Gravity Analysis Regge Bloch All Orbit Symbol4 D Bloch All Orbit Symbol4 Dstatus

A status record for the all-orbit symbol

The declaration blochAllOrbitSymbol4DStatus is a machine-checked status record. It is a collection of flags, each a proved theorem or a named open target, that summarizes the state of a specific computation in the framework's library. The computation concerns a four-dimensional discrete gravity model, where space is built from tetrahedral cells and the geometry is encoded by hinge areas and deficit angles. The status record does not itself perform the computation; it inventories what has been proved about it and what has not.

The record's proved flags include a count of orbit types, the behavior of the fold at zero momentum, and the evenness of the fold as a function of the momentum scale. These are tagged THEOREM. The record also carries a flag for the all-orbit second moment polynomial, a formal coefficient that describes the leading behavior of the fold at small momenta. The record's open flags are marked with status false: the arbitrary-direction cosine two-jet limit, per orbit and for the all-orbit sum, remains an open target. A separate decoy flag records that a single-orbit symbol does not equal the continuum target, which is a proved negative result, not a failure.

The record explicitly does not claim continuum Einstein-Hilbert recovery, does not flip the gap action recovery flag, and does not replace the transported fold of ReggeBlochFold4D. Its scope is limited to factorized, orbit-constant kernels. The axiom footprint is the standard one: [propext, Classical.choice, Quot.sound].

/-- Named OPEN props remain uninhabited status markers (not theorems). -/
theorem open_props_are_status_false :
    blochAllOrbitSymbol4DStatus.orbitM2TendstoClosed = false ∧
      blochAllOrbitSymbol4DStatus.allOrbitM2TendstoClosed = false := by
  decide

/-- DECOY: the closed one-orbit `(1,1)` m² coefficient `-3` is not the
continuum EH target; continuum recovery requires the full all-orbit symbol. -/
theorem decoy_one_orbit_m2_is_not_continuum_target :
    ReggeBlochM2Symbol4D.m2Symbol axisTTPlus = -3 ∧
      blochAllOrbitSymbol4DStatus.continuumEHClosed = false ∧
        blochAllOrbitSymbol4DStatus.oneOrbitIsNotContinuumTarget = true ∧
          blochAllOrbitSymbol4DStatus.gapActionRecovery = false := by
  refine ⟨ReggeBlochM2Symbol4D.m2Symbol_axisTTPlus, rfl, rfl, rfl⟩

What this page does not claim

This answer does not claim the computation is complete; the arbitrary-direction limit is open. This answer does not claim continuum Einstein-Hilbert recovery is proved. This answer does not explain the physical meaning of the orbit types or the deficit kernels.

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/ReggeBlochAllOrbitSymbol4D.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: