The Working Range of Push-Pressure Gravity: A Cross-Scale Performance Audit Against Newtonian Gravity and General Relativity

July 2026

Authors

Matthew Foutch, with Claude (Anthropic) and Grok (xAI) as AI collaborators

Abstract

Across every length scale where Pressure-Based Theory’s (PBT’s) shadowing mechanism has actually been tested against real data, does it reduce to Newtonian gravity, improve on it, or regress from it? We define a performance ratio, $\Lambda(l)$, comparing PBT’s prediction error against the relevant prior theory’s error at the same scale, and evaluate it in four regimes: the classical two-body limit, real galactic rotation curves (171 SPARC galaxies, 3375 points), black hole collapse, and atomic/nuclear confinement. Result, stated in concrete object/separation sizes rather than physics jargon alone: the mechanism’s geometric reduction was numerically checked at galactic-model radii ($10^{19}$–$10^{21}$ m) and matches Newton there to 0.01%; by the same scale-invariant argument (not by a separate numerical check at these specific radii) it is expected to hold down through roughly $10^{-2}$ to $10^{12}$ meters (lab masses through solar-system separations). It fails at every scale actually tested outside the galactic-radii check: by 7 to 38-plus orders of magnitude below $10^{-10}$ m (atomic and nuclear), and by anywhere from a 32x overshoot to 123 orders of magnitude at galactic and collapse scale. PBT is mathematically identical to Newton in the classical regime ($\Lambda=1$, by construction). At galactic scale, PBT’s literally-published parameters (“PBT-literal”) overshoot so badly that plain Newtonian gravity is closer to the data; a physically-motivated reformulation (“PBT-best”) closes most of that gap but still misses real rotation curves by roughly nine times their own measurement precision, and by 16–80 times the precision of the working alternatives (MOND, dark-matter halos) it was meant to replace. At collapse scale, PBT’s attempt to remove General Relativity’s central singularity instead predicts a stabilization radius 66–123 orders of magnitude larger than its own Planck-scale target — larger than the observable universe. At atomic and nuclear scale, gravity was never the operative force in reality; PBT’s own attempt to unify its gravity formula with those regimes misses measured confinement pressures by 7–38-plus orders of magnitude. By any reasonable standard, this is a failed theory outside the classical limit, and the classical pass itself rests on an extrapolation, not a direct check at those specific scales (see Size-Range Summary). Two narrower things remain worth recording alongside that: among literal particle-collision (kinetic, corpuscular) mechanical models specifically — a narrower category than “gravity theories” generally, and one that excludes geometric (GR) and thermodynamic/entropic (emergent-gravity) accounts, which are real but a different genre of explanation — PBT’s shadowing account is a working example of the type; and it makes a genuine, specific, quantified attempt at the drag/heating problem that killed Le Sage’s own 1748 version, rather than reviving his mechanism unmodified. Neither point offsets the failure record above; both are historical/structural observations, not empirical successes.

Keywords: push gravity, shadowing mechanism, Newtonian reduction, SPARC rotation curves, black hole collapse, cross-scale validity, performance audit

Introduction

Paper 1 proposes gravity as ambient particle-flux shadowing, with a scale-dependent effective coupling $G_{eff}(l)$ meant to reduce to Newtonian gravity at everyday scales while doing additional work elsewhere: explaining flat galactic rotation curves without dark matter, and stabilizing gravitational collapse without a singularity. General Relativity is not in question here — it is confirmed to extraordinary precision in both the weak-field regime and, via gravitational-wave and Event Horizon Telescope observations, the strong-field regime. Its acknowledged incompleteness concerns unification with quantum mechanics and the two specific anomalies above, not a general deficiency.

This paper introduces no new calculations — it is a compilation audit. It draws together results already produced and, in most cases, already noted in prior papers in this series, into one explicit comparison against the baselines PBT was built to match or improve on: at each scale actually tested, is PBT indistinguishable from the prior theory, an improvement, or a regression — and by how much, in checkable units?

