Gravity Analysis Regge Exact Flat Hessian Bloch Data4 D Coupling Chunk0 Size

A block of coupling data

The declaration couplingChunk0_size is a bookkeeping statement inside a machine-checked library of formal theorems. It proves that the array named couplingChunk0, the first of sixteen blocks in a larger table, contains exactly 80 entries. The proof is immediate: the array is written out in full, and the checker counts the entries by inspection. The statement does not describe what any entry means physically; it only records how many entries the block holds.

The larger table, assembled from all sixteen blocks, is called couplingTable. It holds 1,208 entries, and the library proves this total by adding the sizes of the blocks: fifteen blocks of 80 entries plus one final block of 8 entries gives 15 × 80 + 8 = 1,208. Each entry is a coupling: a rational number paired with two edge displacement vectors and an offset, used to build a Bloch symbol for a discrete gravity analysis. The table was generated by a script, not written by hand, and the chunking exists to keep the formal checker from exceeding its recursion depth.

In Recognition Science, this declaration plays a supporting role. It is not a physical law and it does not derive any constant. It is a structural fact about a data structure: the first chunk has 80 rows. The value of the declaration is that it makes the total table size checkable and lets the library reason about the whole table without loading all 1,208 rows at once. The table itself is a definitional choice, a model of how couplings are organized, not a theorem about gravity.

The declaration does not claim that the couplings are correct, that the table is complete, or that the Bloch symbol it feeds is the right one for any physical situation. It only certifies a count. A reader who wants to know why these particular couplings appear, or what the Bloch symbol means for the discrete gravity analysis, must look elsewhere in the library.

theorem couplingChunk0_size : couplingChunk0.size = 80 := rfl

/-- 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

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 declaration does not assert that the couplings are physically correct or complete. It does not derive any constant or physical law from the table.

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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