Published Papers

August 2025

Two pieces of this work have permanent external identifiers, independently citable and separate from anything hosted on this site — tracked under Matthew’s ORCID iD.

A Strong-Field Spin-Precession Bound on a Pressure-Medium (Khronometric) Extension of General Relativity, and Constraints on Its Remaining Parameter Choices

Published on Zenodo, 2026-11-09 — a technical constraint paper testing one specific field-theory formalization of the pressure-medium idea (khronometric gravity, the low-energy limit of Hořava–Lifshitz gravity, plus the Blas–Pujolas–Sibiryakov six-derivative extension) against real pulsar-timing bounds.

• Zenodo record: zenodo.org/records/24063959
• DOI: doi.org/10.5281/zenodo.24063959 (version) · concept DOI 10.5281/zenodo.24063958 (all versions)
• Version: Draft 6R.19, 2026-11-09
• Licence: paper text, tables, figures and reference data/outputs are CC BY 4.0; all scripts and source code in the companion archive are MIT. Both © 2026 Matthew Foutch.
• Download: PDF · companion code and reference-output archive

Status: in-house, unreviewed preprint — this text has not been through peer review, and nobody outside the project has checked it. It is a separate, technical companion to the main PBT synthesis below, testing one specific parameterization against real data under a stated no-retuning rule, not a general verdict on push-pressure gravity as a whole.

What it tests. Three parameter choices for the theory’s one free coupling, η: “line L” (the point where the weak-field spin-precession effect would cancel), “region S” (small-coupling alternatives), and the η = 0 boundary itself. All three are evaluated against the Shao et al. (2013) solitary-pulsar spin-precession bounds and a directly-computed strong-field coefficient, rather than the weak-field approximation used in prior literature.

What it finds. The weak-field cancellation that would have protected line L does not survive at strong field — both line L and region S fail the pulsar bounds at the theory’s own working point (η = 10⁻⁷), and a smaller η cannot be substituted after the fact without an independent physical reason to expect one (the paper’s stated “no-retuning rule”). The η = 0 boundary is constrained from both signs of its remaining free parameter and joins smoothly onto η > 0. The paper also reports several results and reusable tools (the strong-field spin-precession coefficient table, stellar-structure and binary-pulsar solvers, and a three-particle spectral-integral engine) as useful to others working in khronometric or Einstein-aether gravity independent of what they mean for this specific theory.

How to cite:

Foutch, M. (2026). A Strong-Field Spin-Precession Bound on a Pressure-Medium (Khronometric) Extension of General Relativity, and Constraints on Its Remaining Parameter Choices. In-house, unreviewed preprint draft, Draft 6R.19, 9 November 2026. Solve the Universe. Zenodo. DOI: 10.5281/zenodo.24063959.

Cross-reference to the OSF/viXra preprint below: the Zenodo record’s own “Related work” field references the OSF preprint (DOI 10.17605/OSF.IO/ZUGT4) described next on this page. The two are companion records — this one a focused technical constraint test, the other the broader PBT synthesis — not duplicate submissions of the same material. Neither preprint record has been revised to cross-link the other beyond what each platform’s own metadata already does; a deliberate two-way citation edit on either platform would be a separate, explicit step.

Pressure Based Theory: Testable Hypotheses and Distinctions from General Relativity and Quantum Field Theory

The formally published, citable synthesis of PBT, registered on two independent platforms.

• OSF Preprints (Center for Open Science) — the version with a real, Crossref-registered DOI: doi.org/10.17605/OSF.IO/ZUGT4. HTML page.
• ai.viXra.org — submission 2508.0022v1, August 2025: abstract page · download the PDF.
• Hosted here — the original source PDF, with all three figures: download.

This is the original piece of PBT with permanent external identifiers, independently citable and separate from anything hosted on this site.

Status, added 2026-07-22: “published” here means registered on preprint platforms (OSF Preprints, ai.viXra.org) that assign permanent identifiers without peer review — not publication in a peer-reviewed journal. See the Catalog for how this compares to proven and accepted physics, and Fringe Ideas for PBT’s own classification. Stated plainly here since a DOI can otherwise read as more institutional vetting than it actually represents. The same status note applies to the Zenodo preprint above.

Corrigendum, 2026-07-21: this paper’s drag-threshold figure ($<10^{-19}$ m/s², repeated below) was found to be a real error during a systematic audit of all 13 site papers — recomputing the same formula and inputs actually gives $\approx9.8\times10^{-16}$ m/s² (still below the stated detection threshold, so the qualitative conclusion is unaffected, but the specific number was wrong). This corrigendum is noted here on the hosted site page; the versions registered with OSF (DOI) and ai.viXra.org are formally submitted external records and have not been revised on those platforms — that would need a separate, deliberate errata/versioning step on each platform, not made here without explicit direction. Correction identified and calculated by Claude (Anthropic). Original authorship and drafting: Matthew Foutch, with Grok (xAI) as collaborative AI.

Abstract

Pressure Based Theory (PBT) proposes a mechanical unification of fundamental forces through particle fluxes in an infinite pressure vessel, extending historical push gravity models like Le Sage’s theory. This paper formalizes PBT’s key testable hypotheses: negligible gravitational drag ($\approx9.8\times10^{-16}$ m/s², corrected 2026-07-21 from an original $<10^{-19}$ m/s²) and avoidance of singularities in black hole collapse. These predictions differ from general relativity (GR), which allows singularities, and quantum field theory (QFT), which incorporates probabilistic interactions without mechanical pushes. We detail experimental setups for falsification, including precision interferometry for drag and horizon imaging for singularities, positioning PBT as a falsifiable alternative to standard models.

Two Core Testable Hypotheses

Negligible Drag Hypothesis. Gravitational or aether drag $\approx9.8\times10^{-16}$ m/s² (corrected 2026-07-21 from an original $<10^{-19}$ m/s²), below current detection thresholds but testable at higher precision. This contrasts GR’s zero drag (pure geometry) and QFT’s vacuum fluctuations without bulk drag. Exceeding this (e.g., $10^{-14}$ m/s², adjusted from the original $10^{-18}$ m/s² for consistency with the corrected threshold) would falsify PBT. Test method: atomic clocks or interferometers (e.g., LISA Pathfinder successors) for orbital anomalies; space-based missions measuring drag in solar system orbits, compared to GR baselines.

Singularity Avoidance Hypothesis. Black hole collapse stabilizes without horizons or true singularities, forming dense cores with finite density — differing from GR’s inevitable singularities (Penrose-Hawking theorems) and QFT’s unresolved quantum singularities. Observing true horizons or information loss would falsify PBT. Test method: Event Horizon Telescope (EHT) imaging of shadows; deviations in ringdown phases from LIGO waves indicating non-singular cores; analysis of mergers for stable remnants.

Light deflection is predicted as $\theta \approx 4GM/(bc^2)$, aligning with GR in weak fields but diverging in strong regimes.

Differences from GR and QFT

Vs. GR: PBT uses pushes over curvature; predicts no singularities but similar weak-field effects (e.g., light deflection 1.75″, matching GR’s own extensively confirmed prediction). Differs in strong fields: stable black holes vs. GR’s collapse — GR’s strong-field predictions (e.g., black hole shadows via the Event Horizon Telescope) are themselves directly confirmed, making this a genuine, checkable point of difference rather than an area where GR is in doubt.

Vs. QFT: Mechanical determinism over probabilistic exchanges; no photons, virtual particles as flux distortions. Predicts EM unification without renormalization issues. PBT resolves dark matter via hierarchies, unlike GR+QFT’s need for it.

Conclusion

PBT’s hypotheses offer a pathway for unification, testable via drag measurements and singularity probes. This published version includes the full Reference Guide as an appendix, summarizing all 12 papers with key equations and links.

Assistance from Grok (xAI) in drafting and refining this work is gratefully acknowledged.

References

• Wikipedia Contributors. “Alternatives to general relativity.” Wikipedia, 2023.
• Wikipedia Contributors. “Le Sage’s theory of gravitation.” Wikipedia, 2023. — see Disproven Theories for the real historical falsification (drag, heating) of this specific model.
• Edwards, M. R. “The gravitation theory of Georges-Louis Le Sage.” APS Meeting Abstracts, 2006.
• Famaey, B. and McGaugh, S. S. “Modified Newtonian Dynamics (MOND): Observational phenomenology and relativistic extensions.” Living Reviews in Relativity, 15(1):10, 2012. — see Unproven Systems At Large for MOND’s own real, credentialed-but-unconfirmed status.
• Hossenfelder, S. “Quantum mechanics is wrong. There, I’ve said it.” Backreaction Blog, 2019.
• Thirring, W. “Mechanical model for quantum field theory.” Journal of Mathematical Physics, 4(3):332–338, 1963.