Gravity Analysis Regge Ttbloch Convention Audit Committed Spike Lhs

The committed spike expression

The declaration committedSpikeLHS is a ledger entry: a discrete record of a specific mathematical expression, frozen in the framework's machine-checked library of formal statements. It takes a small packet of numbers, a symmetric 3 by 3 matrix and a 3-vector, and returns a single real number. The expression itself is built from square roots of 2 and 3, and pi, arranged in a fixed pattern. Think of it as a formula written in stone, with every symbol and every operation pinned down exactly.

The declaration's role is to name one side of a proposed equality. The other side, called reggeTTMoment, is a separate construction that folds a stencil of values into a moment. The framework's GateBConventionTarget states the full equality: under seven conditions, the stencil fold must equal the committed spike expression. Those conditions are the standard ones for a symmetric, traceless matrix and a vector orthogonal to it in three dimensions. The equality is not proved. It is left as a definition, a target proposition that a future proof must instantiate with actual values and demonstrate.

What the declaration establishes is precise and narrow. It fixes a convention: this exact expression, with these exact constants, is the reference form. It does not establish that the convention is correct, that the equality holds, or that the stencil fold matches it. The docstring is explicit: this sidecar is not imported by production modules, and it does not prove Gate B. The equality to the stencil fold remains an honest convention bridge target.

In plain terms, the declaration is a commitment to a form, not a proof of a result. It is the left-hand side of an equation that nobody has yet shown to be true. The framework's value here is bookkeeping: it records what the convention is, so that the open question of whether it matches the stencil fold can be stated cleanly and pursued without ambiguity.

/-- The literal committed spike LHS, with `s2 = sqrt 2`, `s3 = sqrt 3`, and
`p = pi` as required by attempt 2. -/
def committedSpikeLHS (input : SpikeInput) : ℝ :=
  ReggeTTContinuumCertificateSpike.tetBlock0
      input.E00 input.E01 input.E02 input.E10 input.E11 input.E12
      input.E20 input.E21 input.E22 input.x0 input.x1 input.x2
      (Real.sqrt 2) (Real.sqrt 3) Real.pi
    + ReggeTTContinuumCertificateSpike.tetBlock1
      input.E00 input.E01 input.E02 input.E10 input.E11 input.E12
      input.E20 input.E21 input.E22 input.x0 input.x1 input.x2
      (Real.sqrt 2) (Real.sqrt 3) Real.pi
    + ReggeTTContinuumCertificateSpike.tetBlock2
      input.E00 input.E01 input.E02 input.E10 input.E11 input.E12
      input.E20 input.E21 input.E22 input.x0 input.x1 input.x2
      (Real.sqrt 2) (Real.sqrt 3) Real.pi
    + ReggeTTContinuumCertificateSpike.tetBlock3
      input.E00 input.E01 input.E02 input.E10 input.E11 input.E12
      input.E20 input.E21 input.E22 input.x0 input.x1 input.x2
      (Real.sqrt 2) (Real.sqrt 3) Real.pi
    + ReggeTTContinuumCertificateSpike.tetBlock4
      input.E00 input.E01 input.E02 input.E10 input.E11 input.E12
      input.E20 input.E21 input.E22 input.x0 input.x1 input.x2
      (Real.sqrt 2) (Real.sqrt 3) Real.pi
    + ReggeTTContinuumCertificateSpike.tetBlock5
      input.E00 input.E01 input.E02 input.E10 input.E11 input.E12
      input.E20 input.E21 input.E22 input.x0 input.x1 input.x2
      (Real.sqrt 2) (Real.sqrt 3) Real.pi

What this page does not claim

The equality between the stencil fold and the committed spike expression is not proved. The declaration does not establish that the committed spike expression is physically meaningful or correct. The declaration does not import into production modules or affect any derived results.

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

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: