The bath is externally driven, the droplet is not a confined standing wave, and the system includes its own hydrodynamic details. Its relevance is narrower: it shows that a phase-locked oscillator-like object can have its trajectory guided by a structured wave landscape in its surrounding medium.
Taken modestly, these analogies support the single-medium wave-mechanical intuition behind PDOC: perturbed media can shape wavefronts, and oscillator-like objects can respond to structured wave environments. They do not demonstrate the IRCH-specific claim. The distinctive step in PDOC is the recursive-rung cascade: compression at \(Rung_{n}\) perturbs \(Rung^{med}_{n-1}\) through the identity \(Rung^{med}_{n} \equiv Rung^{scaf}_{n-1}\), and that inner-rung phase landscape then couples back to \(Rung^{rest}_{n}\). That cross-rung loop has no direct laboratory analog at present.
Turning that loop into a mechanism is left as future work. A natural starting point is a toy two-coupled-scalar-field model in which the cascade structure is imposed explicitly: compression in an outer-rung field modulates the effective wave speed of an inner-rung field; the inner-rung wave accumulates phase delay through that modulation; and a phase-locked outer-rung oscillator is allowed to respond to the resulting phase landscape. The point of such a model would not be to prove IRCH in miniature, but to test whether the proposed coupling can produce coherent drift at all, and whether its scaling can approach a Newton-like force law. A successful run would give the cross-rung claim a working mathematical foothold; non-Newtonian scaling, excessive dissipation, or no drift would expose where the structural argument fails or has to be tightened.
PDOC can now be summarized in one sentence: compression at one rung perturbs the medium one rung inward, flux travelling through that perturbed inner medium accumulates an anisotropic phase delay, and phase-locked rest at the original rung responds to the resulting phase landscape by drifting towards greater delay.
The mechanism is rung-symmetric in form. The same five assumptions and the same wave-mechanical steps can be written at any rung. What varies between concrete identifications is the choice of \(n\): which rung hosts the source and the test particle, and therefore which rung's flux lives at \(n - 1\) and does the mediating. The section has not yet derived a numerical force law or a quantitative coupling constant; it has only built the structural bridge from recursive medium perturbation to phase-guided motion.
The next two sections put that bridge to work. First we set \(n = 0\) and identify the resulting \(SUB^{flux}\)-mediated interaction with gravity at DYN. Then we turn to confinement, where the same cross-rung logic appears in a different role: not as an aggregate-to-aggregate force, but as the feedback that lets a travelling LCM wave become localized rest.
In the last section we identified five assumptions and then demonstrated how an aggregation of \(Rung^{rest}_{n}\) called a source would create an anisotropic landscape of delayed phase \(Rung^{flux}_{n-1}\) in the vicinity of the source. We showed that a test particle (also a member of \(Rung^{rest}_{n}\)), modelled as a phase-locked oscillator, would experience an acceleration towards the source. We termed this phase-delay oscillator coupling (PDOC). Here we apply it to our home rung, the observable universe.
First let's restate the five assumptions from section 4, but in DYN vocabulary.
With those translations in place, the PDOC claim at DYN becomes:
A DYN rest structure, such as a proton, atom, or larger body, responds to an aggregation of mass by accelerating towards it.
PDOC applied to \(Rung_{0}\) is gravity. The inner-rung flux doing the mediating is what §3 named \(g_{flux}\): the gravity-relevant, matter-resonant subset of \(SUB^{flux}\).
A note on terminology before we go further. In the strict sense, gravity means the \(g_{flux}\)-mediated PDOC acting on \(DYN^{rest}\).
The paper also uses gravity in a looser rung-symmetric sense: PDOC at any rung. In that looser sense, \(s_{flux}\) acting on \(SUB^{rest}\) is "gravity at \(Rung_{-1}\)". From DYN, however, that same deeper-rung interaction will not look like ordinary gravity; it will enter the story differently. The shorthand is useful because one mechanism underlies several named forces, but the observed force depends on which rung is doing the coupling.
The translation above placed the gravity-mediating flux at \(SUB\) rather than at \(DYN\). Why not light (\(DYN^{flux}\)) itself, or some other DYN-scale carrier? Three structural considerations make the SUB-scale identification natural and put pressure on any same-rung alternative.
Universality. Gravity is observed, to high precision, as a composition-independent response of matter to mass-energy. Electromagnetism does not have that form: it couples through charge, current, polarization, and magnetic structure, and so treats different forms of matter differently. A DYN-scale electromagnetic carrier would therefore have to explain why those charge-structured differences disappear in the gravitational limit. The matter-resonant subset of \(SUB^{flux}\), by contrast, is proposed to couple to the eigenfrequency structure of phase-locked rest itself. Since that structure is common to confined matter at DYN, the universality of the response is built into the coupling target rather than added afterwards.
Smoothness. Observed gravitational driving is smooth on every scale we can measure, from Cavendish-balance precision through Solar System orbits. A DYN-scale carrier is not impossible on smoothness grounds alone. Classical fields at our scale can certainly be smooth. But such a carrier would have to couple coherently to particle-scale rest without producing detectable scattering, absorption, radiation pressure, shielding, or medium-drag effects. \(g_{flux}\) gives a cleaner structural separation: it lives one rung inward, couples only through the matter-resonant subset of \(SUB^{flux}\), and acts through accumulated phase delay rather than ordinary same-rung momentum transfer. The result can be smooth at DYN because the observable force is the aggregate response to a low-amplitude inner-rung phase landscape.
Penetration. Gravity reaches the deep interiors of planets, stars, and other dense aggregations. Electromagnetic radiation faces a difficult wavelength-coupling tradeoff: short wavelengths couple strongly to particle-scale structure but are absorbed or scattered, while long wavelengths penetrate matter but no longer resolve particle-scale eigenstructure. No ordinary EM band is known to be both transparent through bulk matter and universally resonant with confined rest. \(g_{flux}\) side-steps that tradeoff: it propagates in \(SUB^{med}\), beneath DYN matter in the rung hierarchy, and so DYN matter is not an obstacle in the same way it is for DYN-scale radiation.
Taken together, these considerations do not prove the SUB-scale carrier, but they make it the natural IRCH identification for the gravity mediator at DYN.
PDOC's translation gives the wave-mechanical content of gravity, but the Newtonian limit still needs a falloff law. The required scaling is familiar: for a compact source of mass \(M\), the cumulative phase delay in \(g_{flux}\) outside the source must behave like a potential, scaling as \(\frac{M}{r}\). The corresponding phase gradient at any test point is the quantity the test particle's standing wave responds to. It then falls off as \(\frac{M}{r^{2}}\). This is the structure of a Newtonian gravitational field, read as a coherent phase imbalance in \(g_{flux}\). The present section identifies that scaling target; deriving it from a full flux-transport model remains future work.
The equivalence principle has a natural structural reading in this picture. The strength of a test body's coupling to the surrounding phase landscape is set by the count of phase-locked rest structures making up the matter (call it \(N\)): more standing-wave structure means stronger total coupling. Inertial mass is also set by \(N\), since accelerating the body means rephasing more standing-wave structure into a new state of motion. Inertial mass is resistance to changes in motion. Both sides scale together. The ratio \(\frac{m_{g}}{m_{i}}\) is therefore constant in the ideal unshielded limit, and the resulting acceleration \(a = \frac{G\,M}{r^{2}}\) is composition-independent. This does not replace precision tests of the equivalence principle; it explains why IRCH expects the same acceleration for aggregates with different masses and compositions.
A caveat about scale. The phase delay produced by a single particle's compression halo is exceedingly small: far too small to drive a measurable phase gradient at any nearby test point. Gravity becomes operationally significant only once matter aggregates enough that the cumulative compression gradient is steep enough to be detected. That threshold is well below planetary mass: lab-scale Cavendish-style measurements with kilogram-scale aggregates already detect it [11, 12], and the standard Newtonian pair-force formulation works wherever the aggregate-scale conditions are met. For truly isolated particles, the model's predicted interaction is far below any current detection limit; the empirically anchored claim is the aggregate Newtonian limit, not a measured particle-pair force.
\(g_{flux}\) propagates through \(SUB^{med}\), a rung deeper than DYN. By rung invariance, \(SUB\)-scale dynamics run on shorter timescales than DYN-scale dynamics by a structural factor. From DYN's perspective, IRCH therefore expects \(g_{flux}\) propagation to appear extraordinarily fast compared with ordinary light, possibly fast enough to look effectively instantaneous in many gravitational settings. Van Flandern-style readings of gravitational timing data, which infer propagation much faster than the speed of light at DYN, are one interpretation consistent with this picture. Standard general relativity reads the same timing behaviour differently, through retarded fields, constraints, and near-zone cancellations; the consequences are taken up in the relativity section.
A natural worry is whether motion through \(g_{flux}\) produces detectable drag. The qualitative reason IRCH expects it to be small is the speed hierarchy: any drag-like asymmetry from coupling a moving standing-wave structure to a much faster background flux should be suppressed by a factor on the order of \(\frac{v}{v_{g}}\), where \(v\) is the matter's velocity at DYN and \(v_{g}\) is \(g_{flux}\)'s propagation speed. If \(v_{g} \gg c\), the ratio is vanishingly small for ordinary matter speeds. This is a scaling argument, not yet a derivation; a quantitative version would have to show that the same mechanism reproduces the tight empirical bounds on drag in planetary and binary-pulsar dynamics.
PDOC at \(DYN\) is a flux-mediated theory of gravity, and so belongs in conversation with the Le Sage family of mechanical gravity theories. The shared motivation is important: both pictures try to make gravity intelligible as a physical interaction mediated by something real, rather than as a force law left mechanically opaque. The structural similarity is that both use a pervasive flux and a directional asymmetry associated with massive bodies. The differences are mechanistic and matter for whether the picture survives contact with thermodynamics.
In the classic Le Sage mechanism, corpuscles transfer momentum to a body by being absorbed or inelastically scattered. The shadow cast by one body is a deficit of corpuscles arriving from its direction, and the net push on a second body comes from that imbalance. The central difficulty is energetic: a corpuscle flux strong enough to reproduce gravitational accelerations tends to carry an enormous energy density, and any appreciable absorption deposits that energy as heat. Purely elastic variants reduce the heating but then have to recover a net force despite the symmetry of elastic scattering from a uniform body.
In PDOC the force is not carried primarily by momentum deposition. \(g_{flux}\) propagates through \(SUB^{med}\); near aggregated \(DYN^{rest}\) that medium is compression-modified, and \(g_{flux}\) accumulates anisotropic phase delay across the modified region. To leading order the flux is treated as passing through with its amplitude largely intact while its phase fronts are bent. A test particle, modelled as a phase-locked standing wave at \(DYN\), accelerates because its eigenmode couples to the gradient of that phase landscape. The proposed coupling is therefore predominantly refractive rather than absorptive.
Why this might evade the Le Sage heating problem is worth making explicit. What "moves" under PDOC is not a chunk of substance being shoved by an incoming flux. It is a pattern: a phase-locked standing wave that re-centres on its new phase reference as the surrounding phase landscape tilts. A wave does not need bulk energy delivered into it to relocate in response to a phase gradient; it reorganizes around the phase environment it finds itself in. Gravity, in this picture, is matter following its own phase-locking conditions through a non-uniform inner-rung phase landscape.
Predominantly, but not perfectly. IRCH cannot send the residual all the way to zero, because later sections use that residual heating as one ingredient in high-compression matter creation. The requirement is a balance: the coupling must be refractive enough to avoid Le Sage-style catastrophic heating, but dissipative enough to provide a real energy channel. That residual is the subject of the next subsection.
Why must any of \(g_{flux}\)'s energy leak into the body, if the coupling is mostly refractive? The intuition is simple: a medium that bends the phase of a passing wave is interacting with that wave, and real interactions rarely remain purely phase-only across all frequencies. Pure phase-shifting and pure absorption are idealizations; real linear responses sit somewhere on a spectrum between them, and the two are formally related through the Kramers-Kronig relations [13] (see Glossary). In IRCH terms, the expectation is therefore neither zero heating nor large absorption, but a small residual dissipative channel whose magnitude has to be derived rather than assumed.
Two structural features of PDOC suggest why that residual might remain small. First, \(g_{flux}\) is not all of \(SUB^{flux}\). It is only the matter-resonant tail: the long-wavelength band whose modes overlap the structures of phase-locked matter at \(DYN\). The shorter-wavelength bulk of \(SUB^{flux}\) averages out at matter scales and contributes neither force nor heat in this sketch. Second, even within that matter-resonant tail, the dissipative part of the response may occupy a narrower frequency window than the refractive part that produces the force. Force can then be broad and steady while heating remains narrow and small. This is a proposed response structure, not a calculated budget.
The Le Sage family therefore identifies the thermodynamic challenge any flux-mediated gravity must face: too much absorption overheats, while too little interaction leaves no force. A perfectly lossless PDOC would fail in the opposite direction, because it would remove the heating channel later needed for baryogenesis in dense bodies. The viable IRCH window sits between those limits: mostly dispersion, with a small but physically meaningful residual escaping through dissipation. If the mechanism is right, that residual would appear as a persistent internal heat contribution rather than as catastrophic heating.
That residual heating is a qualitative prediction of the mechanism, but not yet a quantified one. Its observable effect should also depend strongly on body size. For a roughly spherical aggregate, heat-producing volume grows as \(r^{3}\), while radiating surface area grows only as \(r^{2}\); as bodies grow, their ability to shed a persistent internal heat contribution falls relative to the volume receiving it. Small bodies should therefore accumulate little or no appreciable heat from this channel, while planets, stars, and other large aggregates are the natural places to look for it. Massive bodies should receive a small persistent internal heat contribution from their coupling to \(g_{flux}\), distinct from radiogenic and primordial-heat budgets; the magnitude is not derived here, and any viable version would have to fit existing heat-flow constraints while still leaving enough energy available for the high-compression matter-creation pathway introduced later. The observational consequences play out at multiple scales and are taken up downstream, in §10 and §11. Before we get there, we go one rung deeper to show how light waves can become trapped, which is the subject of the next section on particle confinement.
In the last section we saw how PDOC manifests as gravity at \(DYN\) when the source is aggregate \(DYN^{rest}\). In this section we apply the same principle to the scale that exists at the boundary between \(SUB\) and \(DYN\), where the source is read differently. At this small scale relative to DYN, a compression of \(DYN^{med}\) caused by \(DYN^{rest}\) or \(DYN^{flux}\) is still a large-scale organization from the SUB perspective: it is a compression of \(SUB^{scaf}\). That compression cascades to \(SUB^{med}\), which is \(SUB2^{scaf}\), and from there to \(SUB2^{med}\), the medium through which \(s_{flux}\) propagates.
The difference from gravity is important. In gravity, the source is an aggregate of \(DYN^{rest}\) acting through \(g_{flux}\). In confinement, a subatomic LCM compression is not an aggregate of \(DYN^{rest}\), but it does correspond to a very large aggregate of \(SUB^{rest}\). That makes \(SUB\) the source rung for this application of PDOC, with \(s_{flux}\) playing the same mediating role for \(SUB^{rest}\) that \(g_{flux}\) plays for \(DYN^{rest}\) in gravity. The mechanism is still phase-delay coupling: sufficiently concentrated DYN compression cascades inward, modifies the medium through which \(s_{flux}\) propagates, and lets that flux reinforce the corresponding compression structure in the LCM. The goal is to motivate the fifth assumption from §4.1: Rest is a phase-locked standing wave.As noted, this is circular in the strict logical sense. The assumption demonstrated is itself a pre-condition for PDOC. The value of the section is therefore not a first-principles derivation, but a mechanism showing why that assumption has the right form inside IRCH. The structural defense of this kind of circularity is given in Appendix B.
The LCM can deform in three useful mode families: compression, which changes local density; shear, which displaces the medium laterally; and torsion, which twists it about a local axis. In IRCH, travelling light is treated as a finite wave packet whose motion is carried by phase-locked shear and torsional oscillations. Such a wave does not contain a sustained compression component in the linear limit, but finite-amplitude shear can produce brief, localized compression at points of maximum displacement.
Under ordinary conditions, these transient compression peaks are both weak and widely spaced. They interact only negligibly with \(s_{flux}\), and travelling shear-torsion waves remain effectively transparent to it. The elastic response of the LCM restores the wave as it propagates, allowing light to travel freely through a uniformly dense medium without confinement. Appendix A gives the rung-distance argument behind this difference: \(s_{flux}\) couples appreciably only to extreme compression, while \(g_{flux}\) couples across a much broader DYN aggregation window.
The behaviour of light therefore depends not only on its internal structure but on how that structure interacts with the surrounding state of the LCM. When a travelling shear-torsion wave moves through a region of higher ambient LCM density, its phase velocity decreases. The denser medium resists transverse propagation more strongly. At fixed temporal frequency, the wave's spatial wavelength shortens accordingly: successive shear-induced compression peaks are packed closer together along the wave's path. Independently of the change in spacing, the amplitude of the shear oscillation determines the strength of each transient compression peak. For a given wavelength, higher-amplitude waves therefore concentrate more compression into a smaller spatial region.
As crest spacing decreases and existing compression peaks are brought into closer proximity, the wave packet's coherent coupling to \(s_{flux}\) increases. Once the combined phase-delay landscape becomes sufficiently strong, \(s_{flux}\)-mediated reinforcement begins to favour the densest regions of the packet. A positive feedback loop follows: increased spatial concentration enhances \(s_{flux}\) coupling, which promotes further compression without increasing the underlying shear amplitude.
This leads to a practical criterion for confinement:
At sufficient amplitude and ambient compression, shorter-wavelength waves progressively increase their effective coupling to \(s_{flux}\).
Beyond a critical threshold, the wave is no longer transparent to \(s_{flux}\). The phase-delay coupling becomes strong enough to sustain further compression of the surrounding LCM and increase spatial localization. Once compression passes a limiting value, the travelling wave can no longer maintain an extended configuration and transitions into a confined standing structure, acquiring a sustained compression component that is absent during free propagation.
This is the kind of structure assumption 5 of PDOC requires: a phase-locked standing wave in the LCM with a definite eigenfrequency tied to local elastic properties. In IRCH's matter ontology, confined light is rest.
Pair production tells us that matter does not emerge in isolation: when a high-energy light wave becomes confined, it produces two particles of equal rest mass and opposite chirality, with the originating wave's total energy and momentum conserved across the full interaction. In standard pair production the momentum balance is met by recoil onto a nearby nucleus or external field; in IRCH the same role can in principle be played by the surrounding LCM itself, since the originating wave's compression peak is itself a perturbation of the medium and the confining \(s_{flux}\) coupling acts through that medium. The empirical fact we use here is simply that confinement produces matter in pairs.
Why pairs? In a finite shear-torsion wave packet, the largest distortions occur on opposite sides of the zero-distortion baseline. When the packet is driven into the confinement regime, those two extrema are the natural places for \(s_{flux}\)-mediated reinforcement to concentrate. Rather than the whole packet collapsing into one centre, the response can split the packet into two complementary confinement centres, each drawing on one side of the original oscillation.
This also prepares the chirality argument in the next section. The two extrema are opposite-phase expressions of the same underlying wave: where one side reaches maximum extension, the other corresponds to the complementary phase of the oscillation. If both become confined, they inherit equal energy from the originating packet but opposite phase alignment between compression and shear. Pair production is therefore not an added rule in IRCH; it is the natural outcome of confining a wave packet whose strongest distortions come in complementary phase-related extrema.
The role of the nucleus in standard lab-scale pair production has an additional reading under IRCH worth making explicit. The confinement mechanism developed above requires the wave to encounter LCM compression steep enough to push its effective \(s_{flux}\) coupling past the collapse threshold; a nearby nucleus supplies that compression directly through its own halo, in addition to absorbing the recoil. The nucleus is therefore doing two jobs at once under IRCH: providing the local gradient the wave climbs to reach confinement, and serving as the momentum-recoil partner. The empirical Z² scaling of the pair-production cross section, standardly derived from the heavier nucleus's stronger Coulomb field, is consistent with this dual reading: heavier nuclei carry steeper compression halos. Photon-photon pair production [14], in which two high-energy photons combine to produce a single electron-positron pair without any nucleus, is correspondingly read as the case where constructive overlap between the two waves supplies the localized LCM perturbation and momentum balance that one wave alone cannot.
Once the pair is created and confined, the collapse does not continue without limit. The same feedback loop that localizes the wave also settles into an equilibrium: the standing wave maintains a persistent distortion of the surrounding \(SUB^{scaf}\) (observed at DYN as an LCM compression halo), and the \(s_{flux}\) response to that distortion maintains the confinement of the standing wave. The result is a self-sustaining but bounded structure: a particle defined by its stable compression halo and phase-locked internal motion. The next section starts from that equilibrium and asks what kinds of particles it permits.
The previous section established how sufficiently concentrated LCM compression can engage \(s_{flux}\) through the SUB-rung landing of PDOC, trapping high-frequency LCM oscillations into stable standing-wave structures. This section takes those structures as given and develops both the matter they constitute and the familiar force behaviours they participate in: gravity, electrostatic, magnetic, and the strong nuclear force.
The unifying claim is that a particle is its standing-wave core together with the extended LCM compression strain it sustains. The compact core is what \(s_{flux}\) confines; the extended strain (its compression halo) falls off into the LCM and reaches out to interact with everything else. The halo is what gravity sees as a phase landscape, what other particles see as charge, and what overlapping nucleons share through the strong force. Treating the halo as part of the particle is what unifies "the structure of matter" and "the forces between matter" into a single coherent dependency arc rather than two parallel topics.
The section develops that arc in order. We begin with the compression halo the standing wave sustains, the surface through which it interacts with everything outside itself. Gravity is already the §5 story applied to that halo and is not re-derived here.For gravity, source and response should be kept distinct. The halo is the particle's contribution to medium compression; through the recursive cascade it induces the \(SUB^{flux}\) phase-delay landscape. The standing-wave core is the part of the particle that responds to an external phase landscape by re-centring its motion. Same particle, two roles. We then introduce chirality as the structural distinction that gives matter its second and richer dimension of variety, name concrete particles (electron, positron, proton, neutron), and develop structural accounts of the electrostatic, magnetic, and strong nuclear forces that the chirality structure makes possible. The next section extends that mode picture to the wider diversity of subatomic particles.
The role of \(s_{flux}\) will be named where needed below; for now, the important point is that the standing-wave core and its compression halo are treated as one particle structure.
We take the confined standing wave from §6 as given: a phase-locked three-mode oscillation of compression, shear, and torsion with a definite eigenfrequency tied to local LCM elastic properties. Two features of that structure carry the rest of this section.
First, the torsional component plays a role distinct from compression and shear. As the standing wave oscillates, its torsional motion continually twists the local LCM around the wave's axis, producing a stable helical distortion that organizes the shear and compression motions into a spiral pattern repeating each cycle. The twist allows the structure to close on itself without drifting; it gives matter a definite handedness and a screw-like form even before any chirality detail is named.
Second, every confined standing wave is surrounded by an extended region of elevated LCM compression. Close to the core the field is steep: a tightly localized high-strain region whose recursive inward imprint sustains the \(s_{flux}\) coupling that keeps the wave confined. Further out the strain falls off into the surrounding medium, producing a compression halo that extends well beyond the core's geometric reach. The halo is the surface through which the particle interacts with everything outside itself: gravity (§5) sees aggregated halos as a phase landscape; the electrostatic, magnetic, and strong nuclear forces developed below act through the halo too, but require further structure that gravity does not need. That structure is the chirality distinction taken up next.
The standing-wave structure developed above admits not one configuration but two. This is the particle-level continuation of the pair-creation geometry from the confinement section: the two confinement centres come from opposite-phase extrema of the same originating wave packet. When those extrema settle into bounded standing waves, the compression mode can lock to the inherited shear-torsion pattern in either of two opposite phase relationships: leading shear by 90° or lagging it by 90°. These two configurations are otherwise identical: same eigenfrequency, same compression amplitude, same torsional handedness on each cycle. They differ only in the relative phase of compression and shear, and that single difference produces opposite radial behaviours in the surrounding LCM.
These two phase relationships matter because they can turn the same oscillation into opposite radial strains: one configuration pushes the surrounding LCM outward, while the other draws it inward.Throughout this section, "pushes", "draws", "inward", and "outward" refer to elastic strain and displacement in the LCM, treated as a solid-like medium. They do not mean bulk fluid circulation or material transport. The asymmetry follows from how compression and shear interact in a nonlinear medium. Regions of higher compression change the local wave speed, so shear motion does not simply ride on top of the compression cycle. Instead it is redirected and amplified differently depending on relative phase. This kind of nonlinear coupling is well known: in acoustics, fluid membranes, and elastic solids [15, 16, 17], a ±90° phase shift between expansion and shear produces opposite net flows even when the underlying motions are identical in energy. By analogy, the two phase-locked configurations of the LCM produce two distinct compression-halo behaviours:
The pump magnitude is the same for both configurations; only the direction of the radial response differs. This is the origin of charge as a directional asymmetry of the same underlying mechanism. The compression halo of any particle is the surface through which it interacts with other particles; its chirality determines whether that interaction pushes or draws. The strain is the charge: chirality is not an additional property bolted onto the matter model but a structural distinction in how compression and shear lock together.
A simple linear coupling cannot produce this asymmetry, but the asymmetry is not a free postulate. It follows from a single concrete physical assumption invoked above: transverse wave speed in the LCM depends on local compression. This is the standard situation in any real elastic medium: denser regions are stiffer, with different transverse propagation. Once admitted, the compression-modulated wave speed redirects shear motion in a phase-dependent way, and the nonlinearity required for the push-pull asymmetry follows as a consequence rather than as a separate postulate. A full dynamical derivation of the resulting radial-tendency asymmetry is left as an open problem for future work.
With the standing-wave structure and its compression field in hand, we can name the particles. These identifications are proposed structural readings inside IRCH, not yet replacements for the Standard Model's full quantum-number, quark, flavour, and weak-interaction bookkeeping.
In ordinary low-density LCM, the two phase-locked configurations are stable in their own right.
Both are stable in low-density LCM because their compression fields balance against the ambient medium without runaway dynamics.
IRCH reads the antiproton and proton as second equilibria of the same two modes that appear, at ordinary compression, as the electron and positron. This is a structural identification inside the model, not a derivation of Standard Model baryon structure.This claim knowingly conflicts with the Standard Model's empirically successful baryon and lepton number bookkeeping, under which an electron-like lepton cannot simply become an antiproton-like baryon, nor a positron-like lepton become a proton-like baryon. The force of that bookkeeping is inductive: it summarizes a very successful pattern in observed reactions. IRCH treats those conservation numbers as emergent configuration labels rather than primitive conserved charges, so recovering the observed success of that bookkeeping is a required compatibility target, not something derived here. The first equilibrium is the ordinary electron/positron pair created by confinement: the standing wave is localized, the compression halo is stable, and the ambient LCM's elastic response prevents further collapse. In that regime both particles are stable in their own right, absent an opposite partner with which they can annihilate.
Under sufficiently strong background LCM compression, either mode can in principle cross a nonlinear threshold into a more compact equilibrium. The conditions capable of producing that threshold are not named here; the environmental argument depends on mechanisms developed later in the paper. The two chiralities need not have exactly the same threshold: a small difference in how lead-mode and lag-mode structures respond to background compression is enough to bias which transition occurs more readily. That asymmetry is not developed here; it is taken up later in the electrical-differentiation and matter/antimatter story. The point needed now is simply that sufficiently strong ambient compression can push a confined lepton-like mode out of its low-compression equilibrium:
This high-compression equilibrium is baryonic: the collapsed lag-mode is the proton, and the corresponding collapsed lead-mode is the antiproton. Their extra mass is not extra LCM material piled into the particle; it is stored deformation energy: the energy of a shorter-scale, denser core oscillation together with the persistent compression field that core maintains. The stronger \(s_{flux}\) response keeps the compressed configuration bounded rather than allowing unlimited collapse.
The proton is therefore not just a heavier positron, and the antiproton is not just a heavier electron. They are collapsed-state forms of the two chiral modes under conditions where background LCM compression lets the phase dynamics cross the threshold into a second equilibrium. Their key qualitative properties follow from that identification:
Once formed, the collapsed state's stability does not require the threshold conditions to persist. The structure relies on its own concentrated core energy, not on the local LCM density. The compact compression core maintains a strong recursive imprint in the inward media; \(s_{flux}\) responds to that imprint through phase-delay coupling; and that coupling maintains the compression well that locks the standing wave into its compact geometry. The compression halo remains extended, and in this ontology measurements of proton or antiproton size would probe that halo rather than the much smaller core oscillation itself. The cycle is self-sustaining wherever \(s_{flux}\) is available. By ERMS's mandatory inter-rung coupling commitment, that means everywhere.
This also explains why an electron does not simply annihilate with a proton, or a positron with an antiproton, even though the collapsed baryonic state retains the charge sign of its lepton-mode counterpart. Opposite charge is a halo interaction; annihilation is a core-overlap event. The electron can bind to the proton because their halos have opposite radial strain signs, but the proton's lag-mode core has collapsed into a much smaller, denser, geometrically distinct equilibrium. The electron therefore encounters a positive compression halo, not an equal-scale positron standing wave with the mirror-compatible core geometry required for ordinary electron-positron annihilation. The same reasoning applies with signs reversed for the antiproton.
To appreciate how dramatic this stability is, compare the collapsed core's internal density to ordinary matter. A typical rock has a density of about \(3000\,{\color{gray}\scriptscriptstyle [\mathrm{kg/m^{3}}]}\); the implied energy density inside a proton is roughly \(10^{17}\,{\color{gray}\scriptscriptstyle [\mathrm{kg/m^{3}}]}\). Even white dwarf material (~\(10^{9}\,{\color{gray}\scriptscriptstyle [\mathrm{kg/m^{3}}]}\)) and neutron-star crusts (~\(10^{14}\,{\color{gray}\scriptscriptstyle [\mathrm{kg/m^{3}}]}\)) fall far below it. From the collapsed core's perspective, every macroscopic environment is effectively dilute.
Where do the high-compression conditions for baryonic collapse actually occur in nature, and why does matter dominate antimatter? This section does not answer those questions. They require the later discussion of how large bodies organize, store, and separate energy. The asymmetry question is therefore taken up in §9, where the same mechanism gives rise to a multi-particle prediction of electrical differentiation: the chirality-driven sorting of modes inside sufficiently large gravitating bodies.
The proton/antiproton-as-collapsed-mode account is structurally vivid but bumps against a number of standard quantum numbers and empirical facts. IRCH treats most of these as emergent bookkeeping rather than primitive ontology; this subsection names the open questions so the claim is not asked to do more than it can.
These are the points where the baryon account is most exposed; the section commits to the mechanism while leaving the quantitative work as future targets.
The neutron is not a fundamentally separate particle but a paired configuration of the two helical modes. In IRCH, a neutron forms when a lead-mode and a lag-mode oscillation become phase-locked within a shared compression well.
This is not the historically failed proton-electron neutron model. The lead and lag modes are not free particles packed inside the neutron; there is no proton sitting next to an electron inside a confining shell. Both modes are oscillation patterns in a single shared standing wave with a single shared compression well, phase-locked to each other through the same nonlinear LCM coupling that makes confinement possible at all. The neutron is one composite oscillation, not two stuck together. Several empirical constraints any later derivation will have to satisfy follow from this distinction: the neutron's spin (½, not the 0 or 1 a free pp/pe pair would imply), the continuous beta spectrum in free decay, the observed magnetic moment, and the neutron's nuclear-scale confinement (the paired structure is bound by the same \(s_{flux}\) mechanism as a single nucleon, not by Coulomb attraction between internal constituents). These are flagged here as targets for later quantitative work, not claimed as derived.
In this combined state, the opposite chiral tendencies of the two modes partially cancel, producing a geometry that is neither fully lead nor fully lag. The resulting LCM compression profile is gentler than a solitary proton's: a proton's lag-mode generates an extremely steep gradient, but the paired configuration spreads energy over a wider region. This gives a particle that interacts gravitationally like a proton but lacks either chirality's net electrostatic signature.
Unlike the proton, whose extreme density allows it to remain compact in any environment, the neutron's stability depends on a marginal phase-lock. The paired lead/lag configuration cancels the net compression-shear phase offset towards zero: neither mode wins, and the shared compression well is therefore much shallower than a proton's. That near-zero coupling is inherently unstable on its own. Inside a nucleus, the surrounding nuclear compression environment provides the extra support, especially neighbouring protons. Strong \(s_{flux}\)-induced compression reinforces the neutron's shared well and holds the paired modes coherent. Outside the nucleus, that companion compression is absent. The marginal phase-lock relaxes, the two modes separate, and the system settles into a proton-like collapsed lag-mode, an electron-like lead-mode, and a brief outward fluctuation in the LCM observed as a neutrino-like disturbance. This is only a placeholder reading of the weak channel. Any later version would have to recover the empirical reality of neutrino detection, missing energy and momentum, neutrino oscillations, and the standard weak-interaction phenomenology. The present sketch therefore treats the "neutrino-like disturbance" as a compatibility target, not as a derived replacement for the neutrino sector.
The neutron is heavier than the proton because it confines energy from both helical modes, but it is less compact: the interference between the two compression patterns limits how tightly either mode can draw in the surrounding LCM. The result is a particle with high internal energy but a shallower confinement profile. It relies on nuclear environments for long-term stability, and it plays a central role in nuclear binding (developed below).
The electrostatic force in IRCH is an intra-DYN phenomenon that operates within the LCM itself, made possible by the chirality structure of the standing wave developed above. It is not a direct inter-rung phase-delay force. The mechanism is a nonlinear strain pump in the LCM, sustained by the chirality-bearing standing wave at its centre.
The LCM is an elastic medium, not a fluid. The pump described below sustains a steady strain in the medium, not a transport of material. Where we use fluid-source language, it is as a mathematical analogy for the falloff of the strain field, not a physical claim of material flow.