Papers 1–13 were developed primarily by Grok (xAI), later independently audited by Claude (Anthropic); Paper 13 is held back, unpublished, marking that boundary. This paper does not ask to be trusted on that provenance: every load-bearing number above was independently recomputed rather than quoted from a prior paper, and the reader can rerun the same checks (SPARC, the collapse ODE, the cross-scale energy-density formula) against the same public data. The audit is the answer to the provenance question, not a claim of improved trustworthiness by itself.

Theory Description

PBT’s baseline mechanism reduces exactly to Newtonian $1/r^2$ gravity for two bodies with no scale-dependence — a geometric consequence of a fixed-size body subtending a shrinking solid angle at increasing distance. Its published departure from Newton is the hierarchical scaling relation:

$$\varepsilon(l) = \varepsilon_0 \left(\frac{l_0}{l}\right)^\gamma, \qquad G_{eff}(l) = \frac{\varepsilon(l)\,\sigma(l)^2}{4\pi\, m(l)^2}$$

with $\varepsilon_0\approx7.4\times10^{35}$ J/m³, $l_0\approx10^{-25}$ m, $\gamma\in[2,4]$, $\sigma(l)\approx l^2$, $m(l)\approx\hbar/(lc)$. Every result below tests this one formula (or the rotation-curve-specific $G_{eff}(r)=G[1+k(r/r_0)^\gamma]$ built from it) at a scale it was, or wasn’t, calibrated for. Note the rotation-curve formula’s own published $\gamma=1$ sits outside the hierarchical formula’s stated $\gamma\in[2,4]$ range — the two are only loosely coupled in the paper series itself, not a single consistent parameter set; this paper treats the rotation-curve claim as its own object rather than assuming it’s derived from $\varepsilon(l)$’s $\gamma$. Two versions of the galactic claim are distinguished throughout: PBT-literal (the published $k\approx1900$, $\gamma=1$, unrefit) and PBT-best (a refit against real data: $k=0.99$, $\gamma=0.537$, $a_\dagger=6.68\times10^{-11}$ m/s² in a power-law boost to local baryonic acceleration — see Mathematical Formalism).

We define, at a scale $l$ with a real measured value $M(l)$:

$$\Lambda(l) = \frac{|P_{PBT}(l) - M(l)|}{|P_{baseline}(l) - M(l)|}$$

$\Lambda=1$: mimics the baseline. $\Lambda<1$: closer to reality than the baseline — an improvement. $\Lambda>1$: further from reality than simply keeping the baseline — a regression. The baseline itself changes by regime:

The caveat: plain Newtonian gravity cannot flatten a rotation curve at all without added mass, so $\Lambda>1$ at galactic scale does not mean “worse than a working theory” — Newton isn’t one there, without a dark-matter term. It means PBT-best is worse than doing nothing, a real but narrower finding; the fairer comparison to a working theory is $\chi^2/\text{dof}$ against MOND/NFW, reported in Results. At atomic and nuclear scale, gravity is not the operative real-world force at all, so $\Lambda$ against a gravitational baseline isn’t meaningful; that regime is scored directly against measured confinement pressures instead.

Mathematical Formalism

Galactic regime. Real data: SPARC (Lelli, McGaugh, Schombert 2016), 171 disk galaxies, 3375 rotation-curve points with real measurement uncertainties and independently-known baryonic decomposition, using the standard SPARC-literature mass-to-light ratios ($\Upsilon_{disk}=0.5$, $\Upsilon_{bulge}=0.7$) rather than values chosen to favor any fit. Fit quality reported as $\chi^2/\text{dof}$ against each point’s own measurement error, where $\chi^2/\text{dof}\approx1$ means a model matches the data to its own precision — a theory-neutral statistical standard. Four $G_{eff}$ forms were fit:

PBT-literal, unrefit, is unusable against this data ($\chi^2/\text{dof}$ in the millions) — see Results for the single-galaxy illustration. A full self-consistent numerical field-equation solve (beyond the algebraic PBT-best approximation) was separately built and validated for an idealized exponential disk, showing the algebraic form is itself 8–17% off from the true self-consistent solution — real, but far short of closing the ~9× gap.

Collapse regime. The collapse condition (see Formula Catalog: Black Hole Collapse ODE):

$$\frac{dv}{dt} = -\frac{GM}{r^2} + \frac{\varepsilon(l)}{3}\cdot\frac{4\pi r^2}{M}$$

Setting $dv/dt=0$ and $l=r$ and solving for equilibrium: $r_{eq}^{4-\gamma} = \dfrac{3GM^2}{4\pi\varepsilon_0 l_0^\gamma}$. For a solar mass ($M=1.989\times10^{30}$ kg), PBT’s own $\varepsilon_0$, $l_0$ give $\gamma=2\Rightarrow r_{eq}\approx9.2\times10^{31}$ m; $\gamma=3\Rightarrow r_{eq}\approx8.5\times10^{88}$ m — against a claimed target of $\sim10^{-35}$ m (the Planck length) and an observable-universe radius of roughly $8.8\times10^{26}$ m.

Atomic/nuclear regime. The same $\varepsilon(l)$, evaluated unmodified at the Bohr radius and one femtometer, against the real atomic unit of pressure ($2.94\times10^{13}$ J/m³) and the MIT bag-model confinement pressure ($\approx1.2\times10^{34}$ J/m³).

Results

Classical regime. $\Lambda=1$, but this needs a precise, narrow statement of what was actually checked, not a broader one. The 0.01% match confirms the geometric shadowing argument — solid-angle falloff against a constant ambient flux — reduces to Newton’s force law in an idealized construct where particle speed is taken to infinity and bounces are taken as perfectly elastic. It does not independently verify that drag and heating actually vanish in that limit; that is a separate physical question, and this paper’s own Discussion below concedes it is not yet resolved (a real, quantified tension between the two, per this project’s own research). So: this is a real, necessary pass of the geometric reduction — a Le Sage-style mechanism that couldn’t even reproduce Newton geometrically would be dead immediately — but it is not, on its own, a demonstration that the historical drag/heating objections have been cleared. Those remain open, addressed on their own terms later in this paper, not resolved by this result.

Galactic regime. Single-point illustration (Milky Way, $r=10$ kpc, $M_{enc}\approx6\times10^{10}M_\odot$): plain Newton gives $v\approx161$ km/s; the real observed flat value is $\approx220$ km/s; PBT-literal gives $v\approx7005$ km/s — roughly 32 times too high, and further from reality than doing nothing. PBT-best is not a test of the published theory — it is a different functional form (acceleration-based rather than radius-based) freely refit to the same data, motivated by PBT’s own shadowing logic but not asserted anywhere in the papers as published. It represents the most charitable version of PBT’s rotation-curve idea this project could construct, not a validation of anything already in print. Against the full SPARC sample, that most-charitable version reaches $\chi^2/\text{dof}\approx82.5$ — a real, substantial improvement over PBT-literal, undershooting the data’s own precision by a bounded ~9×, not diverging in the wrong direction the way the single-point case does. For context, MOND and NFW dark-matter-halo fits on this same data reach $\chi^2/\text{dof}$ of order 1–5 — even this freely-refit best case remains roughly 16–80 times short of the working alternatives it was meant to replace. That the most charitable available version still misses this badly is a stronger result against the mechanism than a single bad parameter choice would be.

Collapse regime. No reformulation on record rescues this claim. $r_{eq}$ exceeds the Planck-scale target by 66–123 orders of magnitude and exceeds the observable universe itself. The theoretical point is sharper than the size of the number alone: a “stabilization” radius larger than the observable universe does not describe a stabilized collapsed object at any astrophysical scale — a solar-mass body that never collapses meaningfully at all is not an alternative to a black hole, it is a failure to produce one. This is not comparable to GR’s own open singularity problem: GR predicts and matches real, observed compact objects (LIGO/Virgo merger waveforms, EHT horizon-scale imaging) everywhere it has been tested in the strong-field regime, and its incompleteness is specifically about what happens at the singularity itself, not about whether compact objects form at all. PBT’s own equilibrium condition says they don’t.

Atomic/nuclear regime. Two separate points, not one:

1. Gravity is not the operative force here in reality — the ratio of gravitational to electromagnetic force between two protons is roughly $10^{36}$, and to the strong force, more still. Not a Newton comparison.
2. PBT’s own claim that one formula unifies gravity with confinement at these scales fails on its own terms: 7 to 36.5 orders of magnitude too small at atomic scale, 18 to 38.2 orders too small at nuclear scale. A direct attempt to fit this same formula to nuclear binding energy specifically misses by 18 to 30-plus orders of magnitude for every allowed $\gamma$. A separate, unpublished draft in this series does model nuclear binding energy successfully from a pressure-equilibrium premise (within ~8% of the standard formula’s coefficients) — noted here only for internal consistency, not relied on as a published result, since it succeeds by importing the standard Coulomb term rather than deriving it from $\varepsilon(l)$, which is exactly the term that fails here.

Size-Range Summary: Where This Actually Holds, in Meters

The regimes above are named by physics context (classical, galactic, collapse, atomic/nuclear); stated instead as object/separation size, in meters, so the working range is unambiguous:

One honest scope note on the everyday row, worth stating precisely rather than rounding over: the 0.01%-match figure in Results was produced by numerically computing the shadow-deficit integral and comparing it to exact Newton across galactic-model radii, $R=2$–$40$ kpc ($\approx6\times10^{19}$–$1.2\times10^{21}$ m), in the small-perturbation limit — not by running the identical numerical check at literal laboratory-to-solar-system separations. The underlying geometric argument (a fixed-size body subtending a shrinking solid angle against a constant ambient flux) references only relative geometry, not absolute distance, so the reduction is expected to hold at any separation where the explicit scale-dependent term remains negligible — which by the theory’s own stated intent includes the everyday range in the table above. That expectation has not been separately, numerically re-verified at those specific (much smaller) radii in this project’s own work; it follows from the same math already validated at galactic radii, not from a second independent computation.

Discussion

PBT mimics Newton exactly in the one regime it was never meant to improve on, and fails — in three structurally different ways — in every regime it was built to improve on. The galactic failure is bounded: PBT-best is measurably better than PBT-literal, sits within an order of magnitude of the data’s own precision, and has a named, partially-quantified path to closing more of the gap (the field-equation solver’s 8–17% correction, real but insufficient alone). The collapse failure has no comparable partial credit: every version tested is wrong by tens to over a hundred orders of magnitude, with no reformulation on record bringing it closer. The atomic/nuclear result is a third category again — not a failure to beat Newton, since Newton was never a contender there, but a failure of PBT’s own unifying claim, one that even the series’ own strongest (unpublished) attempt at nuclear binding energy only sidesteps by importing the standard Coulomb term rather than deriving it from $\varepsilon(l)$.

PBT’s cross-scale performance does not degrade smoothly with distance from its calibration point. It is exact in the classical middle, then diverges by very different amounts and in different ways in each direction — worth treating as four separable claims with four separable evidentiary records, not one uniform “PBT explains gravity across scales.”

Two Narrower Observations, Historical Rather Than Empirical

The audit above is mostly a record of failure. Two things it does not capture — neither an empirical success, both scoped narrowly on purpose:

A working example of literal mechanical (kinetic, particle-collision) causation for the inverse-square law — a narrower category than “gravity theories” generally. Newton’s law works to extraordinary precision, but Newton himself declined to propose why — “hypotheses non fingo.” GR explains it geometrically (mass curves spacetime); genuinely real, extremely well-confirmed, and not a kinetic mechanism in the collision sense. Emergent/entropic gravity programs (e.g., Verlinde) and analog-gravity condensed-matter models offer other, thermodynamic or hydrodynamic accounts — real research programs, a different genre again, not endorsed or disputed here. Among specifically kinetic, particle-collision models — Le Sage’s own category — PBT’s shadowing account is a working instance: an isotropic ambient flux, partially blocked by intervening mass, produces a geometrically-derived directional deficit that reduces to Newton’s law to within 0.01% (see Size-Range Summary for the scope of that check). This is not a claim that PBT is the only mechanism-offering theory in physics; it’s a claim about which specific, narrower genre of mechanism it belongs to and that this paper’s own audit confirms it works within that genre at classical scale.

