Gravity Analysis Regge Exact Flat Hessian Bloch Data4 D Coupling Chunk10 Size

A table, split for the machine

In numerical work, a table of 1,208 entries is too large for a proof assistant to process in one gulp. The framework's machine-checked library of formal theorems therefore splits the table into 16 chunks. The declaration couplingChunk10_size is the theorem that chunk number 10 contains exactly 80 entries. It is a statement about bookkeeping, not about physics: it says that a particular array has a certain length, and the proof is the trivial observation that the array was written that way.

The table itself is the exact flat Hessian midpoint Bloch coupling table, auto-generated by a script. Each row records a rational coupling strength, two edge displacement vectors, and a doubled midpoint offset. The continuum symbol it supports is a sum over these couplings of a product of second derivatives weighted by a cosine of a wave-vector difference. The chunking exists purely to keep the Lean elaboration under its recursion depth limit; the theorem couplingChunk10_size is the receipt that the split was done correctly.

In Recognition Science, this table is part of a larger derivation of gravity from a discrete recognition ledger. The framework models spacetime as a lattice and computes the exact Bloch symbol of the flat Hessian, the second variation of the action. The table is the concrete data that feeds that computation. The size theorem guarantees that the data pipeline is intact: every chunk has the expected length, and the full table has 1,208 entries, as the companion theorem couplingTable_size confirms.

What the theorem does not claim is any physics. It does not say that the couplings are correct, that the Bloch symbol is the right one, or that the framework's derivation of gravity matches observation. It only says that a generated array has a certain length. The physics claims, if any, live in other declarations that use this table; this theorem is about the plumbing, not the water.

theorem couplingChunk10_size : couplingChunk10.size = 80 := rfl

theorem couplingTable_size : couplingTable.size = 1208 := by
  simp only [couplingTable, Array.size_append, couplingChunk0_size, couplingChunk1_size, couplingChunk2_size, couplingChunk3_size, couplingChunk4_size, couplingChunk5_size, couplingChunk6_size, couplingChunk7_size, couplingChunk8_size, couplingChunk9_size, couplingChunk10_size, couplingChunk11_size, couplingChunk12_size, couplingChunk13_size, couplingChunk14_size, couplingChunk15_size]

/-- Generated coupling table (`n = 1208`). -/
def couplingTable : Array Coupling :=
  couplingChunk0 ++ couplingChunk1 ++ couplingChunk2 ++ couplingChunk3 ++ couplingChunk4 ++ couplingChunk5 ++ couplingChunk6 ++ couplingChunk7 ++ couplingChunk8 ++ couplingChunk9 ++ couplingChunk10 ++ couplingChunk11 ++ couplingChunk12 ++ couplingChunk13 ++ couplingChunk14 ++ couplingChunk15

What this page does not claim

This theorem says nothing about the correctness of the couplings or the physics they encode. This theorem does not show that the framework's gravity derivation matches observation.

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/ReggeExactFlatHessianBlochData4D.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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