full_turn
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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