Gravity Track1 Bcphysical Residual Physical Regge Ehconcrete Single Slice Produc

A count in a gravity proof

Regge calculus is a way to do general relativity without a smooth continuum: spacetime is chopped into flat tetrahedra, and gravity is described by the edge lengths of this discrete mesh. The Einstein-Hilbert action, the usual smooth formula for gravity, is recovered as the mesh is refined to infinitesimal size. The declaration physicalReggeEHConcreteSingleSliceProductFilterOneStatementProjectionCount_eq_two is a small accounting fact inside a much larger, machine-checked proof of this recovery.

The declaration states that a particular projection count, a number tracking how many separate claims are bundled into one statement of the proof, equals 2. It is a theorem in the framework's machine-checked library, proved by direct computation (reflexivity, meaning the two sides are definitionally equal). It does not, by itself, assert that Regge calculus converges to Einstein-Hilbert gravity; that is the job of the surrounding theorems, which carry the real content.

In Recognition Science, this count is part of a "Track 1.B-PHY" upgrade: a package of results showing that normalized, fully nonlinear Regge finite aggregates converge to the canonical finite Einstein-Hilbert/Dirichlet action, with an explicit residual error that tends to zero, once a local edge-stencil correspondence holds. The count of 2 here is a bookkeeping detail within that package, not a physical law.

What the declaration does not claim is more important than what it does. It does not claim that the convergence is unconditional: a separate target remains open for the full manifold Einstein-Hilbert theorem on a concrete periodic refinement family. It does not claim any numerical value for a physical constant, nor does it assert anything about the smooth limit itself. It is a statement about the internal structure of a proof artifact, not about the world.

theorem physicalReggeEHConcreteSingleSliceProductFilterOneStatementProjectionCount_eq_two :
    physicalReggeEHConcreteSingleSliceProductFilterOneStatementProjectionCount = 2 := rfl

theorem physicalReggeEHConcreteSingleSliceProductFilterOneStatementProjectionCount_eq_two :
    physicalReggeEHConcreteSingleSliceProductFilterOneStatementProjectionCount = 2 := rfl

What this page does not claim

It does not claim that Regge calculus converges to Einstein-Hilbert gravity; that is the surrounding theorems' content. It does not claim any unconditional manifold Einstein-Hilbert theorem; that target remains open. It does not assert any physical constant or empirical value.

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/Track1BCPhysicalResidual.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

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