pith. sign in
theorem

offDiagEntries_eq

proved
show as:
module
IndisputableMonolith.CrossDomain.CrossPatternMatrix
domain
CrossDomain
line
96 · github
papers citing
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plain-language theorem explainer

The off-diagonal block of the Recognition Science cross-pattern matrix contains exactly 16 entries. Researchers verifying the Wave-64 meta-theorem would cite this count when enumerating distinct cross-products among the five patterns. The equality follows from a decision procedure that evaluates the product definition of the off-diagonal size.

Claim. The square of the off-diagonal size among the five patterns equals 16.

background

The module states C26: the five RS patterns (D=5, 2³=8, J(1)=0, φ-ladder, gap-45/cube-faces) form a non-degenerate matrix of cross-products, with n/a entries when J=0 is involved. offDiagEntries is defined as the product of the off-diagonal size with itself. The local setting is the structural meta-claim that each pair of patterns produces a distinct integer or relation, as tabulated in the module documentation.

proof idea

The proof is a one-line decision procedure that evaluates the definition of offDiagEntries as the square of the off-diagonal size.

why it matters

This equality confirms the off-diagonal count inside the Wave-64 cross-domain meta-theorem. It supports enumeration of the 16 relations among D=5, 2³=8, φ, and gap-45 (excluding J=0). The result aligns with the eight-tick octave and phi-ladder landmarks from the forcing chain (T5-T8).

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