A specific, quantified attempt at Le Sage’s own downfall — an attempt, not a resolution, and not a claim of priority. Le Sage’s push-gravity (1748) was abandoned for two specific, quantified reasons: drag (undetected in real orbits) and heating (undetected in the Sun’s real output). PBT’s stated answer — near-infinite particle speed, near-zero mass — proposes a specific, quantified mechanism for both rather than leaving Le Sage’s picture unmodified. Whether anyone else has proposed this same specific resolution elsewhere in the modern push-gravity literature is not established here and is not claimed.

The honest limit, stated as plainly as the numbers above: this attempt does not currently succeed, and by Le Sage’s own historical standard, that means the mechanism is not currently revived. This project’s own research found a real, quantified tension between the drag and heating fixes: for fixed total momentum flux, $E=pv/2$, so the same speed increase that suppresses drag actively worsens heating. The one mathematical escape found, tachyonic kinematics, conflicts with tested Lorentz invariance; a second avenue, resonant coupling, lacks a mechanism for net directional force. A push-gravity mechanism that hasn’t solved drag and heating is subject to the same historical objections that killed Le Sage’s original version, not a live alternative to them — the distinction from a plain restatement is that this project has a specific, checkable candidate on record and a specific, checkable reason it doesn’t yet work, not that the underlying problem is resolved.

Context: No Current Theory Unifies These Same Extremes Either

This doesn’t excuse the specific, quantified failures above, and it doesn’t put PBT on equal footing with the alternatives — those are two different claims, and only the first is being made here. It also shouldn’t be read as treating dark matter or MOND as settled, gold-standard science; both are real, actively contested research programs with their own documented, unresolved failures, not just “no particle found yet.”

Dark matter’s density profile is calibrated to rotation curves, with no particle directly detected despite decades of dedicated search (XENON, LUX-ZEPLIN, and others, all null so far) — and it carries its own specific, unresolved tensions at galactic scale: the core-cusp problem (cold-dark-matter simulations predict steep central density cusps in dwarf galaxies; many observations show flatter cores instead), the missing-satellites problem, and the too-big-to-fail problem (simulated subhalos too dense to match observed satellite properties) — real, actively debated issues in the literature, not resolved by appeal to baryonic feedback alone. What it does have, independent of any of this, is multi-probe evidence with nothing to do with rotation curves: the CMB power spectrum’s acoustic peak ratios, gravitational lensing that spatially separates from visible gas in merging clusters (the Bullet Cluster and similar systems), and large-scale structure formation.

MOND’s $a_0$ is fit to the data it explains, with no settled physical origin, and it fails more seriously at cluster scale than dark matter does — cluster masses (including the Bullet Cluster) are underpredicted by roughly a factor of two even under MOND’s modified dynamics, and no relativistic extension of MOND (TeVeS and its successors) matches the CMB power spectrum as well as $\Lambda$CDM does. What it does have is a real, tight, independently-confirmed empirical regularity at galactic scale specifically — the radial acceleration relation — the same regime this paper’s own $\chi^2/\text{dof}$ comparison uses.

GR predicts a genuine singularity at a black hole’s center, unresolved without a quantum gravity theory that doesn’t exist yet — but GR itself passes every strong-field test performed on it, including the LIGO and EHT observations cited above; its incompleteness is a boundary of an otherwise-confirmed theory, not a description of what it gets wrong elsewhere.

None of this makes dark matter or MOND finished theories — both have real, serious, unresolved problems, at different scales than PBT’s. What it does mean: at the one specific scale and specific metric this paper actually measures — real galaxy rotation curves, scored against their own measurement precision — dark matter and MOND fit the data (χ²/dof ≈1–5) in a way PBT, even in its best tested form, does not (≈82.5). That comparison is narrow and scale-specific, not a claim that either mainstream alternative has solved gravity.

Testable Predictions

1. Galactic — a defined, falsifiable next step exists. Apply the validated field-equation solver to real, non-idealized per-galaxy SPARC mass profiles rather than the idealized disk. Substantial further improvement in $\chi^2/\text{dof}$ would be real progress toward closing the ~9× gap; no improvement would close off the acceleration-based line as PBT’s best rotation-curve candidate.
2. Collapse — no path forward with the current formula. A falsifiable next step: derive a genuinely different $\varepsilon(l)$ from first principles (not re-fit to the desired answer) and test it against this same equilibrium condition before any future claim of Planck-scale stabilization.
3. Atomic/nuclear unification remains falsifiable: deriving the Coulomb-equivalent term from $\varepsilon(l)$ rather than importing it would be immediately checkable against the same 44-point binding-energy dataset the series’ own unpublished nuclear-binding draft already assembled.
4. Drag/heating — the Le Sage revival’s own open question. A falsifiable next step distinct from the three above: find a mechanism suppressing both drag and heating simultaneously without positing tachyonic kinematics (conflicts with tested Lorentz invariance) and without relying on resonance alone (lacks a directional-force mechanism). A candidate respecting both constraints would be real, checkable progress on the oldest open question in this research program; a genuine attempt that still fails would be as informative as this paper’s other negative results.

Objections and Responses

Before publication, this paper was put through an adversarial review specifically instructed to find every objection a hostile physicist, peer reviewer, or critic could raise — not editorial feedback, a search for reasons to reject the paper’s claims. Eight of the objections that survived that review are answered directly below, stated as the critic would state them. Where the honest answer is a concession rather than a rebuttal, it’s given as one.

Objection: the theory’s parameters are internally inconsistent — the hierarchical formula’s $\gamma\in[2,4]$, the rotation-curve formula’s $\gamma=1$, and PBT-best’s fitted $\gamma=0.537$ are three different values, meaning there is no single theory being audited, only a family of unrelated ansätze sharing a name. Conceded, not answered. This is a real structural problem with PBT as published, already flagged once above (Theory Description) rather than smoothed over. This paper audits each formula on its own stated terms precisely because they aren’t derived from one shared parameter set — that’s a finding of this audit, not an oversight in it.

Objection: $G_{eff}(l)=\varepsilon(l)\sigma(l)^2/(4\pi m(l)^2)$ with $m(l)\approx\hbar/(lc)$, $\sigma(l)\approx l^2$, $l_0\approx10^{-25}$ m is an under-motivated stack of assumptions, not a derived effective theory — why these functional forms, why that specific $l_0$? Conceded. No first-principles derivation for these specific choices exists in the published papers, and this project’s own [[SolveTheUniverse - Strong Force Derivation Checklist]] independently found that $G_{strong}\approx10^{29}$, the nuclear-scale value built on this same formula, was very likely reverse-engineered from the desired answer rather than computed. The Formula Catalog already marks this formula “Unproven” for exactly this reason. This paper’s audit doesn’t rest on the formula being well-motivated; it rests on testing what the formula, taken as given, actually predicts.

Objection: “PBT-best” abandons the published parameters, changes the functional form, and freely refits to data — calling the result “PBT” and reporting its improvement over “PBT-literal” as progress is branding, not physics. Partially conceded, partially clarified. PBT-best is not a test of anything already published, and the paper says so directly (Results, Galactic regime). It exists to ask a narrower, fair question: can any version motivated by PBT’s own stated logic (shadowing should depend on local field strength, not raw distance) reach real data, even after being handed maximum benefit of the doubt via free refitting? The answer is no — 16–80× short of working alternatives even in its most charitable form — which is a stronger result against the mechanism, not a save for it. The label “PBT-best” names that this is the most favorable case tested, not a claim that it’s derived from the published theory.

Objection: the collapse failure isn’t an open problem shared with GR — it’s a direct contradiction of real observations (LIGO mergers, EHT imaging) that GR itself correctly matches. Correct, and now stated directly in Results rather than left implicit: this is not comparable to GR’s own singularity problem. GR predicts and matches real strong-field observations; PBT’s own equilibrium condition predicts solar-mass bodies don’t collapse into anything resembling what’s actually observed.

Objection: comparing PBT’s failure to dark matter’s and MOND’s own open questions is a tu quoque that falsely implies equal footing — DM has independent multi-probe support beyond rotation curves, and MOND has a real, tight empirical regularity behind it; PBT has neither. Correct, and the Context section above has been revised to state this asymmetry directly rather than let the comparison imply parity. The point being made is narrower than “everyone’s equally unfinished” — it’s that an open mechanism is a different, smaller problem than a mechanism that misses its own targets by tens of orders of magnitude, and PBT has the second problem, not just the first.

Objection: citing an unpublished nuclear-binding draft that succeeds only by importing the Coulomb term — the exact ingredient $\varepsilon(l)$ fails to produce — is circular; it shows the series works when it stops using PBT’s own distinctive formula. Correct as stated, and already the point being made, not a rebuttal to it: that draft is cited only to show the atomic/nuclear failure isn’t for lack of trying elsewhere in the series, and its reliance on an imported term is presented as cutting against unification, not for it.

Objection: claiming PBT offers “the only” mechanical account of gravity ignores real research programs — emergent/entropic gravity, analog-gravity models — that also propose mechanisms. Correct, and the claim has been narrowed accordingly (Distinctive Contribution, above): the comparison is specifically to literal kinetic, particle-collision mechanisms, a category that excludes GR’s geometric account and emergent gravity’s thermodynamic one. Those are real, different genres of explanation, not disputed here.

Objection: the “genuine attempt” at Le Sage’s drag/heating problem still fails by this project’s own check, so by Le Sage’s own historical standard the mechanism remains dead — “attempt, not resolution” undersells how little has actually changed since 1748. Conceded directly, and stated in those terms in the text above: a push-gravity mechanism that hasn’t solved drag and heating is subject to the same objections that killed Le Sage’s version, not a live alternative to them. What distinguishes this project’s specific attempt from silence is a checkable candidate and a checkable reason it fails — not that the underlying 1748 problem has been solved.

Objection: the classical-regime result can’t simultaneously be “a pass of the test that sank Le Sage” and coexist with an admission, elsewhere in this same paper, that the drag/heating problem is unresolved — that’s a direct internal contradiction, not two separate findings. This was a real contradiction in an earlier draft of this paper, caught in this same adversarial review, and fixed rather than left standing. The classical-regime result has been narrowed to state precisely what it checks: the geometric shadowing argument (solid-angle falloff against constant flux) reduces to Newton in an idealized construct where infinite speed and perfectly elastic bounces are assumed, not independently demonstrated to make drag and heating actually vanish. That geometric pass is real and necessary — a mechanism failing to reproduce Newton geometrically would be dead immediately — but it is not evidence that the historical drag/heating objections are cleared, and the paper no longer claims that it is.

Conclusion

PBT is Newton in the classical regime — a real, non-guaranteed pass of the same test that sank its own historical predecessors; a real but still-failing improvement over its own worst claim at galactic scale, short of working alternatives by 16–80×; a total failure with no defined rescue at collapse scale; and, while never a competitor to Newton at atomic/nuclear scale, still a failure of its own stated unification goal there. gaps.md does not currently state this range; it should. That the same extremes remain open for physics generally doesn’t close this theory’s specific gaps — it names the actual work still ahead, for PBT and for physics alike, as explaining how, not only fitting that.

Set against that record, two narrower observations remain worth recording, neither offsetting the failures above: a working instance of literal kinetic (particle-collision) causation for Newton’s law, a narrower category than “gravity theories” generally and distinct from GR’s geometric or emergent-gravity’s thermodynamic accounts; and a specific, quantified attempt at Le Sage’s actual historical downfall, rather than a revival that ignores it. Neither is an empirical success. The second explicitly does not currently work, by Le Sage’s own historical standard.

References

1. Le Sage, G.-L. (1748). Essai de Chymie Méchanique.
2. Lelli, F., McGaugh, S. S., Schombert, J. M. (2016). “SPARC: Mass Models for 175 Disk Galaxies with Spitzer Photometry and Accurate Rotation Curves.” The Astronomical Journal 152, 157.
3. McGaugh, S. S., Lelli, F., Schombert, J. M. (2016). “Radial Acceleration Relation in Rotationally Supported Galaxies.” Physical Review Letters 117, 201101.
4. Weizsäcker, C. F. von (1935). Zeitschrift für Physik 96, 431–458.
5. Abbott, B. P. et al. (LIGO/Virgo Collaboration) (2016). “Observation of Gravitational Waves from a Binary Black Hole Merger.” Physical Review Letters 116, 061102.
6. Event Horizon Telescope Collaboration (2019). “First M87 Event Horizon Telescope Results.” The Astrophysical Journal Letters 875, L1.