Recall: the standing wave has compression and shear phase-locked at ±90° (chirality), and the local LCM wave speed is modulated by compression. Denser regions slow transverse propagation. The ±90° offset between compression and shear sets up a nonlinear pumping mechanism whose period-averaged effect is a steady radial strain around the particle:
The pump magnitude is the same in both cases. Only the direction of the radial strain differs. This is the origin of charge as a directional asymmetry of the same underlying mechanism.
Once the chirality-driven pump is established, the particle's surrounding strain field has the same mathematical structure as a steady source or sink in a 3D continuum at distances much larger than its core scale. Such configurations produce a far-field whose radial component falls off as 1/r²; the corresponding compression field falls off as 1/r; the resulting force on a second such source goes as 1/r². The potential-to-force step here is the same gradient calculation that recovered Newtonian gravity from the \(g_{flux}\) phase landscape:
This gives the intended structural route to Coulomb-like behaviour, recovered from a continuum-mechanics argument applied to the strain field rather than postulated as a separate force. The full elastic-LCM derivation that confirms the precise 1/r² form, and connects the pump amplitude to the empirical Coulomb coupling, is left as an open derivational target (see Open derivational targets below).
Two consequences follow naturally:
The electrostatic strain field is intra-DYN in how it propagates, but its source is not purely intra-DYN. The charged standing wave exists only because \(s_{flux}\) stabilizes its confined core and compression halo. Chirality then biases that already-confined structure into a steady radial strain condition in the LCM. In that sense, \(s_{flux}\) does not carry the Coulomb force directly; it maintains the standing-wave source that makes the Coulomb-like strain field possible.
The energy of the electrostatic field is stored as deformation of the LCM. The pump does not transport LCM material, and a static strain pattern should not be read as a continuous flow of substance or as a free energy source. When charged bodies move, work is exchanged through changes in the LCM strain field, just as ordinary field energy changes when charges rearrange. A complete version of the model must make this bookkeeping explicit: the inter-rung coupling maintains the charged source, while the long-range electrostatic energy resides in the DYN-level deformation pattern.
The neutron's helical structure is a shared lead/lag phase-lock, not two free charged particles packed together. In that composite oscillation the two opposite chiral tendencies cancel in the monopole channel: one tendency would push the surrounding LCM outward, the other would draw it inward, and the shared configuration leaves no net far-field radial strain. The neutron therefore has no Coulomb-like monopole field and exerts no long-range electrostatic force on other charges. The same chirality-cancellation that removes the net radial pump is what makes the neutron electrically neutral in this picture. The cancellation need not erase all internal structure, however. Torsional and short-range dipole-like components can remain, which is why the neutron can retain a magnetic moment despite having no net charge.
The mechanism above gives a structural account of Coulomb's law but does not derive it quantitatively. The following targets remain for future work:
These are natural continuum-mechanics targets for subsequent work. The present sketch commits to the mechanism and its qualitative consequences without claiming the derivations.
The mechanism rule for this section, stated up front: magnetic behaviour begins when the torsional part of a charged standing wave becomes directional. For a single particle, that directionality appears as an intrinsic magnetic moment. For moving charge, the motion skews the surrounding LCM torsional response into a magnetic field. The Lorentz force law, Biot-Savart geometry, spin magnetic moments, and the relativistic constraints on this mechanism are not derived here; they are part of the quantitative target deferred to the relativity section.
The strain pump from the electrostatic section is not purely radial. Because the standing wave also carries a torsional component along a definite axis, the strain field has a directional asymmetry: a short-range dipole-like structure oriented along the torsion axis. At long range, rapid rotation or averaging of the helical configuration leaves the radial pump to dominate the electrostatic field. At short range, however, the axial torsional structure remains as the particle's magnetic moment. Electrostatic and magnetic effects therefore share a common origin in IRCH, but they are different projections of the charged standing wave: the electrostatic field is the far-field radial strain, while the magnetic moment is the surviving axial/torsional asymmetry.
Even when an electron is stationary, its dual-mode oscillation twists the surrounding LCM into a subtle helical pattern. This built-in torsion acts as an intrinsic magnetic dipole, a directional feature of the electron's compression field. The axis of that dipole is set by the standing wave's torsional orientation; chirality sets the sign of the charged mode, but the magnetic orientation itself can point along either allowed spin direction.
When an electron moves through the LCM, the torsional field surrounding it is carried along and becomes slightly skewed. The LCM does not respond uniformly around the moving helical source: one side encounters greater torsional resistance, while the other relaxes. The standing wave's compression halo and its \(s_{flux}\)-maintained core participate in that asymmetry, so the surrounding torsional response is biased relative to the particle's motion. In the proposed mechanism, magnetic behaviour in moving charges begins as this motion-dependent skewing of the torsional and compression fields.
When many charges move together, as in an electric current, their motion-dependent skewing adds coherently. This does not require the particles' intrinsic spin dipoles to align. Each moving charge contributes a small torsional bias to the LCM, and together those biases can add up to a coherent shear/torsion pattern encircling the flow. The familiar circular magnetic field around a wire is then read as the large-scale imprint of many moving charged standing waves, all skewing the surrounding LCM in a shared direction.
A different form of magnetism appears in ferromagnetic materials. Here, electrons do not need to move as a current for their magnetic moments to align. Instead, lattice geometry, electron-shell structure, and energetic constraints encourage certain orientations of the intrinsic helical modes. In regions where those orientations lock together, the torsional fields of many electrons become mutually reinforcing, and their compression and shear patterns combine into a persistent macroscopic field even in the absence of current. Ferromagnetism is therefore a static alignment of intrinsic moments, while current magnetism is a dynamic field produced by moving charge. Recovering the detailed exchange interactions, domain behaviour, and temperature dependence of ferromagnets remains a separate derivational target.
It is worth noting that helical structure was not assumed. It emerged by imposing a small set of physical requirements on how a high-frequency transverse wave must collapse when forming an opposite pair. The collapse must produce two structures with equal energy but opposite chirality, preserve the symmetry of the original wave, generate stable standing waves supported by both LCM and \(s_{flux}\), and provide a natural geometric distinction between the two modes. A dual-oscillation helical structure is the simplest configuration that satisfies all four constraints. The same geometry is suggestive at larger scales, where unconstrained electrical currents in plasmas can spontaneously organize into helical, filamentary structures [18, 19, 20]. In IRCH, helicity is therefore not an arbitrary decorative choice but a recurring candidate geometry for how the LCM and its inter-rung fluxes organize flowing energy.
The strong nuclear force is, in IRCH, the DYN-visible expression of PDOC applied at the SUB rung. \(s_{flux}\) is to \(SUB\) what \(g_{flux}\) is to \(DYN\): the inward flux whose phase is shaped by compression-modified medium and whose phase landscape is felt by aggregated rest. Where PDOC at \(Rung_{0}\) produces gravity, PDOC at \(Rung_{-1}\) produces what we observe at DYN as the strong nuclear force: \(s_{flux}\) phase-delays through compression-modified \(SUB2^{med}\) near nucleon cores, and those nucleon cores respond to the resulting phase landscape.Strictly, \(s_{flux}\) propagates through \(SUB2^{med}\). DYN compression reaches that medium through the recursive scaffolding chain described in §4.2. Same mechanism, one rung deeper.
This is the same \(s_{flux}\) already used in §6 to explain standing-wave confinement. The difference is the geometry of the coupling. In confinement, \(s_{flux}\) reinforces the compression structure of a single collapsing wave packet until it settles into self-sustaining standing waves. In the strong-force regime, the standing waves already exist. Their nucleon-scale compression halos can participate in a shared \(s_{flux}\) phase landscape, producing an attractive domain between distinct confined cores.
That attractive domain is not the whole nuclear interaction. Nucleons also carry ordinary electrostatic strain when they are charged, and all nucleons carry compact standing-wave cores with steep compression geometry. Those two repulsive effects should be kept distinct. Coulomb repulsion is the long-range interaction of like charge-sign strain fields; it affects proton-proton pairs but not neutron-neutron pairs. The hard core is different: it is a very short-range standing-wave constraint, where two compact compression-rich cores cannot be forced into the same volume without asking the LCM to satisfy incompatible compression, shear, and torsion boundary conditions. The strong-force story is therefore an equilibrium between medium-range \(s_{flux}\) attraction and short-range core exclusion, with Coulomb repulsion added for charged pairs. If the shared halo is too steep, the \(s_{flux}\) attraction can be overdriven, pushing the cores into the hard wall before a stable minimum forms.
Two structural differences between gravity and the \(s_{flux}\) attractive domain follow from rung distance:
The observed nucleon-nucleon (NN) potential [21] is not monotonic. It has three distinct regimes: a hard-core repulsion at very short range, a deep attractive well at medium range, and a rapid falloff at longer range. In IRCH, that shape reflects the competition just named: standing-wave core exclusion at shortest range, \(s_{flux}\) phase-delay attraction at medium range, and loss of \(s_{flux}\) coherence at longer range. Stable binding exists only where the attractive well forms before the cores are driven into the exclusion wall.
Very short range (less than ~0.5 fm): hard-core repulsion. At the shortest separations, the limiting factor is core geometry. Two compact standing-wave cores cannot occupy the same LCM volume without imposing incompatible compression, shear, and torsional phase constraints. This produces a hard repulsive core for proton-proton, proton-neutron, and neutron-neutron pairs, independent of charge.
Medium range (~1 fm): \(s_{flux}\) phase-delay attraction. At slightly larger separation, the cores remain distinct but their compression halos participate in a shared \(s_{flux}\) phase landscape. The resulting phase-delay anisotropy produces the attractive well of the NN potential. This is the strong-force analogue of PDOC attraction, restricted to the nucleon-scale compression window.
Longer range (greater than ~2-3 fm): rapid falloff. Beyond the coherence window, the shared \(s_{flux}\) phase landscape no longer remains organized, and the attractive nuclear component drops rapidly. Proton-proton pairs still retain the Coulomb tail. Neutron-neutron and neutron-proton pairs, having no Coulomb tail, interact appreciably only when they are close enough to enter the nuclear well; within that well, the proton-neutron pair can form the stable deuteron discussed next.
A successful two-nucleon bound state is not just two cores placed side by side. The two cores must contribute to a shared compression halo that \(s_{flux}\) can couple to coherently while still leaving the standing-wave cores at a supportable separation. The shared halo has to land inside a narrow window: not so steep that \(s_{flux}\) over-focuses the cores into the hard wall, and not so soft that \(s_{flux}\) coupling becomes too weak.
Two protons fail on the steep side of that window. Their compression profiles are both compact and sharply curved, so the combined halo is steeper than a single proton's. In this sketch, that steep halo overdrives the \(s_{flux}\) attraction: the cores are pulled towards separations where their standing-wave geometries become incompatible, and the hard-core response ejects the pair from the would-be bond rather than letting it settle. Coulomb repulsion adds a second obstacle at every separation. The exact dynamical threshold remains a quantitative target.
Two neutrons fail on the soft side. A single neutron is already marginal in IRCH terms: its lead/lag phase-lock cancels too much of the compression-shear phase offset, leaving too little \(s_{flux}\) coupling to keep it stable outside a nucleus. Adding a second neutron contributes another soft halo, but does not increase the shared compression enough to stabilize either neutron or produce a deep bound well.
The proton-neutron pair is the exception because it lands between those extremes. The neutron's softer compression profile can absorb and spread some of the proton's sharp curvature, producing a shared halo that is softened enough to avoid overdriving the cores into the hard wall, but still compressed enough for coherent \(s_{flux}\) coupling. That added coupling also stabilizes the neutron's otherwise marginal lead/lag phase-lock. The result is a genuine energy minimum: a bound deuteron that cannot be achieved with like-like pairs.
The same mechanism extends to multi-nucleon binding, but not by simply adding pairwise bonds. In IRCH each nucleon is an oscillating system. Once nucleons enter a nucleus, those oscillators are no longer independent: their compression, shear, and torsional phases must coordinate inside a shared nuclear compression halo. Stable nuclei are therefore collective standing-wave configurations in which the contributing nucleon cores form a supportable geometry, while the shared halo remains softened enough to avoid overdriven collapse into the hard wall and compressed enough to sustain coherent \(s_{flux}\) attraction.
The neutron/proton ratio then has a natural qualitative reading: it tunes shared-halo steepness. Adding protons increases the sharpness, the tendency towards overdriven core focusing, and the Coulomb cost of the collective halo; adding neutrons softens the halo and stabilizes otherwise marginal neutron phase-locks, but too many neutrons soften the structure until \(s_{flux}\) coupling is no longer strong enough. In this sketch, the valley of stability is the band where those contributions balance for a given nuclear size.
That makes nuclear stability a geometry-and-phase problem, not merely a question of halo steepness. The rules determining which multi-core oscillation patterns reduce total energy, which fail to phase-lock, and which become unstable under perturbation are left as derivational targets. A quantitative version would also have to recover the familiar structure that standard nuclear physics already captures: shell closures, pairing effects, spin/isospin channels, decay modes, and the changing neutron/proton ratio of stable nuclei. The stability of the alpha particle, the saturation of nuclear forces with mass number, and the valley of stability are therefore candidate qualitative consequences of this collective shared-halo packing problem, not results derived here.
The strong force and gravity are read as two applications of the same PDOC family: flux phase-delay through compression-modified medium with a small dissipative residual. The quantitative relations between them should not be independent free parameters in a completed IRCH model. They would depend on two structural differences identified at the top of this section: \(s_{flux}\)'s thresholded strength inside extreme compression, and its narrow coherence window, compared with \(g_{flux}\)'s broader aggregation window. Numerical derivations of the strong/gravity ratio, the precise window widths, and similar quantitative relations are not attempted in this sketch but are structurally available targets for future work.
This section is a classification sketch, not a derivation of the Standard Model particle table. The goal is narrower: to show how IRCH would begin to organize the wider diversity of subatomic particles once particles are treated as confined three-mode standing waves in the LCM. A later quantitative version would have to recover the observed particle spectrum, quantum numbers, lifetimes, branching ratios, scattering data, quark phenomenology, and weak-interaction structure. Here we only name the mode-space in which those facts would have to live.
The particles named so far are electrons, positrons, protons, antiprotons, and neutrons. They are treated as comparatively stable configurations of compression, shear, and torsion. They are not the only possible configurations. A confined wave can differ by chirality, by total energy, by how that energy is partitioned among the three modes, by which internal eigenmodes are populated, by the relative phase alignment of the modes, and by whether the resulting compression halo can maintain coherent \(s_{flux}\) coupling.
The mass of a particle is not just its compression. Compression measures stored strain in the LCM and determines how strongly the structure engages \(s_{flux}\), but shear and torsion can also carry energy. The allowed internal modes are set by the LCM's elastic properties and by the boundary conditions of the confined compression halo. Excited particles correspond to higher allowed eigenmodes of the same standing-wave family, not arbitrary extra wiggles.
The compression channel is special because it is the channel through which confinement is maintained. A structure with too little compression cannot hold itself as localized rest: \(s_{flux}\) has too little coherent phase-delay coupling to sustain the bounded compression well. But once confinement exists, the total stored energy of the particle is the total energy of its standing-wave configuration:
That last item matters. A phase alignment is not a separate material piece inside the particle, but it can store energy because disrupting it requires work. The stable configuration is the relationship among the modes, not just the modes considered one by one.
In this reading, the electron and positron are the ground-state lead/lag lepton modes. Their compression, shear, and torsion patterns sit in the lowest stable arrangement available to their chirality. They persist because their compression component is strong enough to keep \(s_{flux}\) engaged, while their shear and torsion modes do not carry excess internal excitation that can relax away.
The muon and tau are natural candidates for excited versions of the same lepton-mode family. They would carry the same charge sign as the electron or positron branch, but with shear and/or torsion not in the ground state. Higher allowed internal eigenmodes, with their corresponding nodal structure and amplitudes, store additional energy, and that additional stored energy appears as greater mass.
On this reading, muon and tau decay are relaxation processes. The excited standing-wave pattern has lower-energy configurations available. It decays towards the corresponding ground-state lepton while releasing the excess energy into whatever channels the full dynamics allow. IRCH does not yet derive those channels. A viable version would have to recover the observed decay products, lifetimes, neutrino phenomenology, and conservation bookkeeping. The useful point at this stage is simply that generations can be read as mode excitations rather than as wholly unrelated particle species.
The confinement section treated pair production as the collapse of a high-energy travelling wave into two opposite-chirality standing waves. The energy of the originating packet is not characterized by one number alone. It depends on wavelength, crest count, amplitude, and how the packet's shear and torsional structure is organized.
Those features matter for what kind of pair can be created. Total energy determines which channels are available at all: a wave packet cannot populate a standing-wave configuration whose stored energy exceeds the energy available to the event. But total energy is not the whole selector. The geometry of the packet also helps determine which standing-wave mode is actually populated: how many crests it carries, how concentrated they are, how large their amplitudes are, and how its torsional/shear pattern is arranged.
Ordinary electron-positron pair production is therefore read as the lowest available charged-pair channel. Higher-energy events can populate higher-energy modes: excited lepton pairs, baryon-antibaryon pairs, or short-lived resonant configurations. In each case, the event creates complementary standing-wave structures whose total energy and momentum must be accounted for across the full interaction. The present sketch does not derive the branching probabilities; it only identifies the IRCH variables that would enter them.
