pith. sign in
theorem

full_turn

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

The equality eight times forty-five equals three hundred sixty is recorded as the full-turn entry in the cross-pattern matrix. Researchers assembling Recognition Science meta-theorems cite this when verifying pattern products. The proof is a direct term reduction to a prior arithmetic lemma.

Claim. $2^{3} 45 = 360$

background

The CrossPatternMatrix module assembles a table of products among five RS patterns: D equals five, the eight-tick cube two to the three, J-cost zero, the golden ratio, and the gap of forty-five. The full-turn relation is the product of the eight-tick and the gap, listed explicitly as 360 in the matrix table. The upstream lemma twoCube_times_gap records the same multiplication by direct computation.

proof idea

The proof is a one-line term that applies the lemma twoCube_times_gap.

why it matters

This supplies the full-turn field inside CrossPatternMatrixCert and is referenced by cardinalitySpectrumCert. It realizes the eight-tick times gap cell in the wave-64 cross-domain meta-theorem, matching the eight-tick octave step in the forcing chain. No open questions are addressed.

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