Gravity Analysis Regge Exact Flat Hessian Bloch Data4 D Coupling Chunk12 Size

A table in pieces

In computational physics, a Bloch symbol describes how waves move through a periodic lattice, and its exact form for a flat four-dimensional grid is a large table of rational numbers. The declaration couplingChunk12_size is a theorem in the framework's machine-checked library of formal theorems. It states that the array named couplingChunk12 contains exactly 80 entries.

This chunk is one of sixteen slices of a larger table called couplingTable. The table records edge-pair couplings: for each pair of edges in a unit cell, it stores a rational coefficient and displacement vectors in four dimensions. These numbers feed a continuum symbol used in a discrete gravity analysis. The full table has 1208 entries, and the theorem couplingTable_size proves the total by summing the sizes of all sixteen chunks.

The theorem is a definitional equality, proved by reflexivity: the array is literally written out with 80 elements, so the statement that its size is 80 is true by inspection. Its role is practical. The table is chunked to keep the machine-checked library from exceeding a recursion depth limit during elaboration. The size theorem lets the library verify that no chunk was accidentally truncated or duplicated when the pieces were assembled.

In Recognition Science, this declaration is part of the framework's gravity analysis, but it does not by itself derive any physical law. It is a bookkeeping guarantee about a data structure. The theorem does not claim that the couplings are correct, that the Bloch symbol matches any measurement, or that the chunk contains all possible couplings. It only certifies the count of entries in one slice of the table.

theorem couplingChunk12_size : couplingChunk12.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 establish that the couplings are physically correct. The theorem does not claim the chunk contains all possible edge-pair couplings. The theorem does not derive any gravitational law or constant.

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)

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