The proton and antiproton were described above as high-compression equilibria of the two chirality branches. Their extra mass is stored as a shorter-scale, denser core oscillation together with the persistent compression field that core maintains. The neutron is a more marginal paired lead/lag configuration stabilized inside nuclei by the shared nuclear compression halo.
Within baryons, IRCH reads quarks cautiously. In standard physics, quarks are not observed as isolated particles; they are confined degrees of freedom inside hadrons. IRCH can interpret that as a clue that quark labels refer to internal phase sectors of baryonic standing waves rather than to independently free LCM-level particles.
On this reading, a quark is associated with the energy of a stable phase alignment inside the baryonic core. The compression, shear, and torsion modes are locked into a relational pattern, and the quark-like degrees of freedom name how that pattern partitions and resists deformation. Trying to pull a quark out is therefore not like pulling a small object out of a larger object. It is an attempt to tear apart a phase relationship that only exists as part of the whole confined configuration. The resistance is real, but it is the resistance of the alignment, not the surface of a detachable constituent.
This is a compatibility claim, not a replacement for QCD. A quantitative IRCH account would have to recover the empirical success of the quark model: hadron spectra, scattering behaviour, jets, colour-like bookkeeping, flavour, mixing, and the strong-interaction phenomenology that QCD captures. The proposed reinterpretation is ontological: quarks are real as internal relational degrees of freedom, not necessarily as independently stable standing waves in the LCM.
Mesons and short-lived resonances are also natural places where the mode-space becomes richer than the stable-particle list. In standard physics, mesons are quark-antiquark states, and many resonances are transient hadronic excitations. IRCH should not flatten all of that into "not enough compression." Some transient particles may be:
The common feature is not that these structures lack energy. Many have more energy than stable particles. The issue is whether the energy is arranged in a self-sustaining standing-wave pattern. If a configuration occupies an excited shear or torsion eigenmode, contains an unstable phase alignment, or carries a compression halo outside the viable support window, it can relax into lower-energy configurations. Decay is then the reorganization of the standing-wave pattern, with the excess energy leaving through allowed channels.
The particle spectrum is therefore not determined by compression alone. IRCH points to several selection variables:
The word "allowed" hides the hardest work. Standard particle physics organizes allowed transitions through quantum numbers and conservation laws: charge, spin, lepton number, baryon number, colour, flavour, parity structure, and weak-interaction rules. IRCH treats many of these as emergent bookkeeping for standing-wave configurations, but it has not derived that bookkeeping. Any later version has to show why the observed conservation patterns work so well, where they are exact, where they are approximate, and how they arise from the underlying mode geometry.
In this view, the wider diversity of subatomic particles is a spectrum of possible standing-wave patterns. Compression determines whether \(s_{flux}\) can confine the structure; shear and torsion determine much of its internal excitation; phase alignment determines whether the modes can persist together; and decay is the relaxation of unstable patterns into lower-energy allowed configurations. The sketch is incomplete, but it gives the particle table a place to live inside the IRCH ontology: not as a list of unrelated primitives, but as a catalogue of possible mode geometries in a recursively stabilized medium.
In §7, matter was developed as chiral standing-wave structure: lead-mode and lag-mode configurations, electron/positron and antiproton/proton branches, and the possibility that high-compression environments can push a lepton-like mode into a collapsed baryonic equilibrium. §8 broadened that into a mode-space for the wider particle spectrum. The present section follows one consequence upward in scale: in large gravitating bodies, LCM density gradients and persistent \(g_{flux}\) heating may create environments where those chiral branches sort, interact, and transform differently.
This is offered as a candidate baryogenesis channel. Instead of treating matter/antimatter asymmetry as only a one-time cosmological event, IRCH asks whether a tiny chiral threshold difference could be amplified by radial sorting inside dense bodies. If lag- and lead-mode structures have slightly different lepton-to-baryon collapse thresholds, then matched matter/antimatter production would annihilate while the small excess branch survives. The geological and solar-system consequences of any surviving matter production are taken up in §10.
The thought experiment below uses an Earth-sized planet as its starting point: familiar enough to keep the speculation disciplined, but large enough for gravity, heat retention, electrical differentiation, and deep compression gradients to matter. The first-pass averaged calculation is deliberately unpromising. Using conventional estimates of nuclear spacings, bulk density, and gravitational potential, the LCM inside Earth looks too dilute to support anything exotic: nuclear compression halos barely overlap, and the gravitational potential difference from surface to core barely nudges photon energies. The IRCH proposal is that this average hides local structure. Persistent residual heating, radial LCM gradients, chiral buoyancy, charge separation, and compression hotspots could combine to create rare threshold-crossing environments. The subsections below develop that qualitative chain and identify where quantitative support is still needed.
On this IRCH reading, the Earth's heat would not be the remnant of primordial formation or radioactive decay alone. The \(g_{flux}\) dissipative residual identified in §5.3 would supply a small persistent internal heat source, distinct from radiogenic and primordial-heat budgets. The magnitude is not derived here; the proposal is that the mechanism would contribute persistently to the interior energy budget. Whether that contribution is large enough to matter, and whether it fits the measured heat-flow constraints, are quantitative questions returned to at the end of the subsection.
That budget need not be steady over geological time. A planet's ability to shed heat is controlled by its surface area, while the region receiving and storing internal energy scales more like volume. As a body grows, or as its interior reorganizes, the balance between residual input and surface loss can shift. If the \(g_{flux}\) residual contributes more energy than the surface can radiate away, heat would accumulate until some internal process increases transport, releases energy episodically, or converts part of the stored energy into a different form.
If such depositions are present, they would raise the local energy budget of the deep interior. In ordinary terms, that means more thermal motion, more energetic radiation in the high-energy tail of the local field, and more high-energy close encounters between nuclei. Such encounters, though brief, could produce intense local LCM compression well above the ambient level. What averages to a soft interior may hide microregions where the LCM is stressed close to confinement thresholds.
In those transient regions, creation of a lead/lag lepton pair becomes the first relevant IRCH step: electron-like and positron-like modes. The claim is not that the bulk Earth is hot enough for ordinary pair production by standard thresholds. Rather, the proposal is that local compression spikes inside a dense LCM environment can improve the odds that energetic wave packets cross the confinement threshold described in §6. Whether this happens at a meaningful rate is not known here; it is one of the central derivational targets.
Gravitational aggregation supplies the next ingredient: a radial LCM-density gradient. The core sits in the deepest compression well; the surface sits in a shallower one. The gradient is gentle when averaged over macroscopic scales, but it gives lead- and lag-mode structures a preferred direction to respond to.
The lag-mode (positron-like) and lead-mode (electron-like) chiralities developed in §7 are proposed to behave differently in that gradient. The gradient acts like a buoyancy field for the two chiral halos. Lag-mode structures carry a denser, inward-strained halo and are biased towards deeper compression. Lead-mode structures carry an outward-strained, comparatively less-dense halo and are biased towards less-compressed regions.
If that mode-dependent buoyancy holds, the predicted outcome is a subtle radial sorting:
This is the proposed origin of electrical differentiation. It does not require a fully separated charge reservoir at the start; it begins as a slight asymmetry in how the two chiral branches respond to the radial LCM gradient. Whether the sorting actually occurs in the way described, at what rate, and whether it produces the observed compositional layering, are derivational targets for any later quantitative version.
The inward-biased lag-mode branch would not remain a population of ordinary free positrons in the standard sense. In dense matter, positron-like structures would encounter bound electrons quickly. Where ordinary electron-positron geometry is available, annihilation removes both members of the pair. If lead-mode structures are also being biased outward, the deep interior is not replenished symmetrically. Over time the net effect would be an increasingly electron-deficient, positively strained core region.
That electron deficiency matters because it changes which close approaches become possible. A lag-mode structure near an electron-rich atom is likely to meet an electron first. A lag-mode structure in an electron-deficient, high-compression region can approach nuclei more directly. This is the doorway to the collapse channel discussed below.
In the IRCH story, the relevant deep-Earth environment is not a free gaseous plasma but a dense, viscous, electrically conducting interior with plasma-like current behaviour. In such a medium, currents need not wander diffusely; magnetized conductive media can self-organize into filamentary and pinched structures [19, 20]. In IRCH, analogous z-pinch-like structures would act as LCM compression hotspots: narrow, persistent sites where matter is denser, currents are stronger, and the LCM is driven into non-linear regimes. Whether such structures form at the relevant scales inside Earth is left as future modelling work.
This picture is at least compatible with the geomagnetic field. A network of conductive filaments in a churning plasma shell could plausibly produce strong, long-lived magnetic fields and accommodate the irregular reversals seen in the paleomagnetic record [22]. The \(g_{flux}\) dissipative residual would supply continuous power, and the liquid plasma would supply the fluidity. Recovering the detailed observed field structure, intensity, and reversal statistics is a separate target.
The collapse event requires all of the preceding pieces at once: persistent energy input, a radial LCM gradient, chiral sorting, an electron-deficient core, dense conductive plasma behaviour, and local compression hotspots. Under those combined conditions, a lag-mode structure can approach a nucleus in an environment already biased towards extreme compression.
The nuclear core is surrounded by an extremely dense and steep LCM compression halo. For an ordinary positron-like equilibrium, that surrounding halo can be denser than the lag-mode's own lepton-like core is built to sustain. In IRCH terms, the lag-mode then finds itself in a region where the outside is trying to impose a more compressed state than the particle can maintain in its lepton-like equilibrium. If the inward strain succeeds, the surrounding LCM is pulled into the standing-wave structure, the \(s_{flux}\) response strengthens, and collapse toward the proton equilibrium begins.
Strictly, the lepton-to-baryon transition is not exclusive to the lag-mode branch. In IRCH both chiral lepton branches are capable in principle of crossing into their corresponding baryonic equilibria: lag-mode towards proton-like rest, lead-mode towards antiproton-like rest. The important point is that their thresholds need not be exactly equal. Because the two branches carry opposite strain orientations, a small threshold asymmetry is expected; because the radial LCM gradient sorts the branches differently, that small asymmetry can be amplified in a planetary interior.
This gives IRCH a natural route to matter/antimatter asymmetry. If proton-like collapse occurs even slightly more often than antiproton-like collapse under the sorted conditions, subsequent proton-antiproton annihilation removes the matched portion and leaves only the excess of the more abundant branch. The present section does not derive the size of that excess; it identifies the mechanism by which a tiny chiral threshold difference could become a macroscopic matter surplus.
This is the proposed planetary baryogenesis channel. It is not derived quantitatively here, and it depends on several prior conditions being simultaneously satisfied. But it gives the rest of the section a clear causal chain: gravitational aggregation creates the gradient, \(g_{flux}\) heating supplies opportunities, chirality sorts charge, charge differentiation opens nuclear access, and dense compression halos provide the collapse environment.
The heat budget would therefore be dynamic rather than merely dissipative. Residual \(g_{flux}\) heating can accumulate when escape is inefficient; compression hotspots and nuclear close-approaches can concentrate that energy; baryonic collapse events can then convert a portion of it into rest mass. In this sketch, planetary growth is not a smooth continuous inflation but a long-timescale energy cycle: gradual heat accumulation, local threshold crossings, annihilation of matched matter/antimatter production, and intermittent survival of new matter.
If this part of IRCH is correct, high-compression regions should sometimes convert accumulated internal energy into surviving proton formation through the baryonic-collapse channel described above. Newly formed hydrogen introduced into a silicate melt does not float immediately to the surface; it dissolves into minerals, forms hydroxyl, shifts redox balances, and increases conductivity [23]. Over geologic time, as that hydrogen binds to oxygen, the deep interior would slowly accumulate hydrous phases and, where conditions permit, water [24, 25]. Whether the predicted rate is consistent with existing geochemical budgets remains to be checked.
If a deep-interior water source is real, it would create a long-term trend that standard tectonic and sea-level explanations of Earth's past flooding episodes do not include: gradual accumulation of interior-generated water and its slow outward expression through volcanism, mantle degassing, and mineral dehydration. Standard models account for the geological evidence on their own terms; the IRCH-specific addition is offered alongside, not against, those accounts.
If the net growth channel operates over geological time, new ocean basins would form, continents would separate, and water cycles between interior and surface would reshape the geography of the planet over time. Maxlow, Carey, and others explored this possibility from a different direction [26, 27].
Put together, the proposals give the Earth a qualitatively coherent picture under IRCH:
None of these proposals, on their own, prove IRCH. They sketch a qualitatively coherent picture; making it quantitatively credible against existing geophysical constraints is left as future work.
The rate question is the hard empirical boundary. Any real planetary-growth channel would have to fit heat-flow constraints [28], present geodetic bounds on Earth-radius change [29], lunar recession and angular-momentum history [30], planetary ephemerides [31], isotope and geochemical budgets, and the absence of large unexplained mass changes in Solar System dynamics. The present section does not claim those constraints are satisfied; it identifies the constraints that a quantitative version must meet.
The mechanism developed in §9 does not stop at explaining how matter could come to dominate antimatter. If proton formation is an ongoing channel rather than a one-time cosmological event, then bodies meeting the high-compression conditions should grow slowly over geological time, and the architecture of the Solar System should reflect that.
A long-standing obstacle for expansion-style readings of planetary history has been the absence of a physically grounded mechanism capable of driving sustained planetary growth. IRCH does not claim to resolve the entire geological debate, but it does offer a candidate mechanism of the kind expansion models have historically lacked. The remainder of this section traces the consequences. It starts with Earth, where independent lines of evidence converge on a picture of slow internal growth, and then moves outward to other bodies.
Earth is the world we know best, and the one in which several independent geological, palaeobiological, and palaeontological lines of evidence converge on the picture of slow internal growth that IRCH's baryogenesis channel would predict. None of the ideas summarized below is original to IRCH: the geological arguments have been developed by many researchers, with Carey and Maxlow among the best-known names; the biomechanical argument belongs to Hurrell; and the magmatic-extinction record is well established in its own literature. What is new is that a single physical mechanism, developed independently from the particle ontology, would be expected to leave traces in all three of these otherwise unrelated bodies of evidence.
The idea that Earth's radius may have changed over geological time has appeared in many forms throughout the history of geophysics. Although it sits outside the modern mainstream, it has been examined seriously by Samuel Warren Carey, a founding professor of geology at the University of Tasmania and an early advocate of continental drift before developing his expansion model, and by Dr. James Maxlow, who produced detailed reconstructions in which continental fits close cleanly on a smaller ancient globe [32, 26, 27]. A full discussion of the evidence and counter-arguments is beyond the scope of this paper; readers interested in the broader debate are encouraged to consult those primary works.
The expansion framing starts from a simple geometric observation: if the continents are treated as older, buoyant crustal blocks and the ocean basins as younger additions, then Earth's surface can be read as a two-stage record: an older continental shell disrupted by later creation of oceanic surface area. This is not the standard plate-tectonic interpretation, and IRCH does not assume it as established. The narrower question is whether the present crustal architecture is at least the kind of pattern one would expect if slow internal matter production had opened new surface area over time.
The strongest version of the geometric claim is that reduced-radius reconstructions can close the continents with fewer gaps and overlaps than constant-radius Pangaea reconstructions. Carey, Owen, and Maxlow each developed versions of this argument, using continental margins, ocean-floor age patterns, and small-Earth model construction to argue that a smaller ancient globe gives a cleaner fit [26, 33, 34, 35, 27]. Critical discussions have disputed the inference to expansion [36, 37]; the point here is only that the geometric-fit question has been part of the serious literature around the hypothesis.
That geometric argument is not isolated from the present crustal record. Earth's oldest crust is thick, buoyant, and granitic, forming the continents; the surrounding oceanic crust is thin, mafic, and geologically young. In the standard account, Pangaea was a supercontinent surrounded by oceanic domains on an Earth of roughly modern radius. In the expansion-compatible reading considered here, Pangaea is reinterpreted as the late-stage continental shell of a smaller Earth, before the modern global rift-and-spreading network opened around the Triassic-Jurassic transition. As long linear rifts connected into a global system, the first true spreading zones opened, and oceanic crust began forming continuously at ridges and migrating outward. In an IRCH reading, this two-layered architecture and its sharp temporal transition look like a planet that, at some point, acquired a permanent pressure-release mechanism for matter accumulating internally: old crust drifting away rather than thickening in place.
The timing matters. Pangaea existed at roughly the same interval in which expansion reconstructions place the onset of the modern global rift system. In the standard account, Pangaea was surrounded by ancient oceanic crust, most famously Panthalassa, and global plate reconstructions since ~200 Ma treat the older oceanic domains as largely consumed by subduction [38]. Expansion readings treat the same fact differently. They ask whether the near-absence of surviving pre-Jurassic ocean floor in the major present ocean basins, together with the youth of the mapped oceanic crust [39], is better read as evidence that the modern oceanic surface area was largely created during and after the breakup of Pangaea.
A separate line of evidence comes not from rocks but from bones. By his own account, Stephen Hurrell came to the expansion idea independently, approaching it from his background as an engineering designer and from the question of whether ancient animals could move comfortably under present-day gravity [40]. He examined the biomechanics and scaling limits of ancient organisms. The largest sauropod dinosaurs are the most striking case: their limb cross-sections, joint loading, and gait kinematics push hard against the strength of bone and connective tissue under present-day gravity [41]. Reading the same anatomy on a less massive Earth makes the scaling more comfortable. This is a crucial structural distinction: it implies not merely a smaller planetary radius but a smaller planetary mass in the past. A radius-only expansion (constant mass) would produce stronger surface gravity in the past, not weaker; Hurrell's findings therefore point towards an expansion driven by increasing mass over time, which is precisely what IRCH's baryogenesis channel would supply.
This reading is at least compatible with one broad feature of the deep-time fossil record. The pre-200-Ma interval is marked by major mass extinctions tied to enormous flood basalts: the Siberian Traps, the Central Atlantic Magmatic Province, the Viluy Traps, and others [42, 43]. In the IRCH interpretation, these events look like possible signatures of a planet straining against a closed shell: matter created internally, with no global rift system to relieve the pressure, escaping through catastrophic eruptions that pile material on top of existing crust. Standard models account for the magmatic events on their own terms; the IRCH-specific addition is that the timing and concentration of these eruptions is what would be expected if a slow internal source of new mass had to vent through a still-closed lithosphere. That closed-shell behaviour is the bridge to Venus, where IRCH reads the same basic pressure problem in a world that never developed Earth's global release network.
Earth and Venus are often described as planetary twins: similar in size, density, and overall composition. Yet their geological histories have followed strikingly different paths. From an IRCH perspective, this divergence centres not on initial conditions, but on how each planet's crust has responded to the slow accumulation of internally generated matter.
Venus is tectonically active. Recent work points to Earth-like lithospheric thickness and heat flow consistent with active rifting [44], and the planet hosts long extensional troughs such as Devana Chasma and the chasmata of Aphrodite Terra alongside coronae and other features that show localized plate-like behaviour. What appears to be absent is a globally connected network of plates and spreading centres of the kind that organizes Earth's surface laterally [45]. In an IRCH reading, Venus may sit between a fully closed-lithosphere regime and the mature, globally connected rift architecture Earth has developed. It may be a transitional state: tectonically alive in places, but without the planet-wide system that would let internal growth vent steadily.
If that reading is right, internally produced material has no fully developed steady outlet. Under IRCH, this includes newly created mass from compression-driven hydrogen synthesis. Its dominant escape route remains episodic volcanism. But volcanism deposits new material on top of the old crust, thickening and stressing it rather than relieving internal pressure. Over time, heat and strain can build until larger-scale resurfacing relieves the buildup. This offers a coherent IRCH reading of Venus's globally young surface and the evidence for large-scale resurfacing [46]: a world that, lacking a mature continuous outlet, periodically resets through more disruptive episodes.
In IRCH terms, Earth and Venus become two snapshots of how planets respond to internal LCM-driven evolution. Venus shows what happens when matter creation pressures build beneath a lithosphere whose tectonic outlets remain immature or partial. Earth shows what becomes possible when rifting has matured into a global architecture of renewal.
In conventional astrophysics, the gas giants are usually understood through some version of core accretion in the protoplanetary disk: a solid core forms from refractory and icy material in the outer disk, then sweeps up cold hydrogen and helium from the surrounding nebula until the envelope dominates the body's mass [47]. Water-ice worlds populate the outer Solar System because volatiles condense beyond the frost line. This model is well developed and accounts for a wide range of observations; what it does not include is the possibility that bulk composition could be significantly altered by ongoing matter production after formation.
IRCH does not aim to replace formation models, but it changes how the composition record should be read. If matter creation is an ongoing channel inside sufficiently dense interiors (§9), present-day bulk composition is a superposition of inherited and emergent material, not a frozen record of formation. The matter most readily produced would be hydrogen: the simplest condensed lag-mode structure. The emergent contribution should therefore bias compositions towards hydrogen enrichment over geological time. A rocky planet of sufficient mass and lifetime could, in principle, gradually enrich itself in hydrogen, with gas-giant compositions readable as a possible late-stage outcome of planetary evolution rather than only an inheritance from formation. The size of that contribution is not derived here; until it is, formation models that infer early Solar System conditions by reading back from current composition carry an unstated assumption about how much of today's bulk inventory is original.
Jupiter, then, can be read as a world that has had both formation-era hydrogen and any subsequent contribution time to accumulate. Its interior structure is well characterized: a hydrogen-helium envelope, with hydrogen transitioning from molecular behaviour in the outer layers to metallic behaviour at depth [48, 49]. IRCH does not change those structural inferences. What it adds is a candidate reading of the metallic-hydrogen regime as the natural configuration for lag-mode structures under extreme background compression: a reading consistent with the conductive behaviour and the strong dynamo-driven magnetic field that imprints itself throughout the Jovian system [50].
Exoplanet surveys add a relevant observational note. Since the discovery of 51 Pegasi b [51], gas giants have been found at orbital distances ranging from well inside Mercury's orbit ('hot Jupiters') out to and beyond Earth's. The standard interpretation is that these worlds formed beyond their systems' snow lines and reached their current orbits through some combination of disk migration, high-eccentricity tidal migration, and (in some cases) in-situ formation [52]. IRCH does not contest that account, and the observations alone do not distinguish between the proposals. The narrower point worth noting is that close-in gas giants are at least compatible with the picture developed here: in a framework where a sufficiently massive interior could continue to enrich itself in hydrogen over geological time, gas giants at small orbital separations are not difficult to accommodate, regardless of how they reached their present orbits.
Hydrogen does not stay where it is made. In silicate systems, oxygen is abundant, and hydrogen readily participates in hydration, reduction, hydroxyl formation, and water-bearing mineral chemistry. In IRCH, water therefore need not be only an inherited volatile; it can also be a chemical consequence of hydrogen synthesis in oxygen-bearing environments. A body of sufficient mass and internal LCM compression does not merely preserve water from formation. It may manufacture some of it over time.
This recasts the icy moons of Jupiter and Saturn. In the traditional view, the ice-rich moons are remnants of volatile-rich planetesimals that formed beyond the frost line. In IRCH, their watery compositions take on an additional significance. A moon embedded in a giant planet's LCM envelope does not orbit inertly: it experiences a raised baseline LCM compression, because it is immersed in the extended compression field of the host. For a world like Europa or Enceladus, this changes the baseline conditions. The threshold for LCM-wave breakdown would drop; interior heating would become more efficient; and hydrogen produced in core or mantle regions could chemically transform the body over time. The icy shells and subsurface oceans associated with these moons [53, 54] become natural places to look for the signature of hydrogen emerging continually and encountering oxygen-rich rocks awaiting hydration.
The magnetic evidence strengthens that reading, cautiously. Ganymede is the clearest case: Galileo observations show an intrinsic magnetic field strong enough to carve out a magnetosphere inside Jupiter's larger magnetosphere [55, 56]. Europa and Callisto are different. They do not appear to have comparable internally generated fields, but Galileo measured induced magnetic responses that are naturally explained by electrically conductive layers, most plausibly salty subsurface oceans [57]. Enceladus offers the Saturnian analogue: Cassini magnetometer data detected Saturn's magnetic field being diverted by ionized material from the moon's plume, tying the ocean-plume system directly to a magnetospheric plasma interaction [58].
In ordinary planetary language, these observations show that several icy moons are electrically active bodies embedded in giant-planet magnetospheres. They are not isolated ice balls. Some contain conductive oceans; one has a genuine internal magnetosphere; others load, bend, or disturb the parent planet's plasma environment. For IRCH, this matters because the dense-plasma story used in §9 does not require stellar-core conditions throughout the moon. It requires conductive interiors, time-varying fields, current paths, chemical reservoirs, and localized sites where compression and heating can concentrate. Giant-planet magnetospheres help supply exactly that kind of external driver: rotating tilted fields, charged particles, Alfvénic coupling, and persistent electromagnetic stirring.
The claim here is not that magnetometer observations prove baryogenesis inside icy moons. They do something narrower but important: they show that the physical setting is already closer to the IRCH preconditions than a cold-accretion picture alone would suggest. A moon near a giant planet is subject to two reinforcing conditions at once: a raised ambient LCM density from the host's extended compression field, and a large-scale, time-dependent magnetic environment from the host's magnetosphere. If IRCH's LCM compression thresholds are real, that combination would be expected to lower barriers for local heating, current concentration, and hydrogen-producing confinement events. Once hydrogen enters an oxygen-bearing interior, the subsequent water chemistry follows by ordinary chemical pathways.
Even Io finds a natural place in this narrative. It is the most volcanically active object known, and its extreme activity is usually ascribed primarily to tidal flexing [59]. Under IRCH, that remains part of the story, but Io also occupies the deepest region of Jupiter's compressed LCM environment. Its interior would be stirred by both tidal motions and a highly modulated \(g_{flux}\) residual. Each compression cycle would raise the probability of LCM-wave confinement events; each temperature rise would increase the frequency of nuclear close-approaches. The result is a world in which volcanism is not merely an effect of tides but a structural outcome of living within Jupiter's gravitational energy field.
In this broader view, the Solar System becomes a hierarchy of LCM environments nested within one another. Earth, Venus, the gas giants, and the icy moons are not separate puzzles but different responses to the same proposed process: ongoing matter creation under conditions of compression, conductivity, heating, and magnetic organization. Earth represents the case where internal growth may have found a global release architecture; Venus the case where that outlet remains immature or partial; the gas giants the hydrogen-rich endpoint of long accumulation; and the icy moons the case where a host planet's compression field and magnetosphere may lower the threshold for local hydrogen production.
The deeper point is structural. This section has treated baryogenesis as a local process: matter appearing inside planets and moons, changing their mass, chemistry, and internal dynamics over time. The next section applies the same idea recursively, but at much larger scales. If rest accumulation can change a body at \(DYN\), then ongoing rest creation and destruction at every rung sets the cosmological budget that the rest of the paper has to close. That balance must be statistical rather than runaway.
In §9 and §10, baryogenesis was developed as a local process: matter creation events inside individual planets and moons. This section considers what the same process implies when it operates everywhere at once across the universe.
ERMS's recursive medium emergence postulate, in the background since §3, says that every rung's medium is the persistent organisation of the matter at the rung one step inward. Local matter creation at our rung therefore has consequences not just for our matter but for whatever plays the role of medium for the rung outward: its persistent structure is shaped by the matter dynamics that produce rest mass here. The question is whether our rung's matter dynamics produce something tensile, persistent, and transverse-mode-supporting enough to fill that role. Those dynamics include gravity, large-scale flux flow, and ongoing matter creation.
In §10 we used planet-sized bodies as the first test cases because their geology gives us something concrete to compare against. But if the baryogenesis channel is real, stars are not exceptions to it. They are stronger candidates: larger, hotter, more gravitationally compressed, and threaded by conductive plasma and magnetic structure on scales planets can only approach locally.
This does not mean ordinary stellar physics has to be discarded. Fusion, radiative transport, convection, magnetic reconnection, and stellar winds could remain the language in which stars are quantitatively described, though ongoing baryogenesis might change the interpretation of those processes in ways not developed here. IRCH adds a possible underlying rest-mass source: in sufficiently steep LCM density gradients, wave confinement and chirality sorting can turn energy flow into new rest mass. Stellar interiors would then be places where inherited matter, fusion products, and ongoing baryogenesis all contribute to the long-term matter budget.
The stellar case matters for cosmology because it removes any special pleading around planets. If baryogenesis operates only in rare planetary niches, it is a geological curiosity. If it operates wherever gravity, heat, conductivity, and steep LCM gradients cooperate, then it becomes a universal local process. Cosmology is the accounting problem that follows.
PDOC makes gravity predominantly refractive, but not perfectly lossless. The residual heating discussed in §5 means that \(g_{flux}\) gives up a small amount of energy wherever attractive gravitation occurs. Locally this appears as a heat contribution inside massive bodies. Cosmologically it creates a source/sink problem: if \(g_{flux}\) is continually drained by matter, why does gravity not weaken as we look across cosmic time?
IRCH's answer is that \(g_{flux}\) is not a fixed reservoir but the matter-resonant long-wavelength tail of \(SUB^{flux}\), continually refreshed by inner-rung dynamics. We observe cosmological redshift at our rung; by rung invariance, \(SUB^{flux}\) propagating through \(SUB^{med}\) undergoes its own redshift, with its long-wavelength end continually drifting into the matter-resonant band that DYN matter experiences as \(g_{flux}\). That redshift drift is one recharge channel; at least one further channel is developed later in the paper. The replenishment is not a separate postulate added to rescue the heating channel. It is what rung invariance requires once we accept that flux propagating at any rung redshifts.
The closure check is quantitative. For cosmological steady state, the combined recharge rate from the available channels has to balance the dissipative depletion rate produced by matter. The mechanism is structurally available; verifying that the rates naturally match over cosmological timescales is one of the open closure checks for IRCH.
§5 developed gravity at \(DYN\) as PDOC: \(g_{flux}\) phase-delays through compression-modified \(SUB^{med}\) near aggregated \(DYN^{rest}\), producing a phase landscape that drives matter towards the source. Once depletion and replenishment are included, gravity acquires an additional structural feature at large scales: it is bidirectional, attractive at filaments and repulsive in voids.
The bidirectionality follows from the small dissipative residual. \(g_{flux}\) passing through aggregated matter loses a small amount of energy to that matter. The depletion is small per pass, but cumulative over the path lengths involved at cosmological scales. The \(g_{flux}\) flux density emerging from a filament is therefore measurably reduced relative to the \(g_{flux}\) flux density arriving from the void side of the same filament.
A test mass placed in this landscape responds to the anisotropy of \(g_{flux}\) flux density at its location, in addition to the local phase-delay landscape from any nearby aggregated mass. The sign of the effect depends on where the test mass sits:
Observed peculiar-velocity reconstructions already contain a related phenomenology, though not the IRCH mechanism itself: the Local Group has been described as moving away from the Local Void, and the "dipole repeller" analysis identifies an underdense region contributing to large-scale flows alongside overdense attractors [60, 61]. Standard cosmology reads these as the gravitational effect of underdensities within the usual density field. IRCH reads them as useful empirical handles on the same qualitative signature: voids participate dynamically, rather than serving only as empty background.
The same depletion landscape may also reshape how a galaxy's gravitational field falls off with distance. In the standard picture, a galaxy is treated as a mostly point-like distribution whose field falls off as 1/r² at large distances; rotation curves are then expected to drop off correspondingly. The observed rotation curves of disk galaxies stay flat far from the centre [62]. Standard cosmology accounts for this via cold dark matter, and modified-gravity programs such as MOND [63] offer an alternative phenomenology that also fits a wide range of observations [64]. IRCH proposes a different kind of explanation: the flattening may arise from running PDOC through the non-uniform \(g_{flux}\) landscape produced by depletion and replenishment, rather than from a centred 1/r² field alone.
In this picture, rotation-curve flattening would follow from the same depletion landscape that makes voids repulsive. A galaxy is a region of dense matter, and the \(g_{flux}\) passing through it is significantly depleted. The depletion pattern is not spherically symmetric: matter is concentrated along a disk, with voids and filaments distributed around it. The \(g_{flux}\) density a test object orbits through is therefore shaped by both the galaxy's internal structure and the surrounding cosmic-web environment, not by a centred 1/r² falloff alone. Two effects contribute:
This is a qualitative mechanism, not a quantitative derivation. Whether the depletion picture reproduces observed rotation curves, including the empirical regularities captured by MOND-like phenomenology, is a future-work calculation. The structural form is in place; if it holds up quantitatively, IRCH would reduce the need for a separate dark component in this part of the phenomenology. Until then, the claim is only that the mechanism points in the right direction.
The observed cosmic web is the filamentary large-scale organization of galaxies and flows [65, 66, 67]. It is read here as a tensile lattice: filaments held in attractive tension, voids in active repulsion, the whole network maintained by ongoing depletion and replenishment of \(g_{flux}\). This is exactly the kind of persistent organization ERMS requires a rung's scaffolding to be.
ERMS identifies the medium of any rung with the scaffolding of the rung one step inward. Symbolically: \(DYN^{med} \equiv SUB^{scaf}\) from our perspective on LCM, and equivalently \(DYN^{scaf} \equiv SUP^{med}\) from the perspective of the next rung outward. The medium of any rung is not a primitive; it arises from the persistent organization of structures and dynamics at the inner rung.
The cosmic web is exactly such a persistent organization at our rung. It is persistent over cosmological timescales as a coherent organization; spatially connected across the universe through filaments; capable of supporting transverse modes because it is held in tension between attractive filaments and repulsive voids (a passive attraction-only network would collapse, but a tensile network can carry transverse waves much like a stretched membrane); and dynamically maintained by inter-rung coupling rather than relying on a static scaffold that would slowly degrade.
The identification \(DYN^{scaf} \equiv SUP^{med}\) then says: what we observe as the cosmic web is, from the next rung's perspective, the medium of its observable scale. By rung invariance, \(SUB^{scaf}\) should be the same kind of thing one rung inward. That is the structure that constitutes our LCM: a persistent tensile lattice, maintained by the same rest-and-flux bookkeeping at SUB scale.
