Gravity Analysis Regge Ttbloch Convention Audit Spike Input

The spike input packet

In the framework's machine-checked library, SpikeInput is a plain data packet: a structure that bundles a 3 by 3 matrix of real numbers and a 3-component real vector. The matrix is meant to be symmetric and traceless, and the vector is meant to be in the matrix's kernel, though those conditions are not enforced inside the structure itself. A separate definition, spikeInput, takes any such matrix and vector and packages them into this form. The name comes from the surrounding audit, which checks whether a numerical transcription of a gravity equation matches a convention used elsewhere in the framework.

The audit belongs to a family of convention checks. The task is to verify that two different ways of writing the same physical expression agree: one side is a sum of six block terms from a stencil, the other is a single committed scalar formula. The spike file is the scalar language that both sides must be translated into. SpikeInput is the translation layer: it marshals the matrix and vector into that scalar language, so the comparison can run. The committed left-hand side itself is a separate definition, committedSpikeLHS, which uses the square roots of 2 and 3 and the number pi as constants.

What the declaration does not do is prove anything. The target proposition, called Gate B, is left open as a definition rather than stated as a proven statement. A future proof would need to instantiate three ingredients from the actual raw stencil: a support set, a phase quadratic function, and an amplitude function. It would then need to show that the moment fold equals the committed spike left-hand side under seven equations: the symmetry of the matrix, its tracelessness, and three kernel conditions on the vector. That equality remains a target, not a result.

The honest position is plain. SpikeInput establishes only the packaging of data for a convention check. It does not establish that the convention holds, and it does not establish any physical claim about gravity. The convention bridge remains open, and the framework says so explicitly in its own documentation.

/-- Scalar packet passed to the committed spike transcription. -/
structure SpikeInput where
  E00 : ℝ
  E01 : ℝ
  E02 : ℝ
  E10 : ℝ
  E11 : ℝ
  E12 : ℝ
  E20 : ℝ
  E21 : ℝ
  E22 : ℝ
  x0 : ℝ
  x1 : ℝ
  x2 : ℝ

/-- Matrix/vector marshalling into the scalar language of the spike file. -/
def spikeInput (E : Fin 3 → Fin 3 → ℝ) (x : Fin 3 → ℝ) : SpikeInput where
  E00 := E 0 0
  E01 := E 0 1
  E02 := E 0 2
  E10 := E 1 0
  E11 := E 1 1
  E12 := E 1 2
  E20 := E 2 0
  E21 := E 2 1
  E22 := E 2 2
  x0 := x 0
  x1 := x 1
  x2 := x 2

/-- 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 answer does not claim that Gate B is proved. This answer does not claim that SpikeInput enforces symmetry, tracelessness, or kernel conditions automatically. This answer does not claim any physical result about gravity follows from the existence of the structure.

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)

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