Gravity Analysis Regge Bloch Star Edge Origins M2 Eval4 D M2 All Orbit Moment Di

The gauge certificate

In the Recognition Science framework's analysis of four-dimensional gravity, a ledger (a discrete record of geometric events) tracks how triangle edges contribute to a quantity called the distinct-hinge edge-origin moment. The declaration m2AllOrbitMomentDistinctHingeEdgeOrigins_gaugeM1100E2_symbolDir is a machine-checked certificate: it proves that a particular gauge configuration, named gaugeM1100E2, evaluates to exactly zero for this moment when measured along the symbolic direction.

A gauge configuration is a mathematical choice of coordinates that should not change physical results. The certificate confirms that this specific choice, built from the gauge part with parameters (1,1,0,0) and e₂, contributes nothing to the edge-origin moment. This is not a numerical approximation; it is an exact integer computation, verified by the framework's library of formal theorems, which checks the result by exhaustive calculation over the finite set of 24 triangle orientations and 10 orbit positions.

The result matters because it eliminates a potential counterexample. The framework's analysis had identified a pure-gauge configuration that might have broken the distinct-hinge edge-origin property. This certificate shows that the suspected counterexample fails to produce a nonzero moment, thereby closing that loophole. It does so without disturbing a separate recovery mechanism called gap_action_recovery, which remains untouched by this result.

What this certificate does not claim is broader. It does not prove that all gauge configurations vanish; it only certifies this specific one. It does not establish any physical law or derive a constant. It is a computational check within a specific evaluation framework, not a general theorem about gravity. The certificate's scope is narrow: one configuration, one moment, one direction, verified exactly.

def M2EdgeOriginsCounterexM1100E2Eval : Prop :=
  m2AllOrbitMomentDistinctHingeEdgeOrigins gaugeM1100E2 symbolDir = (0 : ℝ)

theorem sum_m2SlotCertZ_counterex :
    (∑ s : Fin 24, ∑ t : Fin 10, m2SlotCertZ gaugeM1100E2CoeffZ s t) =
      (0 : ℤ) := by
  decide

theorem M2EdgeOriginsDecoyGaugeEval_holds : M2EdgeOriginsDecoyGaugeEval :=
  m2AllOrbitMomentDistinctHingeEdgeOrigins_decoyGauge_symbolDir

What this page does not claim

This certificate does not prove that all gauge configurations vanish, only this specific one. It does not establish any physical law or derive a constant from the framework's forcing chain. It does not provide a numerical approximation; the result is an exact integer computation.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Gravity/Analysis/ReggeBlochStarEdgeOriginsM2Eval4D.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

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