pith. sign in
theorem

eight_dvd_360

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.RSConstants
domain
NumberTheory
line
168 · github
papers citing
none yet

plain-language theorem explainer

The declaration establishes that 8 divides 360. Researchers assembling Recognition Science constants cite it as a stable anchor that keeps repeated arithmetic out of bridge lemmas. The proof is a one-line decision procedure that confirms the relation directly.

Claim. $8$ divides $360$.

background

The module collects small decidable arithmetic facts on integers that recur in the reality repo, such as 8, 45, 360, 840 and the prime markers 11, 17, 37, 103, 137. These serve as boring but stable anchors that keep later bridge lemmas readable and avoid re-proving the same arithmetic in many places. The local setting is RS constants (prime facts and factorizations).

proof idea

The proof is a one-line wrapper that invokes the decide tactic to verify the divisibility statement directly.

why it matters

This fact anchors arithmetic inside the RSConstants module and supports factorizations involving 360 that appear in Recognition Science calculations. It aligns with the eight-tick octave structure (period 2^3) by confirming divisibility by 8. No downstream theorems are listed; the result is fully proved and closed.

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