Gravity Master Theorem Unconditional Closure Status Unconditional Has Open Targe

The closure status

In physics, a master theorem is a central result from which many others follow. The Recognition Science framework's gravity master theorem is a large, machine-checked collection of formal theorems: a library where every statement is verified by a computer proof checker. The declaration closureStatus_unconditional_has_open_target records the honest status of that collection: it establishes that formal witnesses, meaning computer-verified proofs, are installed for five key inputs to the master theorem, and it simultaneously records that six physical targets remain open.

The five installed witnesses cover concrete physical content. One witness proves that a discrete Regge calculus, a lattice approximation of spacetime, converges to the continuum Einstein-Hilbert action, the standard action of general relativity, on a periodic six-tet cubic torus. Another proves a discrete Bianchi identity, a conservation law in general relativity, holds at every vertex. Others cover amplitude linearity, the Page curve of black hole evaporation, and stochastic gravitational wave signals distinct from inflation. Each of these is a theorem with a computer-verified proof in the library.

The same declaration also records what is not closed. Six physical targets are marked open: D2 quadrature, general triangulation, tensor train recovery, Lorentzian causal triangulations, boundary GHY terms, and the echo mechanism. The theorem closureStatus_unconditional_has_open_target proves that at least one of these six is open, by a trivial logical step from the status record. This is a formal way of saying the master theorem is not complete: the installed witnesses do not yet cover these targets.

The declaration does not claim that the open targets are impossible, nor that they are close to being closed. It does not claim that the installed witnesses constitute a full physical theory of quantum gravity. It merely records, in machine-checked form, the exact boundary between what has been proved and what remains to be proved. This is the framework's way of being precise about its own limits.

For a reader, the practical consequence is clear: the gravity master theorem is a partially built structure, with five verified pillars and six unbuilt wings. The open targets are named, so researchers and readers can see exactly what work remains. The declaration is a map of unfinished business, not a claim of completion.

/-- At least one load-bearing physical target remains open; in fact D2
quadrature is still open on the current scoped route. -/
theorem closureStatus_unconditional_has_open_target :
    closureStatus_unconditional.d2_quadrature_open = true ∨
    closureStatus_unconditional.general_triangulation_open = true ∨
    closureStatus_unconditional.tensor_tt_recovery_open = true ∨
    closureStatus_unconditional.lorentzian_causal_triangulations_open = true ∨
    closureStatus_unconditional.boundary_ghy_open = true ∨
    closureStatus_unconditional.echo_mechanism_open_or_rejected = true :=
  Or.inl rfl

theorem concretePhysicalRegEHContinuumProp_holds :
    concretePhysicalRegEHContinuumProp :=
  fun D => Track1BCPhysicalResidual.physicalReggeEHConcreteProductFilterTarget_holds D

theorem concretePhysicalBianchiProp_holds :
    concretePhysicalBianchiProp := by
  intro V B _
  exact Track1BCPhysicalResidual.physicalSchlafliBianchiMasterProp_holds V B

/-- The theorem-built assembly exists, but the full physical quantum-gravity
framework is not closed.  This record is intentionally conservative: it keeps
the useful master theorem available while preventing downstream papers or
certificates from counting scoped witnesses as complete physical recovery. -/
def closureStatus_unconditional : MasterTheoremUnconditionalClosureStatus where
  theorem_built_witnesses_installed := true
  full_physical_closure := false
  d2_quadrature_open := true
  general_triangulation_open := true
  tensor_tt_recovery_open := true
  lorentzian_causal_triangulations_open := true
  boundary_ghy_open := true
  echo_mechanism_open_or_rejected := true

What this page does not claim

The open targets are not claimed to be impossible or even difficult to close. The installed witnesses do not constitute a complete quantum gravity theory. The declaration does not claim that the master theorem is physically validated by experiment.

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/MasterTheoremUnconditional.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: