Gravity Analysis Regge4 Dexact Action Symbol Exact Action Symbol Status Flags

A status ledger for a gravity calculation

In numerical relativity, Regge calculus approximates spacetime with flat four-dimensional blocks, and its central object is the action, a quantity whose second derivative describes curvature. The Recognition Science framework's library, a machine-checked collection of formal theorems, contains a declaration named exactActionSymbolStatus, which is a set of seven true-or-false flags. It is a status ledger, a discrete record of which claims about this action's exact symbol have been established and which remain open.

The flags record that the continuum symbol has rebounded to the exact fold, that the fold is retained as legacy, that the star offsets for two orbit types are defined, and that edge-origin mass-squared certificates are banked. These are marked true. The flags for the other orbit offsets being incomplete, for the SRS being inhabited, and for gap action recovery are marked false, with a theorem proving that the latter two are false. This is a formal way of saying that certain parts of the calculation are complete and others are not yet done.

The declaration does not claim that the exact action symbol is fully derived. A separate definition, exact_star_member_offsets_incomplete, is set to False, and a theorem proves this, meaning the offsets for the other orbit types are not yet complete. The framework's own documentation states that the relation between the geometric fold and the algebraic dictionary is measured, not equal, and that the dictionary is exactly twice the geometric hinge moment at two banked witnesses. This is a precise, machine-checked status report, not a claim of full success.

What this means for a reader is that the framework has a rigorous way of tracking the progress of a difficult calculation. The status flags are not a proof of the physics; they are a formal inventory of what has been proved, what is modeled, and what remains open. The value is in the clarity: a machine-checked ledger that prevents overclaiming and keeps the open problems visible.

/-- Status package for the exact-action continuum rebind. -/
structure ExactActionSymbolStatus where
  continuumReboundToExact : Bool
  foldRetainedAsLegacy : Bool
  t11t12StarOffsetsDefined : Bool
  otherOrbitOffsetsIncomplete : Bool
  edgeOriginsM2Banked : Bool
  srsInhabited : Bool
  gapActionRecovery : Bool

/-- Local status flags remain open; geometric ContinuumSymbolIs Tendsto
is the Preflight ledger gate.  Edge-origin m² decide-certs are banked
elsewhere and do not inhabit `S_RS`. -/
theorem exact_action_srs_still_open :
    exactActionSymbolStatus.srsInhabited = false ∧
      exactActionSymbolStatus.gapActionRecovery = false := by
  decide

theorem exact_star_member_offsets_incomplete_closed :
    exact_star_member_offsets_incomplete = False := rfl

/- Legacy fold retained for comparison; after `H_fold` it is not the
continuum symbol. Continuum Props bind to `finiteExactReggeSymbol`.
Former `fold_retained_as_legacy_only` concluded `True` from an inequality
hypothesis: that is a repository status note, not a math claim. Status is
recorded by `exactActionSymbolStatus.foldRetainedAsLegacy`. -/

What this page does not claim

The exact action symbol is fully derived for all orbit types. The declaration proves the physical correctness of the Regge action model. The status flags are a claim about the continuum limit of the model.

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/Regge4DExactActionSymbol.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: