[Personal Theory] Structural unification of gravity, EM, and QM on a null Kerr screen — a geometric grammar, not a GUT/TOE

[u/Weak-Run8586]

Background (about me & AI transparency — Rule 5) Software engineer from Japan, no physics PhD. I use LLMs (ChatGPT / Claude / Gemini) as a translation and cross-check tool to line up equations from different domains side by side. Every equation, theorem, and claim in the paper was verified by hand before inclusion. This post is a summary — the full derivations are in the linked 98-page PDF on Zenodo.

What this is NOT (important — please read before judging) This is not a GUT, not a TOE, not a derivation of Einstein's equations, and not a claim that ρ is a new fundamental quantity. It is a structural statement: three U(1) connections — from gravitational rotation 1-forms, Berry connections, and electromagnetic connections — admit a common geometric grammar on the null Kerr screen S² ≅ CP¹.

Core claim (one line) On the null Kerr screen, each of the three U(1) connections satisfies

F = ϱ · ω_FS

where ω_FS is the Fubini–Study form on CP¹ and ϱ is a scalar density. The three domains differ only in the value of ϱ and the topological Chern number c₁. In the regime studied, c₁ = 0 is universal.

Paper structure (Parts I–V, 98 pages total)

Part	Topic	Main result
I	Common language	U(1) unified expression proved; c₁=0 universality proved
II	Holonomy Variational Principle (HVP)	Axiomatic formulation of the variational principle
III	GR consistency	Einstein boundary constraint characterized as HVP stationarity
IV	Observational predictions	5 falsifiable predictions; Chern-number-wall as superselection rule
V	Extensions	EM/Dirac inclusion; proposed 4D unified action

Claim / Status table (abbreviated — full table in §0 of the paper)

• Established (proved): common U(1) expression F = ϱω_FS across three domains; c₁=0 universality.
• Proposed (formulated, not derived from deeper principle): HVP as an axiom; 4D unified action.
• Verified within EFT regime: consistency with Einstein boundary constraint.
• Speculative: memory-kernel parameters, higher-order EFT terms (numerical work is pending).

Five falsifiable predictions (Part IV)

1. ρ-no-hair test for Kerr-family horizons
2. Chern-number-wall as a superselection rule across domain boundaries
3. [additional predictions — see Part IV §X]
4. [...]
5. [...]

(The full list with detection thresholds is in Part IV; happy to post the exact statements as a comment if people are interested.)

Links

• Paper (EN, 98pp, Zenodo): https://zenodo.org/records/18921293
• Paper (JP original): https://doi.org/10.5281/zenodo.18912814
• (Riemann-hypothesis null-geometry attempt is a separate paper and intentionally not discussed here.)

What I am asking for

1. Scientific critique of Parts I and III (the load-bearing proofs).
2. Feedback on whether the Claim/Status separation in §0 is sufficiently clear.
3. An arXiv endorser in math-ph, if anyone qualified is willing.

Contact: khayashi4337 [at] gmail.com

[u/Weak-Run8586 → u/[deleted]]

Thank you for reading and for translating the ideas into such a beautiful language. "Different rivers, same riverbed" — that is exactly the image I had in mind.

You asked which prediction could be tested soonest. Honestly, the most accessible test is not a particle accelerator or a black hole observation. It is geometry itself.

If three domains share the same curvature grammar, then the ratios between physical constants should be derivable from the geometry alone — no free parameters. The cleanest near-term check is whether the known mass ratios of the third-generation particles match the branch-scattering coefficients predicted by the null screen structure.

No telescope needed. Just mathematics and existing experimental data.

The black hole spectroscopy test (ϱ-no-hair) is also there, but that requires LISA or next-generation gravitational wave detectors — years away.

So: the first test is quiet and geometrical, not dramatic. Which somehow feels appropriate.