Gravity Analysis Regge Exact Flat Hessian Bloch Data4 D Coupling Chunk13 Size

A table in pieces

A ledger, a discrete record of events, can grow too large to handle in one piece. The framework's machine-checked library of formal theorems faces that problem when it stores the exact flat Hessian midpoint Bloch coupling table, a list of 1208 rational numbers that describe how edges in a four-dimensional lattice interact. To keep the formal verification manageable, the library splits the table into sixteen chunks. The declaration couplingChunk13_size proves that the thirteenth chunk contains exactly 80 entries.

Each entry in the table is a coupling, a number that measures the strength of interaction between two edges. The entry records a rational weight, the displacement of each edge in four dimensions, and a doubled midpoint offset. The full table concatenates all sixteen chunks, and a separate theorem proves the total size is 1208. The chunk-size theorem is a small but necessary bookkeeping fact: it lets the library reason about the whole table without ever loading all of it at once.

In Recognition Science, this table feeds a larger analysis of gravity. The framework models spacetime as a discrete lattice, and these couplings are the exact coefficients for a Bloch symbol, a function that describes how waves propagate through that lattice. The chunk-size theorem itself does no physics. It only certifies that the data is correctly partitioned, a prerequisite for any later theorem that consumes the table.

What the declaration does not claim is just as precise. It does not assert that the couplings are physically correct, that they match any measurement, or that the table is complete. It does not prove anything about the behavior of gravity. It only establishes a structural fact about a data structure: chunk thirteen has 80 entries. That is the whole content, and it is exactly what the formal proof delivers.

theorem couplingChunk13_size : couplingChunk13.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]

What this page does not claim

The theorem does not assert any physical correctness or match to measurement for the coupling values. The theorem does not prove anything about the behavior of gravity itself. The theorem does not claim the table is complete or that chunk thirteen is representative of the others.

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.

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