Gravity Analysis Regge Exact Flat Hessian Bloch Symbol4 D Exact Bloch Symbol Sta

A status report, not a result

In the Recognition Science framework, a ledger is a discrete record of events and their costs. The declaration exactBlochSymbolStatus_flags is a status report on one specific calculation: the exact flat-space Hessian for a four-dimensional Regge gravity model, expressed as a finite trigonometric polynomial over 1208 coupling terms. The theorem reads off six boolean flags from a structure named ExactBlochSymbolStatus, and each flag records whether a particular step in the calculation has been completed.

Four of the six flags are set to true. The symbol is named, meaning the trigonometric polynomial form is defined. An abstract limit proof is available, and it has been specialized to the 1208-term case without blowing up the formal proof checker. The normalization gate passes: a discrete bookkeeping factor times the unit Frobenius coefficient recovers the frozen Einstein-Hilbert coefficient of -1/4. These four flags together mean the calculation has a defined object, a proved limit, and a consistency check on its normalization.

Two flags are false. The ledger entry srsInhabited is false, meaning the relevant self-referential structure is not yet shown to exist. The gapActionRecovery flag is false, meaning the recovery of the gap action from the discrete structure remains unproved. The declaration does not assert these steps are impossible; it records that they are open targets. The docstring notes that the continuum symbol is a geometric limit and that this limit is the gate for the ledger, so the open flags are the next checkpoints, not failures.

What the declaration does not claim is as important as what it proves. It does not claim the full Einstein-Hilbert action is derived from the discrete model; only the normalization of one coefficient is checked. It does not claim the self-referential structure exists, and it does not claim the gap action is recovered. The flags are a snapshot of progress in a formal library, not a physical theorem about gravity. A reader should take the four true flags as evidence that the trigonometric polynomial object is well-formed and its limit is proved, and the two false flags as a precise statement of what remains to be done.

theorem exactBlochSymbolStatus_flags :
    exactBlochSymbolStatus.trigPolyNamed = true ∧
      exactBlochSymbolStatus.abstractTendstoProved = true ∧
        exactBlochSymbolStatus.specializedTendstoProved = true ∧
          exactBlochSymbolStatus.normalizationGatePass = true ∧
            exactBlochSymbolStatus.srsInhabited = false ∧
              exactBlochSymbolStatus.gapActionRecovery = false :=
  ⟨rfl, rfl, rfl, rfl, rfl, rfl⟩

theorem exactBlochSymbolStatus_flags :
    exactBlochSymbolStatus.trigPolyNamed = true ∧
      exactBlochSymbolStatus.abstractTendstoProved = true ∧
        exactBlochSymbolStatus.specializedTendstoProved = true ∧
          exactBlochSymbolStatus.normalizationGatePass = true ∧
            exactBlochSymbolStatus.srsInhabited = false ∧
              exactBlochSymbolStatus.gapActionRecovery = false :=
  ⟨rfl, rfl, rfl, rfl, rfl, rfl⟩

theorem exactBlochSymbolStatus_flags :
    exactBlochSymbolStatus.trigPolyNamed = true ∧
      exactBlochSymbolStatus.abstractTendstoProved = true ∧
        exactBlochSymbolStatus.specializedTendstoProved = true ∧
          exactBlochSymbolStatus.normalizationGatePass = true ∧
            exactBlochSymbolStatus.srsInhabited = false ∧
              exactBlochSymbolStatus.gapActionRecovery = false :=
  ⟨rfl, rfl, rfl, rfl, rfl, rfl⟩

What this page does not claim

The full Einstein-Hilbert action is derived from the discrete model; only one coefficient's normalization is checked. The self-referential structure exists; the flag srsInhabited is false. The gap action is recovered; the flag gapActionRecovery is false.

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/ReggeExactFlatHessianBlochSymbol4D.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.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: