Gravity Analysis Regge Exact Flat Hessian Bloch Data4 D Coupling Chunk11 Size

The chunk's size

In numerical work, a large table of coefficients is often split into smaller pieces so a computer can process it without hitting memory or recursion limits. The table here holds 1,208 rational coupling terms used in a four-dimensional gravity analysis. The declaration couplingChunk11_size is a machine-checked theorem stating that the eleventh chunk, an array of such terms, has exactly 80 entries. This is a bookkeeping fact, not a physical law.

The table itself is generated by a script, not written by hand. Each entry records a rational coupling strength, two edge displacement vectors, and a midpoint offset, all needed to build a Bloch symbol for a flat-space Hessian. The full table is assembled by concatenating 16 chunks, and a companion theorem confirms the total: 15 chunks of 80 entries plus one final chunk of 8 gives 1,208. The size theorem for chunk 11 is one of 16 identical statements, each verified by direct computation in the machine-checked library of formal theorems.

In Recognition Science, this chunk is part of a larger forcing chain that derives physical structure from a recognition cost function. The framework models gravity through discrete edge couplings on a lattice, and this table supplies the exact coefficients for one step of that analysis. The theorem about the chunk's size does not say anything about the values of those coefficients, nor about what physical predictions follow from them. It only certifies that the array has the expected length, so that later proofs can rely on the chunk being complete.

What the declaration does not claim is worth stating plainly. It does not prove that the coupling values are correct, that the Bloch symbol is physically meaningful, or that the gravity model matches observation. Those would be separate claims requiring their own evidence. The size theorem is a structural guarantee: the data is shaped as intended, nothing more. For a reader, the practical consequence is that this chunk can be trusted as a complete block of 80 terms when the full table is assembled.

theorem couplingChunk11_size : couplingChunk11.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 certify the numerical values of the coupling coefficients. It does not establish that the gravity model matches any measured physical quantity. It does not derive the existence or uniqueness of the Bloch symbol from first principles.

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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