Gravity Analysis Regge Bloch Fold4 D Transported Slot Term Axis Seed Masks

The transported slot term

In the Recognition Science framework's machine-checked library of formal theorems, the declaration transportedSlotTerm_axis_seedMasks establishes a precise algebraic fact about a term that appears in a four-dimensional gravity analysis. The term itself, the transported slot term, is a component of a larger sum, called the Bloch fold, which is built from a discrete grid of points, each carrying a phase factor. The declaration proves that for two specific difference masks, labeled (1,2) and (2,1), the contributions from this term to the axis-TT class are identically zero for every wave vector. In plain language, it shows that certain geometric configurations contribute nothing to this particular part of the calculation.

This is a theorem, meaning it is a proved statement within the framework's formal system, with no unproved assumptions beyond the standard axioms of the underlying logic. The proof is a structural one: the area supports of the masks miss the axis-TT class loads entirely, so the contribution vanishes. The declaration is part of a larger campaign to build a phase-decorated fold for a specific type of triangle hinge in one Kuhn cell, using a particular midpoint plane-wave convention. The result is one of several consistency gates in that campaign, checking that the transported fold behaves as expected.

What the declaration does not claim is as important as what it does. It does not evaluate the mass-squared Taylor coefficient against the Einstein-Hilbert or TT continuum symbol; that is explicitly left for a later step. It does not prove that the Recognition Science sum converges to the Einstein-Hilbert action in four dimensions, and it does not establish any physical recovery of a gap. The theorem is a piece of internal algebraic consistency, not a physical law. It says nothing about whether the framework's gravity model is correct; it only certifies that this particular formal construction is internally coherent.

/-- Honest transported finite-momentum `(1,1)` Bloch fold (72 instances). -/
def blochFold11 (H : Mat4) (m : Fin 4 → ℝ) : ℝ :=
  ∑ s : Fin 24, ∑ t : Fin 10, transportedSlotTerm H m s t

/-- Honest transported finite-momentum `(1,1)` Bloch fold (72 instances). -/
def blochFold11 (H : Mat4) (m : Fin 4 → ℝ) : ℝ :=
  ∑ s : Fin 24, ∑ t : Fin 10, transportedSlotTerm H m s t

What this page does not claim

This does not prove S_RS_converges_EH_4d. This does not flip gap_action_recovery. This does not claim any physical significance for the vanishing contributions.

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/ReggeBlochFold4D.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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