A natural follow-up: if \(SUP^{med}\) exists as the cosmic web, and \(SUP\) supports its own rest mass by rung invariance, why don't we see any \(SUP^{rest}\) structures? By scale translation, such an aggregation would appear as an enormous region in which the cosmic web itself is denser: filaments packed more closely, voids smaller, the scaffolding compressed relative to the surrounding background.
The reason we should not expect one nearby is statistical. Rung invariance says every rung looks the same in its own native units: rest is concentrated in aggregations while most volume lies between them. At our rung, that is true at many nested scales: between planets, stars, galaxies, and filaments. Scaling up one rung outward, a random \(DYN\) point is overwhelmingly likely to lie in a \(SUP\)-vacuum for the same reason. It is likely to be far from any \(SUP^{rest}\) structure. The statistical isotropy of the cosmic web on the largest scales we can measure is what we would expect if our location is typical. The picture would predict observable anomalies only in unusual proximity to a \(SUP^{rest}\) aggregation; identifying what such anomalies might look like, and searching for them, is left as future work.
This closes the medium-emergence side of the cosmological picture: local rest creation, gravity, flux depletion, and replenishment can organize the cosmic web into a candidate \(DYN^{scaf}\). It does not yet close the rest budget. If matter creation is ongoing, then over sufficiently large volumes and timescales some complementary process must remove standing-wave rest from the rung's inventory. The next section takes up that missing half of the bookkeeping.
The previous section made cosmology into a bookkeeping problem. If matter creation operates locally and continually, and if the cosmic web is to remain statistically stationary as a medium-forming scaffold, then the rung also needs a process that removes standing-wave rest from its inventory over sufficiently large volumes and timescales. This section develops that missing half of the budget: in IRCH, matter destruction occurs where LCM compression crosses a phase boundary. This extreme condition is realised in the cores of active galactic nuclei (AGN). The same picture also supplies a structural account of relativistic jets and an alternative mechanism for the excess redshifts observed in quasars.
Matter creation alone would lead to runaway accumulation. For the universe to remain in dynamic steady state, an active destruction process must operate elsewhere. In IRCH, matter destruction happens where LCM compression crosses a phase boundary. This condition is realized in the cores of active galactic nuclei (AGN) and, more generally, in the interior of any sufficiently dense gravitationally bound object whose central compression is high enough.
LCM is the medium of \(DYN\), and by recursive medium emergence it equals \(SUB^{scaf}\): the persistent tensile organization at \(SUB\). The bidirectional-gravity story we developed for the cosmic web at our rung repeats at \(SUB\): SUB-scale filament-like dense regions attract, SUB-scale void-like regions repel, and the resulting tensile balance at \(SUB\) is what makes LCM elastic at our scale. LCM's ability to support transverse modes arises from the SUB-scale tensile structure beneath it. That property is what lets LCM carry light and standing-wave matter.
Under sufficient compression of LCM, the SUB-scale voids that maintain that tensile balance shrink. The depletion/recharge cycle that holds the SUB-scale lattice together can no longer function the same way. At some critical LCM compression, the SUB-scale tensile structure collapses, and LCM loses the elastic property that matters here: its ability to support transverse modes.
Once LCM cannot support transverse modes locally:
This section introduces phase-state extensions of the ERMS aspect symbols. The suffix \(\phi\) marks a phase-changed role state, not a new rung and not a derivative.
concept Rung_{n}^{medφ} [Medium] Phase-changed medium of the rung after it has lost the ability to support shear and torsional distortions.
concept Rung_{n}^{fluxφ} [Flux] Freely propagating modes supported by the phase-changed medium.
At DYN, \(DYN^{flux\phi}\) would appear as longitudinal pressure or compression energy carried by \(DYN^{med\phi}\), rather than as ordinary transverse light.
Phase-boundary mode conversion occurs when a region of \(Rung^{med}_{n}\) crosses into \(Rung^{med\phi}_{n}\). Ordinary \(Rung^{rest}_{n}\) and transverse \(Rung^{flux}_{n}\) depend on the unprimed, transverse-supporting medium. Once the medium is in the \(\phi\) state, those structures are no longer supported as such, and their energy converts into supported channels: \(Rung^{flux\phi}_{n}\), inner-rung modes, and bulk energy of \(Rung^{med\phi}_{n}\).
What this section calls matter destruction is the \(DYN^{rest}\) instance of phase-boundary mode conversion. The bookkeeping role is destruction because standing-wave rest leaves the DYN matter inventory; the mechanism is mode conversion because the energy remains present in forms the phase-changed medium can support.
In an AGN, accreting material is drawn into the central region under increasingly extreme compression. The observable claim is that black-hole interiors are not geometric singularities in this picture, but extended phase-changed regions of LCM. From outside, matter appears to vanish at a critical depth because standing-wave rest is no longer supported there.
Several details remain to be worked out before this account is quantitatively complete: the threshold criterion for the phase change; where the phase boundary sits relative to the standard event horizon (the two need not coincide); whether \(s_{flux}\) attenuation contributes to softer matter destabilization before the boundary; and the energy bookkeeping at and across the boundary. These are flagged as future work.
AGN jets are narrow, bipolar beams extending outward from the central engines of active galaxies. In IRCH, the central claim is simple: a jet can be bulk \(DYN^{med\phi}\) ejected from the phase-boundary region along the polar direction. This is not light. It is phase-changed medium moving as a non-equilibrium column, driven by pressure gradients through the path of least resistance.
The relation between the phase boundary and the standard event horizon is left open. In IRCH terms, the event horizon is more naturally read as a refractive turning surface for transverse modes: a region where LCM compression and gradient steepness prevent light from escaping. The phase boundary is different. It is the compression threshold at which LCM loses transverse-mode support and enters the \(\phi\) state. The phase boundary may sit inside, near, or outside the refractive turning surface; this paper does not derive the ordering.
While the flow remains \(DYN^{med\phi}\), it is not governed by the transverse-wave speed limit \(c\), because \(c\) is the propagation speed of transverse modes in elastic LCM. The surrounding region is more complicated. Around the column, LCM is in a turbulent transition zone between \(DYN^{med}\) and \(DYN^{med\phi}\). Steep \(DYN^{med}\) gradients in that zone can meet the matter-creation conditions developed in §9, producing standing-wave matter and transverse radiation along the jet.
The visible jet is therefore secondary in this picture. Detectors see light emitted by matter and transverse modes generated around the phase-changed column, not the bulk \(DYN^{med\phi}\) flow itself. Magnetic fields, disk winds, and nozzle effects may still shape the observed emission; IRCH only adds a bulk-medium component that conventional transverse-mode observations would not see directly.
This distinction sets up the quasar-redshift mechanism below. Matter forming along the column edge forms in elastic LCM close to ambient conditions, so it should mostly share the parent galaxy's redshift. The intrinsic-redshift signature belongs to regions where the bulk column has returned to elastic support as a coherent but still denser-than-ambient volume. Matter formed there locks to the elevated local medium density and emits at frequencies an ambient observer reads as intrinsically redshifted.
Under this reading of AGN, the ejected \(DYN^{med\phi}\) should phase-change back to \(DYN^{med}\) at the jet termination zone. It is reasonable to expect that the recovered region is initially denser than ambient and relaxes toward ambient on its own timescale.
Matter forming at the boundary of that dense region should have eigenfrequencies close to ambient and emit at close to the parent galaxy's redshift (radio lobes).
Matter forming inside the dense region should phase-lock to the elevated local density, with slower internal clocks. The light it emits arrives at an ambient observer intrinsically redshifted — not because the source is receding, but because the emitter's clock is locally slow. This is the IRCH reading of the statistical quasar-galaxy associations catalogued by Halton Arp [68]: a quasar near a closer parent galaxy can carry the parent's cosmological redshift plus an intrinsic excess set by the local medium state in the termination zone.
This is offered as a structural possibility opened up by the AGN-jet medium-ejection picture, not as a derived prediction. What density elevation accounts for observed quasar redshifts, the relaxation timescale, and the empirical separation between cosmological and intrinsic components are quantitative questions for future work.
The previous two sections set up the large-scale bookkeeping of IRCH. §11 identified the cosmic web as a candidate medium-forming scaffold for the SUP rung. §12 supplied the complementary rest-removal channel through phase-boundary mode conversion in AGN cores. With creation, removal, and scaffolding in view, the framework now owes the reader an account of two empirical observations that any cosmology has to address: cosmological redshift and the cosmic microwave background.
This section develops that account without invoking metric expansion. Both phenomena are read as wave-mechanical consequences of a statistically stationary but locally dynamic LCM. Cosmological redshift leaves residual energy in \(SUB^{scaf}\); the CMB is treated as a candidate outward, thermalized \(DYN^{flux}\) emission of that same LCM reservoir.
This is the most provisional part of the construction. Non-expansion redshift models have historically struggled because the empirical requirements are unusually tight: redshift, time dilation, surface-brightness dimming, image sharpness, and the CMB must all be accounted for together. IRCH also cannot fall back on metric expansion, because that route conflicts with the recursive rung structure developed earlier. The treatment here is therefore deliberately qualitative and cautious. The mechanism makes sharp physical commitments: universal phase-fractional response, amplitude-independent path coupling, and reservoir-mediated re-emission. The derivation of the cosmological-redshift rate and CMB temperature from first principles is left as future work. The purpose is to show that IRCH has a structurally plausible non-expansion account of these observables, and to make the open derivational targets explicit.
One possible route would be to let the LCM undergo slow uniform outward scale evolution, with cosmological redshift and the CMB arising from phase-lock asymmetry between bound and unbound waves under that expansion. The idea is natural if rest accumulation and rest release are treated as slightly imbalanced: each rung would gradually build rest into its own scaffolding, literally expanding the medium. That route is tempting because it makes the usual redshift bookkeeping easy: wavelengths, durations, and background temperature would all inherit the same scale factor. But it does not survive rung invariance.
The objection is structural. First, because the LCM is \(SUB^{scaf}\), any cosmological-scale evolution of the LCM would be an evolution of SUB-scale structure. Rung invariance says the same kind of law should recur in SUB-native units, not that SUB and DYN share the same dimensionful clocks and rulers. Translated into DYN units, SUB-scale dynamics run on much shorter timescales than DYN-scale ones, so such evolution should appear to us as rapid time-evolution of bulk LCM properties unless an additional synchronising rule is introduced. Second, adding rest to scaffolding everywhere does not by itself explain how the medium would expand while preserving a statistically stable filament/void architecture. One would need a special reorganisation law that keeps average void size, filament thickness, density, and connectivity evolving coherently. IRCH has no such law. The LCM is therefore treated throughout this narrative as statistically stationary rather than metrically expanding.
We still observe cosmological redshift. The rest of the section therefore develops an alternative mechanism that preserves the rung-invariance constraint.
"Static LCM" in what follows should be read as statistically stationary, not frozen. The LCM's statistical structure is steady: average void size, filament thickness, filament density, filament length, and overall filament/void distribution do not drift secularly over cosmological time. But \(SUB^{rest}\) is continuously being added by SUB-rung baryogenesis and removed from the rest inventory by SUB-rung analogues of AGN-core phase-boundary mode conversion, with the two rates balancing globally. Individual filaments and voids are always changing shape; the LCM is a dynamically sustained tensile structure, not a frozen solid.
This distinction matters for wave propagation. A perfectly time-independent linear medium conserves wave frequency: it can delay, refract, lens, or scatter light, but it cannot produce a systematic redshift. A redshift mechanism needs either local time-dependence in the medium or a relaxational mode-conversion channel that lets coherent wave energy move into other degrees of freedom. The statistically stationary LCM supplies the right category: no global metric evolution, but continual local rearrangement and phase-lock adjustment, with internal degrees of freedom that propagating waves can excite and that can re-emit into inner-rung flux.
\(DYN^{flux}\) wavelengths are taken to be much larger than the typical filament/void scale of \(SUB^{scaf}\). A propagating DYN wave therefore does not resolve individual SUB-feature boundaries;Here "feature" means a local structural element of \(SUB^{scaf}\): a filament, void, or filament/void boundary in the SUB-rung scaffold. it sees an effective medium homogenised over many features per wavelength. Per-density-transition phase-lock arguments, of the kind that would apply to waves near the medium's feature scale, are the wrong framing for this regime.
In the long-wavelength limit, the wave couples to the bulk state of the medium rather than to a specific local feature pattern. The relevant question is what the medium's dynamic steady state does to a DYN wave whose wavelength averages over many such features. That state includes continuous local rearrangement, baryogenesis, and matter destruction at the SUB rung. Image sharpness can be preserved if the effective-medium response is forward-coherent: the wave should not encounter discrete per-feature transitions that scatter it angularly.
The proposed mechanism is path-integrated phase-lock through directional SUB-rest impedance memory. As a DYN-light wave propagates, it weakly polarises or strains the SUB-rest scaffold along its propagation direction. For this mechanism to work, the directional impedance memory must be temporary but not instantaneous: it must persist long enough to participate in the continuing wave train, while still relaxing on a finite timescale. A small fraction of the wave's coherent energy per unit distance is stored in that directional impedance state and enters the LCM reservoir. Some of that energy can be re-emitted inward into long-wavelength \(SUB^{flux}\) modes; later subsections also consider outward thermalized re-emission into \(DYN^{flux}\). The long-wavelength SUB channel is motivated by the effective-medium limit: the DYN wave couples to the bulk state of \(SUB^{scaf}\), so the stored excitation is scaffold-scale within SUB and its inward relaxation should preferentially populate the corresponding long-wavelength end of \(SUB^{flux}\). The matter-resonant tail of those re-emitted modes is what DYN matter observes as \(g_{flux}\), making this a second candidate recharge channel alongside the direct redshift of \(SUB^{flux}\) itself. Which channel dominates is left as a quantitative closure question.
The transfer is rest-mediated mode conversion, not direct wave-to-wave leakage. The SUB-rest scaffolding of the LCM acts as the matter intermediary: DYN light excites SUB-rest, and SUB-rest's natural radiative response re-emits SUB-flux. This is the rung-extension of standard wave-in-material physics, where waves couple to the medium's matter and matter re-emits flux. No new mechanism is required; the existing matter-to-flux generation pattern is applied one rung inward.
The first quantity to anchor is spectroscopic redshift. The observed wavelength is compared with the corresponding emitted, or rest, wavelength supplied by local laboratory physics.
For the mechanism to satisfy the observational hard constraints, \(1 + z\) is the total wavelength stretch factor. One of the most important checks comes from Type Ia supernovae, whose light curves are used as cosmological clocks: distant events are observed to unfold more slowly by this same factor \(1 + z\). To state that timing test, we introduce the observed light-curve timing scale and the corresponding local/template timing scale before cosmological stretching.
This timing relation is not a definition of \(z\); it is the empirical match the mechanism has to reproduce. In other words, the mechanism must stretch wavelength and Type Ia light-curve timing together. That stretch must depend on path length (\(D\)), not on how bright or energetic the particular explosion was.
The loading must therefore be amplitude-independent: brightness changes the wave amplitude but not the redshift coefficient. A bright supernova does not condition the path more strongly simply because it is bright; otherwise Type Ia time dilation would depend on source luminosity. The candidate law is instead phase-fractional: each path segment applies the same small fractional re-spacing to the wave's current phase ruler. The fractional leakage rate is set by the medium-scale recycling and the directional impedance response; it is not set by the photon's wavelength or amplitude or by the source's brightness, fluence, or duration.
The per-distance target needs one more group of symbols: the empirical Hubble-scale rate, the DYN light speed, the resulting redshift coefficient, and a running coordinate along the path.
The next step is a target statement, not a completed derivation. If directional SUB-rest impedance memory is to explain both cosmological redshift and Type Ia time dilation, its coarse-grained effect must be a universal fractional stretch per unit path length. The same coefficient must apply to wavelength and to Type Ia timing; otherwise the mechanism would redshift spectra without reproducing the observed light-curve stretch.
Integrating that path law over the full source-to-observer distance gives the total stretch.
Read together, these claims say that emitted wavelengths and emitted intervals arrive stretched by the same path factor. The sharp commitment is that the directional impedance response transforms the whole propagating wave train coherently: photon energy, wavelength, period, and arrival-cadence intervals are all scaled by the same factor along the path. This is what Heymann's wavefront-stretching transformation [69] and Nash's photograviton bookkeeping [70] accomplish in their respective frameworks, and both establish that a universal fractional propagation law of this form delivers the standard (1+z) observational tests through bookkeeping inheritance. IRCH's contribution is to ground that universal law in a specific microphysical mechanism: directional SUB-rest impedance memory, rather than postulating it.
Achromaticity follows from the phase-fractional nature of the response: the medium re-spaces the current wavelength and period by the same fraction per unit path length, rather than adding a fixed delay or fixed energy loss per crest. Image sharpness is preserved only if the impedance response is forward-coherent; the wave couples to the bulk averaged medium state rather than to per-feature scattering.
The actual derivation of the impedance-response function is left as future work. That includes what SUB-rest degree of freedom stores the directional memory, what its relaxation timescale is, and how the universal propagation law falls out of the microphysics.
The redshift mechanism just described would deposit energy in \(SUB^{scaf}\): the LCM itself. DYN-light redshift leakage is one identifiable input to that reservoir, but it should not be treated as the only one. The LCM is not a passive optical material. It is a statistically stationary but locally dynamic scaffold, with \(SUB^{rest}\) being created and removed by phase-boundary mode conversion, inner-rung flux passing through it, and dissipative channels operating at SUB scale.
The reservoir is not a separate substance or hidden store. It is the nonequilibrium mechanical state of \(SUB^{scaf}\) itself: small scaffold-scale strains, filament readjustments, torsional offsets, and kinetic motions distributed through the SUB-rest web. These motions carry real energy in the LCM, but they are not necessarily organized as a single coherent propagating wave. They are therefore not immediately compatible with coherent flux modes. They must first mix, dephase, and relax into modes that adjacent flux bands can carry.
At least two reservoir inputs are therefore potentially available:
The faster timescale of SUB dynamics matters here. From DYN, even weak coupling from these channels could look like a smooth, persistent background throughput. The CMB energy density is small enough that the open question is not simply whether the LCM has enough energy available, but why only a small outward fraction should thermalize into the observed microwave background.
Once energy is stored in a rung's scaffold, it need not re-emerge in the same form or at the same rung boundary. The reservoir is the intermediary. It receives candidate inputs, mixes them through scaffold-scale strain and relaxation, and only then emits into adjacent flux bands. No input is identified directly with an output.
At the LCM, the reservoir is \(SUB^{scaf}\). Its candidate inputs are DYN-flux redshift residuals and \(s_{flux}\)-driven readjustment of the SUB scaffold. Its candidate outputs are inward re-emission into the long-wavelength tail of \(SUB^{flux}\) and outward re-emission into ordinary \(DYN^{flux}\):
This reservoir picture does not erase the directional response required by cosmological redshift. The path effect belongs to the directional component of the scaffold response: an above-background coherent train, such as a supernova light curve, can bias \(SUB^{scaf}\) along its propagation direction without scattering the image. The reservoir effect belongs to the aggregate scaffold state: many inputs arrive from many directions, and the scaffold need not preserve them as separate source-labelled memories before re-emission. Identifying the degree of freedom and relaxation timescale that make both behaviours compatible remains an open derivational target.
By rung invariance, every medium-forming scaffold should have an analogous reservoir structure. The LCM reservoir is \(SUB^{scaf}\) viewed from DYN; one rung outward, \(DYN^{scaf}\) should likewise be able to store, mix, and re-emit energy. Its inward output would populate the long-wavelength tail of \(DYN^{flux}\), just as the LCM reservoir's inward output can populate the long-wavelength tail of \(SUB^{flux}\).
In this proposal, the CMB candidate is the outward, thermalized \(DYN^{flux}\) output of the LCM reservoir. The observed CMB is ordinary DYN microwave radiation, so its microwave scale must come from DYN-visible thermalization and mode selection in that output.
The blackbody character must come from statistical equilibration of the re-emitted DYN-flux through weak mode mixing, in the same broad way real blackbodies form in systems with enough coupled emitters and modes. The many-direction input at each point gives a plausibility argument for source-memory loss, but not a derivation of thermality. The detailed temperature, angular power spectrum, polarisation, and lensing signatures observed in the microwave sky are constraints the mechanism must eventually meet; deriving them is left as future work.
The single sharpest open test concerns high-redshift CMB-temperature observations. SZ-effect and quasar-absorption-line measurements give \(T_{cmb}\,z\) consistent with \(T_{0}\,\left( 1 + z \right)\), which is naturally produced under metric expansion. Under the LCM-reservoir picture, the local CMB temperature is set by reservoir equilibrium and outward coupling, giving no immediate reason for distant systems to sample a locally hotter CMB. The candidate resolution is that the apparent (1+z) scaling reflects the redshift of the observed light en route from the absorber to us rather than a difference in local CMB temperature at the absorber, but this needs a careful re-derivation under the static-LCM picture. A clean account of \(T_{cmb}\,z\) observations under this framework remains the most empirically constraining open test for the candidate.
Gravity in IRCH is not perfectly lossless. The dissipative residual identified in §5 means that \(g_{flux}\) is continually drained wherever attractive gravitation operates. Without a replenishment mechanism, gravity would weaken across cosmic time. §11 identified the inner-rung replenishment chain structurally; the reservoir picture developed here provides one candidate source.
The inward output of the LCM reservoir can populate the long-wavelength tail of \(SUB^{flux}\). The matter-resonant fraction of that tail is \(g_{flux}\) from our perspective. This remains a candidate replenishment channel alongside the direct redshift of \(SUB^{flux}\) itself; the relative contribution of the two channels is not yet derived.
For cosmological steady state, the inner-rung replenishment rate has to balance the depletion rate produced by gravitational PDOC across the universe. The mechanism is now structurally specified enough to state the closure check: the inward output of the LCM reservoir, together with any direct \(SUB^{flux}\) redshift contribution, must replenish \(g_{flux}\) at the rate gravitational coupling drains it.
If the universal propagation law encoded in the wavelength, period, and redshift stretch-factor claims is granted, the four standard \(1 + z\) tests follow through Heymann/Nash bookkeeping [69, 70]:
Image sharpness is preserved through the forward-coherent character of the impedance response: distant images do not blur from cumulative scattering because the medium's response is to the bulk averaged state, not to per-feature transitions.
The single test the mechanism does not yet pass cleanly is high-redshift CMB temperature scaling, as discussed in §The cosmic microwave background. Under the LCM-reservoir picture, the apparent \(T_{cmb}\,z = T_{0}\,\left( 1 + z \right)\) signature requires either a careful derivation of how observed light from high-z absorbers carries CMB-temperature information through the redshift channel, or a structural reason why the reservoir equilibrium sampled at distant systems should track spectroscopic redshift. This is flagged as the sharpest derivational gap in the picture.
The mechanism makes the following sharp commitments, each of which distinguishes IRCH from FLRW cosmology and from previous static-universe alternatives:
The following derivational gaps are explicitly flagged for future work:
These are derivation work, not sketch failures. The mechanism is structurally specific enough to be falsifiable in principle: any observation that demonstrates source-property-dependent cosmological redshift, wavelength-dependent cosmological dimming, or CMB temperature structure incompatible with a statistically stationary LCM reservoir would discriminate against the picture.
The paper began with a few foundational assumptions: locality of interactions, waves require media, forces that appear to act at a distance must be physically mediated. From those assumptions and the constraints of ERMS, the narrative developed PDOC as the universal coupling mechanism, then gravity as PDOC at \(DYN\), then particle confinement as \(s_{flux}\)'s 2-out role, then particles and forces as the chirality-bearing standing waves and their interactions, then baryogenesis as the local rest-creation channel, then cosmology as the equilibrium of cross-rung energy and matter flow at large scales, then AGN cores as the matter-destruction channel that closes the rest budget, and finally cosmological redshift and the CMB as wave-mechanical signatures of light propagating through that statistically stationary LCM.
The closure described here completes the loop. The cosmic web that emerges at the largest scales we can observe is not just a result of the picture. It is the specific structural form the framework requires for its own recursive medium emergence to function. The ontology-building arc, from the smallest scales we observe (subatomic particles) to the largest (the cosmic web), ends not at a boundary but at a handoff: the same structure that closes our rung's story opens the next rung's.
This closing identification is also where the framework most clearly shows its hand. ERMS is committed to recursive medium emergence; IRCH has been committed to that requirement throughout. The cosmic web's tensile structure is not an incidental cosmological observation but the empirical pressure point that ERMS imposes on any provisional implementation. If the cosmic web's structure had turned out incapable of playing the scaffolding role, the framework would have struggled to close. It had to be tensile, connected, and persistent enough. That it appears to fit the requirement is at least suggestive compatibility with the framework's recursive-emergence commitment.
Whether it is realized, exactly how, and what predictions follow at \(SUP\) scale, remain open. The constructive arc closes here not because the story ends but because we have run out of rungs we can directly probe.
Relativity is often introduced through the language of spacetime curvature: a mathematical surface that bends and twists in response to mass and energy. The geometric picture is precise as a calculational tool, but it offers no underlying mechanical substrate: curved spacetime is a mathematical object, not a physical one.
This section reads relativity through the IRCH ontology developed in the foundational sections. The LCM is a real, elastic medium; matter is a phase-locked standing wave in that medium; the apparent geometric features of relativity are read as mechanical responses of waves living in a compressible substrate. Einstein's equations remain correct in their predictions, but IRCH offers a different ontological picture for what may be happening underneath them.
The candidate reading in this section is that many effects normally attributed to spacetime geometry can be interpreted as wave behaviour inside the LCM. On this view, the LCM is not merely located in space and time; it is the physical substrate through which DYN observers experience spatial distance and clock rate.
The LCM is treated here as a physical, elastic medium that can be compressed, stretched, and shaped by energy and matter. Since matter is made of standing waves in that medium, observers and measuring instruments are also part of the same substrate they measure.
Under this interpretation, several relativistic effects acquire a possible medium-level reading:
This offers a concrete way to read one of relativity's central constraints: the apparent constancy of the measured speed of light. The proposal is not that observers can step outside the LCM and compare it to an external standard. The proposal is the opposite: observers are LCM-bound systems, so their standards of distance and duration are tied to the same local medium state as the light they measure.
From this viewpoint, relativity remains correct as a predictive formalism. IRCH only offers a different ontology underneath it: the geometric variables may correspond to changing physical conditions in the LCM, and observers made of LCM standing waves measure from within those changing conditions. Recovering the full Lorentz symmetry of the standard formalism remains a derivational requirement, not something this qualitative reading proves by itself.
When relativity is taught using spacetime diagrams, length contraction is often presented as a geometric effect: moving objects "shrink" along their direction of travel because of how coordinates transform. That presentation is mathematically precise but says nothing about what physically happens to the object.
In IRCH, length contraction can be read as a candidate mechanical effect. It is what would happen when an object moves rapidly through a real, compressible medium, provided the resulting deformation reproduces the Lorentz behaviour measured by observers made of that same medium.
As an object accelerates relative to the local LCM, it may disturb the medium around it. At low speeds this would have almost no noticeable effect, but as the speed approaches the propagation speed of transverse waves in the LCM, the medium response could become directionally asymmetric.
In the simplest mechanical reading, that response creates a directional compression gradient: higher LCM density ahead of the object, normal LCM density behind it. The gradient would grow steeper as speed increases. Because matter in IRCH consists of standing waves stabilized by the surrounding LCM, a denser medium in front could exert a real inward pressure on the wave structure.
In this simplified LCM-rest-frame sketch, the compression is described as front-loaded: the medium ahead is compressed more than the medium behind. That picture is only an intuitive starting point. By itself, a one-sided squeeze would define a preferred frame and would not yet reproduce the reciprocal symmetry of special relativity.
If the mechanism works, an object moving relative to the local LCM would be physically reconfigured along its direction of motion, while its internal rulers, atoms, and even the biochemical processes that constitute perception would reconfigure with it. From the inside, nothing appears distorted. No internal measurement reveals the contraction because the measuring instruments themselves contract by the same proportion.
In the IRCH candidate reading, length contraction would happen because fast motion through the LCM creates a directional compression gradient, and matter made of LCM standing waves adapts to the compressed medium.
The open requirement is substantial and should not be hidden: this mechanical response must reproduce the full Lorentz symmetry of observed physics, including the symmetry of inertial frames and the strong empirical limits on ether-wind and drag effects [71, 72, 73]. The derivational target is therefore sharper than "objects compress in a medium": IRCH must show why all inertial observers built from LCM standing waves recover the Lorentz transformations, why no ether-wind signal appears, and why an apparent rest-frame compression would be experienced internally as the symmetric relativistic effect. The account above is a candidate ontology for the mathematics, not a substitute for those constraints.
Any elastic-aether model interprets spacetime curvature as variations in the density or tension of the medium itself. What IRCH adds is a dynamic role for inner-rung flux in actively maintaining the outer-rung medium it sustains gravitationally. Tracing that role across rungs surfaces a structural argument with consequences for whether the system can have a beginning at all.
In the geometric view of relativity, matter and curvature stand in a tidy cause-and-effect relation: matter and energy bend spacetime, and gravity is the motion of objects through that curvature. IRCH does not have such a clean separation. Matter is a region of denser LCM, but the LCM itself is not a primitive substrate; it is \(SUB^{scaf}\), the persistent tensile organization of \(SUB\)-rest. What keeps that organization tensile, what makes LCM elastic at our scale, is gravity at \(SUB\): the \(SUB\)-scale analogue of the bidirectional cosmic-web equilibrium developed in §11.4, holding \(SUB\)-rest in tension. Gravity at \(SUB\) is in turn mediated by \(SUB2^{flux}\), which from \(DYN\)'s perspective is the role-named \(s_{flux}\). In this reading, \(s_{flux}\) helps make LCM elastic, not by confining DYN matter, but by gravitating at \(SUB\) and maintaining the tensile structure that constitutes our medium.
The argument does not stop at one rung. \(s_{flux}\) itself is a wave, and it needs its own substrate: \(SUB2^{med}\) (= \(SUB3^{scaf}\) by the recursive identity). For that medium to exist as an elastic transverse-mode-supporting substrate, \(SUB3^{rest}\) must be held tensile by gravity at \(SUB3\), which is mediated by \(SUB4^{flux}\). So \(SUB2^{med}\) is maintained by \(SUB4^{flux}\), a flux two rungs deeper than \(s_{flux}\) itself. That \(SUB4^{flux}\), in turn, propagates in \(SUB4^{med}\), which is maintained by \(SUB6^{flux}\), which propagates in \(SUB6^{med}\), and so on. The chain steps by two rungs at each level, because each medium is the scaf one rung in, and each scaf needs gravity at its own rung mediated by flux from one rung deeper still. The chain has no terminator.
The recursive dependence chain is an argument for unbounded inward depth. To construct any rung's medium from scratch, one would need its inner-rung flux already present and gravitating; that flux would need the inner-rung medium beyond it; the regress has no first step. The architecture cannot be assembled bottom-up because there is no bottom.
This is the structural reason IRCH does not naturally accommodate a finite first beginning. It is not that the system reaches some metaphysical paradox at \(t = 0\); it is that the dependence chain has no foundation to start from. The universe is not something that can be assembled from a bottom layer and then allowed to evolve. In this ontology, it exists through the rungs simultaneously. The infinite, non-origin framing follows from this dependence chain rather than being assumed alongside it.
The argument is parallel to, but distinct from, the unbounded-recursion argument in §15.3 for non-locality. Both rest on the same structural fact about ERMS: the rung hierarchy is unbounded inward. They derive different consequences. There, unboundedness lets mediation chains carry influence at arbitrarily fast \(DYN\)-scale speeds and, in the limit, become genuinely non-local at \(DYN\). Here, unboundedness blocks the construction of the architecture from any finite starting point and so blocks any meaningful notion of a beginning.
In IRCH, time is always measured with respect to a substrate. There is no rung-independent observer, and so no rung-independent "absolute" time to anchor measurements against. What the framework does have is a hierarchy of substrate-bound timescales: by rung invariance, inner-rung dynamics run faster than outer-rung dynamics, and any rung's clocks resolve only what its own substrate can support. All measurement, sensation, and physical activity in living systems occurs through LCM-standing-wave structures, so what we have access to is LCM time: the timescale set by transverse-mode propagation in our own medium. \(SUB^{flux}\) operates on a different timescale entirely, set by \(SUB^{med}\)'s propagation properties. From a DYN observer's vantage point, \(SUB\)-scale dynamics complete much faster than any LCM-based instrument can resolve, so \(SUB^{flux}\) propagation appears, to us, effectively instantaneous. That does not amount to a claim about an absolute timebase.
An empirical anchor for this picture comes from Tom Van Flandern's analysis in The Speed of Gravity: What the Experiments Say [74], which reviewed timing delays, planetary motions, and signal propagation and argued that gravity must exceed \(2 \times 10^{10}c\), at least twenty billion times the speed of light. Twenty billion is one specific magnitude compatible with the IRCH picture: \(SUB^{med}\)-scale propagation appears, from DYN, at speeds many orders of magnitude beyond \(c\), and Van Flandern's bound is one empirical interpretation of the timing data that aligns with the structural claim that inner-rung mediation runs much faster than outer-rung observers can resolve. Other interpretations of the same data exist within general relativity (retarded-potential effects can mimic instantaneous propagation), and a definitive empirical resolution would require a measurement designed specifically to discriminate between the two readings. The general structural argument is developed in the QM section: mediation routed through unboundedly inner rungs can carry influence at unbounded \(DYN\)-scale speed without violating locality at any finite rung step. The same argument suggests that very fast cross-rung transmission may be physically possible if patterns can be coupled into \(SUB^{flux}\).
But a fast carrier is not automatically a usable communication channel. The distinction matters:
Encoding information into \(SUB^{flux}\), and reading it out on the other end, requires ordinary physical processes: electronics, detectors, biological cognition. All of these are constrained by LCM time and the speed of light. More importantly, IRCH has not yet derived that \(DYN\)-scale apparatus can address, modulate, and decode \(SUB^{flux}\) with enough control to send chosen messages. The conservative claim is therefore cross-rung transmission and correlation, not a completed engineering account of superluminal communication.
