Gravity Analysis Regge Ttbloch Convention Audit

Convention audit

In physics, a convention is a choice of notation: which direction counts as positive, how matrices are arranged, or how a complicated expression is split into pieces. Different papers often use different conventions for the same underlying calculation, and translating between them is a common source of errors. The convention audit, a machine-checked comparison of two notations, exists to catch such translation mistakes before they propagate.

The audit in question compares two ways of writing a gravitational wave calculation. One is a "stencil fold" method, which builds up a result by adding contributions from a small grid of surrounding points. The other is a "committed spike transcription," a fixed reference expression written in a simpler scalar language. Both are supposed to represent the same physical quantity: a component of the gravitational field under the Regge-Teitelboim and transverse-traceless (TT) gauge conditions.

The module defines a formal target proposition, Gate B, which states that the stencil fold equals the committed spike expression, provided seven specific equations hold. Those equations express the symmetry of the field matrix and the transversality condition. The module does not establish this equality. It leaves the target as an open definition, a precise statement of what a future proof must establish. The audit's value is that it makes the required bridge explicit and machine-checkable, rather than relying on an informal hand-wave that two notations "clearly" match.

In Recognition Science, this audit fits a broader pattern: the framework treats physical laws as derived from a discrete ledger of recognition events, and it uses machine-checked libraries of formal theorems to keep those derivations honest. This particular module is a sidecar, deliberately not imported by production code, so it can audit a transcription without affecting the main derivation chain. Its plain-language lesson is that a convention bridge is a claim to be proved, not assumed.

/-- Gate B target proposition, left open as a definition rather than stated as
a theorem.  A future proof must instantiate `support`, `phaseQuadratic`, and
`amplitude` from the actual raw stencil and show that the moment fold matches
the committed spike LHS under the seven TT equations, without using
`tt_continuum_certificate`. -/
def GateBConventionTarget (support : Finset Bucket) (phaseQuadratic : Bucket → ℝ)
    (amplitude : Bucket → ℝ) (E : Fin 3 → Fin 3 → ℝ) (x : Fin 3 → ℝ) : Prop :=
  E 0 1 = E 1 0 →
  E 0 2 = E 2 0 →
  E 1 2 = E 2 1 →
  E 0 0 + E 1 1 + E 2 2 = 0 →
  x 0 * E 0 0 + x 1 * E 1 0 + x 2 * E 2 0 = 0 →
  x 0 * E 0 1 + x 1 * E 1 1 + x 2 * E 2 1 = 0 →
  x 0 * E 0 2 + x 1 * E 1 2 + x 2 * E 2 2 = 0 →
  reggeTTMoment support phaseQuadratic amplitude =
    committedSpikeLHS (spikeInput E x)

/-- Gate B target proposition, left open as a definition rather than stated as
a theorem.  A future proof must instantiate `support`, `phaseQuadratic`, and
`amplitude` from the actual raw stencil and show that the moment fold matches
the committed spike LHS under the seven TT equations, without using
`tt_continuum_certificate`. -/
def GateBConventionTarget (support : Finset Bucket) (phaseQuadratic : Bucket → ℝ)
    (amplitude : Bucket → ℝ) (E : Fin 3 → Fin 3 → ℝ) (x : Fin 3 → ℝ) : Prop :=
  E 0 1 = E 1 0 →
  E 0 2 = E 2 0 →
  E 1 2 = E 2 1 →
  E 0 0 + E 1 1 + E 2 2 = 0 →
  x 0 * E 0 0 + x 1 * E 1 0 + x 2 * E 2 0 = 0 →
  x 0 * E 0 1 + x 1 * E 1 1 + x 2 * E 2 1 = 0 →
  x 0 * E 0 2 + x 1 * E 1 2 + x 2 * E 2 2 = 0 →
  reggeTTMoment support phaseQuadratic amplitude =
    committedSpikeLHS (spikeInput E x)

What this page does not claim

This module does not prove that the two notations agree. This module does not derive any physical constant or law. This module is not part of the main production derivation chain.

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/ReggeTTBlochConventionAudit.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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