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Exact order-three ambiguity of the Einstein-Maxwell-dilaton coupling a^2 in metric jets, and its fourth-order collapse

Mathematical physics · posed by This work (2026); lineage: Rainich 1925, Misner-Wheeler 1957, 2026 · solved

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Statement

Is the EMD coupling square a2a^2 a function of the metric three-jet on an explicit active, non-null, simple-spectrum family of truncated Einstein-Maxwell-dilaton data, and can one more derivative recover it? Proved: no function of the common metric three-jet returns a2a^2 - the order-three ambiguity is exactly a free affine shear orbit (R\mathbb{R}) mixing B=asin⁡2θB=a\sin 2\theta with the phase gradient - while the fourth-order quotient recovers a2=A2+B2a^2=A^2+B^2, with equality fiber exactly a=±ba=\pm b (Z2\mathbb{Z}_2). In particular Kaluza's a=3a=\sqrt{3} and the control a=1a=1 collide through metric order three.

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. construction · #1

    James Kehoe, using GPT 5.6 Sol, Fable

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    Proposed and proved the theorems, wrote the Lean 4 formalization and the manuscript under human direction, with repeated adversarial audit cycles; the human author set scope, claim boundaries, and verification gates.

    Finite-jet theorems about compiled truncated EMD equation certificates: the exact shear-orbit fiber classification of the complete first seed channels, an explicit collision family with one metric three-jet realized by an actual cubic metric germ (genuine Frechet Ricci value and first derivative), the compiled impossibility theorem, and the fourth-order recovery with equality fiber a=±ba=\pm b. Not settled here: promotion to analytic EMD solution germs (separate written argument pending specialist audit, in the parent repository), chart covariance beyond the fixed presentation, density of the active locus, degenerate branches, and any sufficiency of a2=3a^2=3 for a Kaluza uplift.

  2. Machine-checked by Lean on #1 · not a person

    lean: partially checkedLean

    scope Lean formalization of the core argument; statement correspondence not independently audited

    Source-audited by this site on 17 August 2026: the repository was cloned at v0.1.0 and all 77 Lean files scanned with comments stripped - zero sorry, zero admit, zero axiom declarations, zero native_decide, toolchain pinned at v4.32.1 with Mathlib. Not compiled here (the repo's CI is claimed to). Lean-checked rather than Lean-verified per this site's standing split: the statements' correspondence to the informal claims has not been independently audited, and the same pipeline produced both the proofs and the formalization. No human peer review.

    Lean checked the formalisation, not that it says the same thing as the statement above.

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