Gravity Analysis Regge Exact Flat Hessian Bloch Data4 D Coupling Chunk15 Size

A table in eight pieces

In numerical work, a large table of coefficients is often split into smaller pieces so that a computer can process each piece without exhausting its memory. The declaration couplingChunk15_size is a theorem in the framework's machine-checked library of formal theorems. It states that the array named couplingChunk15, which is the last of sixteen slices of a larger table, contains exactly eight entries. The proof is a direct computation: the theorem's statement is couplingChunk15.size = 8, and the proof is the single word rfl, meaning the equality holds by definition.

The larger table is called couplingTable, and it holds 1208 entries. The other fifteen chunks, couplingChunk0 through couplingChunk14, each hold 80 entries. The full table is the concatenation of all sixteen chunks, and a separate theorem, couplingTable_size, proves that the combined size is exactly 1208. The role of couplingChunk15_size is therefore bookkeeping: it confirms that the final chunk is much smaller than the others, which is consistent with the table being divided unevenly to keep each piece under a processing limit.

Each entry in the table is a coupling, a record of a rational number and two displacement vectors in four dimensions, used in a formula for a Bloch symbol in a gravity analysis. The theorem does not say anything about the meaning of the entries, only how many there are in this one slice. It does not claim that the entries are correct, that the table is complete, or that the gravity analysis itself is valid. It is a statement about the size of a data structure, nothing more.

In Recognition Science, this theorem is part of a larger effort to formalize a specific calculation in a machine-checked way. The value of the theorem is that it lets a reader or a computer verify, without trusting a human author, that the final chunk has the expected number of entries. This is a small but necessary step in ensuring that the larger table, and the analysis that uses it, is built on verified foundations.

theorem couplingChunk15_size : couplingChunk15.size = 8 := 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]

theorem couplingChunk0_size : couplingChunk0.size = 80 := rfl

What this page does not claim

The theorem does not claim that the entries in the chunk are mathematically or physically correct. It does not claim that the coupling table is complete or that the gravity analysis is valid. It does not claim that the chunking scheme is the only or optimal way to organize the data.

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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