Gravity Analysis Regge Ttbloch Convention Audit Gate Bconvention Target

The Gate B target

In the Recognition Science framework's machine-checked library of formal theorems, GateBConventionTarget is a definition, not a proved theorem. It states a precise conditional proposition: if a certain matrix E is symmetric and traceless, and a vector x is in its kernel, then a computed quantity called reggeTTMoment must equal a fixed reference value called committedSpikeLHS. The declaration names the seven conditions on E and x explicitly, and then asserts the equality that would follow from them.

The declaration is a bridge target, a checkpoint in an audit of conventions. It does not assert that the conditions are satisfied by any actual physical system, nor that the equality has been derived. The docstring is explicit: attempt 2 does not prove Gate B. The equality remains an honest convention bridge target, meaning a future proof must instantiate the support, phase, and amplitude from the raw stencil and show the moment matches the committed spike left-hand side under the seven TT equations, without using a certain certificate named tt_continuum_certificate.

What the declaration does establish is a precise statement of what would need to be shown. It gives the exact logical form of the claim, so that a proof attempt has a fixed target. It also records that the interface moment is now a stencil fold, not a definition wired to the spike blocks, which is why the equality is not yet established. This is a piece of bookkeeping in a formal audit, not a physical result.

In plain terms: the declaration says "if these seven symmetry and kernel conditions hold, then this computed moment equals this reference value," and it leaves the "if" unproved. It is a goal statement, a named open problem within the framework's library, not a claim about gravity itself.

/-- 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)

/-- 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

The declaration does not prove that the seven conditions hold for any physical system. It does not establish that the equality between reggeTTMoment and committedSpikeLHS is true. It is not a statement about the physical content of general relativity, only about a formal convention bridge.

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: