Gravity Analysis Regge Bloch Local Incidence M2 Eval4 D Regge Bloch Local Incide

A status report on a gravity candidate

The declaration reggeBlochLocalIncidenceM2Eval4DStatus_flags is a compact status report on a specific candidate for discrete gravity, called Path B. It records five yes-or-no flags about the candidate's behavior. Three flags are set to true: the candidate's averaged local structure matches a reference construction on the tested cases, an unwanted directional dependence persists, and a factor-of-four discrepancy persists. Two flags are set to false: the candidate does not close the event horizon, and it does not restore a property called gap action recovery.

The three true flags describe what the candidate does achieve. The first says that on all tested rays, the mean-local Path B value equals the distinct-hinge value, a consistency check. The second and third say that two known problems, an anisotropy in the e0 direction and a factor of four residual, survive the averaging procedure. These are not achievements; they are documented failures that the framework's machine-checked library records as facts.

The two false flags are the negative results. The candidate does not close the event horizon, meaning its position-resolved structure does not reproduce the expected horizon behavior. It also does not flip the gap action recovery flag, meaning a separate mechanism for recovering the action gap remains inactive. These are stated as theorems, not as opinions, and they are proved by direct computation in the framework's machine-checked library of formal theorems.

What the declaration does not claim is just as important. It does not claim that Path B is a viable theory of gravity; in fact, it documents specific failures. It does not claim that the event horizon is impossible to close, only that this particular candidate does not close it. It does not claim that the anisotropy or factor-four residual are fundamental, only that they persist under the mean-local averaging tested here. The declaration is a precise, bounded status report, not a verdict on the whole framework.

theorem reggeBlochLocalIncidenceM2Eval4DStatus_flags :
    reggeBlochLocalIncidenceM2Eval4DStatus.meanLocalEqualsDistinctHingeOnWitnesses =
        true ∧
      reggeBlochLocalIncidenceM2Eval4DStatus.e0AnisotropyPersistsUnderMeanLocal =
        true ∧
        reggeBlochLocalIncidenceM2Eval4DStatus.factor4ResidualPersistsUnderMeanLocal =
          true ∧
          reggeBlochLocalIncidenceM2Eval4DStatus.positionResolvedClosesEH =
            false ∧
            reggeBlochLocalIncidenceM2Eval4DStatus.gapActionRecovery =
              false := by
  decide

theorem reggeBlochLocalIncidenceM2Eval4DStatus_flags :
    reggeBlochLocalIncidenceM2Eval4DStatus.meanLocalEqualsDistinctHingeOnWitnesses =
        true ∧
      reggeBlochLocalIncidenceM2Eval4DStatus.e0AnisotropyPersistsUnderMeanLocal =
        true ∧
        reggeBlochLocalIncidenceM2Eval4DStatus.factor4ResidualPersistsUnderMeanLocal =
          true ∧
          reggeBlochLocalIncidenceM2Eval4DStatus.positionResolvedClosesEH =
            false ∧
            reggeBlochLocalIncidenceM2Eval4DStatus.gapActionRecovery =
              false := by
  decide

/-- Position-resolved Path B does not close EH (status false / OPEN). -/
theorem pathB_positionResolved_does_not_close_eh :
    Regge4DPathBPositionResolvedClosesEH = False :=
  Regge4DPathBPositionResolvedClosesEH_status_open

theorem does_not_flip_gap_action_recovery :
    reggeBlochLocalIncidenceM2Eval4DStatus.gapActionRecovery = false :=
  rfl

What this page does not claim

The declaration does not claim Path B is a viable theory of gravity. The declaration does not claim the event horizon cannot be closed by any candidate. The declaration does not claim the anisotropy or factor-four residual are fundamental or unavoidable.

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/ReggeBlochLocalIncidenceM2Eval4D.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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