This is where the causality burden sits. If \(SUB^{flux}\) can only carry coarse correlations that \(DYN\) observers cannot address directly, then no-signalling is preserved. If controllable message encoding becomes possible, the framework would need a preferred-frame or endpoint-limitation account strong enough to block the usual tachyon-style paradoxes. That account is not completed here.
A civilization that learned to encode patterns into \(SUB^{flux}\) would, in principle, have access to a carrier whose propagation delay is far smaller than electromagnetic delay over interstellar distances. Whether that becomes practical communication depends on the unresolved endpoint physics: how the signal is written, how it is read, and whether the protocol remains causally well-behaved.
This has potential implications for SETI, but they should be read cautiously. If technological civilizations developed a way to use \(SUB^{flux}\) for signalling, then electromagnetic communication could become a poor proxy for advanced communication. EM transmission is slow and limited by LCM constraints, whereas \(SUB^{flux}\) would offer a much faster carrier if it can be controlled.
IRCH therefore suggests a narrow caveat for electromagnetic SETI: if such signalling is physically and causally available, some advanced communication could move through channels our current instruments cannot yet manipulate or detect.
This is only a possibility, not an explanation of SETI's silence. It marks a potential blind spot in search strategy if cross-rung communication ever becomes technologically accessible.
The active-galactic-nuclei section identified three forms of redshift as observable consequences of one underlying principle. We restate them here in relativity vocabulary, because the gravitational case lives most naturally in the relativity discussion.
Clock rate tracks local medium state via phase-lock.
The familiar "deep potential well → slower clocks" reading of gravitational redshift is recovered in IRCH as "denser local medium → slower clocks". The three redshift cases can therefore be read under one shared principle: the medium varies over a path through statistically stationary LCM, across spatial density gradients, or under local gravitational compression, and matter's clock tracks it.
In standard cosmology, cosmological redshift, gravitational redshift, and (where it is accepted) intrinsic quasar redshift are typically developed as distinct phenomena, each with its own physical story. The IRCH picture brings all three under one principle without that being an argument against the standard treatments: each remains a valid description in its own terms, and the unification here is offered as a structural observation about what these effects share when read through a wave-mechanical ontology.
This brief section sketches how IRCH reads the quantum-mechanical regime. It is not an attempt to derive the formalism of QM; it is a structural observation about why the formalism takes the shape it does, given the IRCH ontology developed in the foundational sections. The key philosophical pivot is that reality is not grounded in one continuous substrate, but in a scale-separated hierarchy of recursively emergent, interdependent media. The same law-forms recur in each rung's native units, while their dimensional scales translate differently into DYN units.
In IRCH, every form of detectable matter is a composite standing-wave pattern in the LCM, including the apparatus doing the detecting. Measurement pushed down towards the characteristic wavelength of that medium therefore loses access to any rigid external anchor: target and probe are excitations of the same substrate, and LCM wave stability enforces bandwidth/location tradeoffs. Heisenberg uncertainty is read here as a structural property of our medium, not a universal principle of existence. The "quantum limit" is likewise a boundary of LCM-based observers, not of the universe as a whole; other rungs have their own limits, accessible only through their own rung-native physics.
That deeper-scale picture has one consequence worth isolating. If the LCM is only one layer in an unbounded mediation hierarchy, then quantum non-locality may be the DYN-facing signature of that hierarchy rather than a primitive exception to mechanical mediation.
ERMS posits an open, integer-indexed hierarchy of rungs, unbounded inward and outward (§3). By rung invariance, every rung has the same law-forms in its own native units, but inner-rung timescales translate as faster when viewed from \(DYN\). Let \(k_{0}\) be a lower bound greater than one on that apparent inward speedup at each interface.
The argument is a proof by recursion. One inward step gives an apparent \(DYN\)-speed at least \(k_{0}\,c\). If depth \(n\) gives at least \(k_{0}^{n}\,c\), then one further inward step gives at least \(k^{n+1}_{0}\,c\). Because the hierarchy is unbounded inward, \(n\) can grow without limit. Apparent \(DYN\)-scale speed therefore becomes unbounded, even though each step remains finite-speed and locally mediated in its own rung's native units.
In the infinite-depth limit, any finite \(DYN\) distance can be crossed in arbitrarily small \(DYN\) time. The finite-depth case gives apparent non-locality. The unbounded case gives literal non-locality at \(DYN\): two arbitrarily distant \(DYN\) locations can, in principle, be connected instantaneously through the infinite inward dependence of the media that constitute them.
The commitment retained is locality of mediation at every finite rung step: each finite segment of the recursive chain has contiguous physical carriers. The commitment given up is subluminality at \(DYN\): \(DYN\)-scale influence is not capped at \(c\) when it routes through inward recursion. These are logically independent properties, though they are often discussed together. A superluminal-looking influence is usually read as a violation of locality on the assumption that the mediation lives at one ontological level. IRCH treats the two separately, retaining local mediation across the recursive hierarchy while allowing literal non-locality to appear at \(DYN\) in the unbounded inward limit.
This is structurally different from the Copenhagen no-signalling framing. In standard operational quantum mechanics, Bell-violating correlations are encoded in the global quantum state and constrained by the formalism's no-signalling structure. The formalism does not require, and usually does not specify, a mechanical carrier inside spacetime that coordinates the outcomes. IRCH reads the same class of correlations differently: not as evidence against mediation, but as a possible DYN-facing signature of an inward mediation hierarchy. Finite-depth correlations can have inner-rung mediators that appear faster than light at \(DYN\) but are finite at their native scales. In the unbounded-depth limit, the mediation chain itself has no finite innermost carrier, and DYN sees the limiting behaviour as genuine non-locality.
This resembles, but is not identical to, the pilot-wave / de Broglie-Bohm framing. Pilot-wave theories posit a non-local hidden field at a single ontological level; IRCH instead posits a recursive hierarchy whose finite steps are local, but whose unbounded inward dependence can produce literal non-locality at the observed rung. Whether the two frameworks are equivalent in observational predictions is an open question.
The argument is structurally compatible with Van Flandern's empirical interpretation of gravitational propagation (developed in the relativity section). Van Flandern argued that gravitational influence must propagate at least twenty billion times the speed of light. In IRCH, \(g_{flux}\) lives at \(SUB^{med}\), one rung inward, and its native propagation speed appears from \(DYN\) as some large factor times \(c\). Twenty billion is one possible magnitude for that factor; the framework predicts the structural fact (inner-rung mediation is much faster at \(DYN\)) without committing to a specific value.
Cross-rung non-locality does not by itself permit faster-than-light signalling at \(DYN\) in the no-signalling sense. The argument from the relativity section's discussion of \(SUB^{flux}\) transmission generalizes: encoding and decoding signals into an inner-rung carrier requires \(DYN\)-scale apparatus, and that apparatus is bound by \(DYN\) time. What inner-rung mediation clearly can carry, in this sketch, is correlations: paired observable events that match faster than \(c\) would allow if the mediation were intra-DYN. Whether it can carry addressable messages is a stronger claim, and one the present paper treats as open.
This is why IRCH can allow cross-rung non-locality at \(DYN\) without directly colliding with relativity's empirical successes there. Special relativity describes how matter and light behave in \(DYN\), where they are bound by \(c\). Cross-rung mediation does not make ordinary DYN matter or DYN light outrun that constraint; it operates through \(SUB^{med}\) or deeper, on timescales \(DYN\)-bound experiments cannot directly clock.
The point of the section is structural: IRCH retains its abstract's commitment that any force appearing to act at a distance must be mediated through such a medium, and the commitment is non-trivial because the mediation hierarchy is unbounded. Finite-depth apparent non-locality and limiting \(DYN\)-level non-locality are consequences of the same recursive hierarchy. Neither requires a violation of locality at any finite rung step.
Although IRCH is not defined mathematically, it does make several qualitative predictions that differ from standard interpretations and could, in principle, be tested. These predictions arise directly from the framework's internal mechanisms: PDOC, wave confinement, medium interactions, particle structure, path-integrated phase-lock through statistically stationary LCM, LCM-reservoir re-emission, and the cross-rung equilibrium cycles.
The development of this sketch was highly iterative and heavily assisted by modern AI tools. The role of AI requires careful qualification. The central commitments of the paper did not originate as AI suggestions, but AI systems were used throughout as test beds and adversarial research assistants. Claims and constraints were posed to multiple systems, which stress-tested them against patterns from the literature they had been trained on. The results were then filtered against the framework's own standards. AI also drafted prose under direction, with the final wording edited to reflect the intended argument rather than the tools' tendencies. Most AI suggestions were rejected; what remained passed repeated rounds of conceptual filtering.
Before clarifying which commitments are original to this sketch, it is important to acknowledge the deeper lineage that makes AI useful at all: the thousands of scientists, educators, writers, engineers, and students whose work forms the substrate upon which such tools are built. There is no practical way to identify every individual influence, but their collective contribution underlies every AI-assisted iteration.
For attribution rather than priority, the following load-bearing commitments should be read as the author's responsibility. They were not taken from AI suggestions, though many crystallized through AI-assisted pushback on earlier views:
A clear example of where AI did contribute is the three-mode standing-wave account of the electron and positron, which first appeared in the Two-Medium Model [7]. The idea of combining three oscillatory modes with phase-locked offsets surfaced in dialogue with an AI system and would likely not have been found unaided. Those modes were compression, shear, and torsion. The structural constraints that shaped it were mirror symmetry, three-dimensional non-flippability, pair-production balance, and geometric stability. The AI generated raw candidate ideas; the conceptual standards determined whether they were tenable. The final standing-wave geometry emerged through that interaction.
PDOC is a second example. The goal was to retain a flux-mediated story for gravity while avoiding the overheating problem that sinks Le Sage-style absorption accounts. The reinterpretation of the flux interaction as predominantly dispersive surfaced in dialogue with an AI system: refractive phase-delay rather than absorption. The cross-rung structure that ended up wrapping those wave-mechanical bones came from the recursive scaffolding identity and matter-resonant-subset coupling developed in this paper.
If you believe that any ideas in this document overlap with work you have published, and you would like your contributions acknowledged or referenced, please feel free to open an issue or submit a pull request at the project repository [75]. I will review it and update the references accordingly.
I present this work not as a finished theory, but as an invitation: to reconsider whether some aspects of physical law might gain clarity from a different underlying ontology, and to explore whether the ideas outlined here might be refined, challenged, or developed further by those with greater expertise and technical resources.
This glossary collects recurring technical terms used in the paper. It is not a separate argument; it is a reader aid for terms whose meanings can otherwise drift between ordinary physics usage and IRCH-specific usage.
This appendix expands on two related points that come up across the main text. First: why an inward flux can register compression at DYN at all, given that each flux propagates in its own medium. Second: why \(s_{flux}\) specifically couples appreciably only to extreme LCM compression, not ordinary compression. Along the way the appendix makes explicit the two DYN landings of PDOC at our rung: \(g_{flux}\) acting on \(DYN^{rest}\) (observed as gravity) and \(s_{flux}\) acting on \(SUB^{rest}\) (observed as confinement and the strong nuclear force). It also reconciles the shadowing/pressure language used in parts of the main text with the underlying phase-delay mechanism.
Compression is the channel, but ordinary LCM compression is not enough to give \(s_{flux}\) a strong handle. Because \(s_{flux}\) is two rungs inward, the overlap between what counts as long-wavelength structure for \(SUB2^{flux}\) and what counts as short-wavelength structure in DYN is narrow. Only very short-wavelength, densely packed DYN compression gives \(s_{flux}\) a strong handle.
Each flux propagates in its own medium: \(g_{flux}\) in \(SUB^{med}\), \(s_{flux}\) in \(SUB2^{med}\). A flux phase-delays only where its own medium is compressed or impedance-shifted; what produces a force on rest is anisotropic phase delay (uniform delay just changes timing). DYN compression registers at all because the media are recursively identified: \(DYN^{med} \equiv SUB^{scaf}\), so compressing LCM is compressing \(SUB^{scaf}\). That is the persistent organization of aggregated SUB rest. Its compression perturbs \(SUB^{med}\), which then perturbs \(SUB2^{med}\). Compression cascades inward. Each flux feels the cascade where it lives: \(g_{flux}\) after one inward step, \(s_{flux}\) after two. This is why \(g_{flux}\) couples across a broader DYN aggregation window (gravity is long-range) while \(s_{flux}\) couples only to extreme compression (confinement and strong force are short-range).
What we observe at DYN depends on which rung's rest the flux acts on:
Both are gravity at their respective rungs (in the loose sense established at the end of §5). Same phase-delay mechanism, different DYN observables. Where the main text describes \(s_{flux}\)-mediated effects in shadowing or inward-pressure language, that language is DYN-shorthand for \(s_{flux}\)'s gravity acting on \(SUB^{rest}\) aggregations. Examples include \(s_{flux}\) shadow at the core, \(s_{flux}\) opacity, and inward \(s_{flux}\) momentum flux. The mechanism is the same as gravity at DYN; only the DYN-level observable differs.
The LCM-reservoir picture developed later does not replace this conclusion. It adds a bookkeeping channel after energy has entered \(SUB^{scaf}\): scaffold-scale strain, readjustment, and kinetic motion can mix before re-emerging inward as \(SUB^{flux}\) or outward as \(DYN^{flux}\). This appendix is narrower. It explains why inward flux can couple to DYN-visible compression in the first place, and why \(s_{flux}\) couples strongly only where LCM compression reaches the extreme, short-wavelength structures relevant to confinement and the strong force.
The paper rests on phase-delay oscillator coupling (PDOC), developed in §4 from five assumptions about wave-supporting media, recursive medium emergence, and rest as phase-locked standing waves. Other sections in turn use PDOC to motivate each of those assumptions in concrete settings. The most explicit case is §6, where PDOC's confinement mechanism motivates assumption 5 (rest is a phase-locked standing wave) at our rung. The reasoning is circular in the strict logical sense: PDOC rests on the assumptions, and the assumptions are motivated by what PDOC implies.
The circularity is not a defect of this particular implementation; it is a structural consequence of the framework's commitment to an unbounded inward hierarchy of media, each emerging from the rung one step inward. Under that commitment, developed structurally in §14.3, no rung can be described in terms of foundational primitives outside the framework. Every primitive at one rung is a consequence of dynamics at deeper rungs; those dynamics rest on still-deeper primitives, without a base case. A linearly derivable description would require a privileged starting point, and any such point would itself need explanation, pushing the regress one level deeper. If nature truly is recursively constituted in this way, any description of it will necessarily involve cycles of dependency.
What self-consistency requires of such a description, then, is two things:
The paper's qualitative form makes these conditions assessable case by case rather than algebraically, but the standard of evaluation is the same. The same unbounded-recursion structure underlies the no-beginning argument in §14.3 and the apparent-non-locality argument in §15.3. This appendix names what those derivations rest on architecturally: an infinite-recursion ontology cannot be founded, only closed.
Each of the five PDOC assumptions can be checked against where the rest of the paper supports it through PDOC's own implications:
The loop closes for assumptions 1, 2, and 5: three of the five. It does so through §6 and §7. Assumptions 3 and 4 sit outside the loop: they are inherited from the framework's foundations (ERMS) and from prior physics (classical wave mechanics) respectively, rather than re-motivated by what PDOC implies. That outside-the-loop status is structural rather than a deficit; the question for the framework is whether the inherited commitments do useful work without being abused, not whether they can be derived from inside the loop.
The closures above vary in strength. §6's motivation for assumptions 1 (dual-mode) and 5 is concrete and developed in detail. §7's motivation for assumption 2 follows directly from the standing-wave structure.
Outside the loop, the applications of assumption 3 are where the paper is most asserted rather than derived. §14.3's claim that LCM's elasticity follows from \(s_{flux}\) gravitating at \(SUB\) rests on the cosmic-web tensile equilibrium working at \(SUB\) by rung invariance. The model of how this works is currently structural rather than quantitative. §11.6's identification of the cosmic web with \(SUP^{med}\) rests on the cosmic web behaving like an elastic medium without yet deriving that behaviour from a detailed model. §12.1's LCM phase-boundary picture names the threshold at which extreme compression collapses the SUB-scale tensile balance, but does not derive it. §13's LCM-reservoir picture likewise assumes that \(SUB^{scaf}\) can store, mix, and re-emit scaffold-scale energy into adjacent flux bands; the response function and thermalisation process are not yet derived.
The most natural way to tighten the medium-side claims is a continuum-mechanics model of the cosmic web as a tensile structure under bidirectional gravity, predicting how the medium stores strain, responds to compression, changes character at phase boundaries, and relaxes stored energy back into flux. By rung invariance, that same model would predict LCM's elastic properties at \(SUB\), the threshold at which extreme compression collapses the SUB-scale tensile balance, and the reservoir response used in the redshift/CMB section. Such a model would let the structural arguments above be checked quantitatively rather than asserted, and would tighten the empirical contact between IRCH's medium ontology and observable cosmic-web data.