pith. sign in
theorem

aliasing_ratio

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.RSConstants
domain
NumberTheory
line
66 · github
papers citing
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plain-language theorem explainer

The inequality 37/45 < 1 holds in the rationals and functions as a stable arithmetic anchor inside the RSConstants module. Researchers deriving prime factorizations or bridge lemmas in Recognition Science cite it to avoid re-verifying the same decidable fact. The proof is a direct one-line term application of norm_num.

Claim. In the rational numbers, $37/45 < 1$.

background

The module collects small, decidable arithmetic facts about integers that recur in the reality repo, including 8, 45, 360, 840 and the prime markers 11, 17, 37, 103, 137. These facts are treated as boring but stable anchors that keep later bridge lemmas readable without repeated arithmetic. The upstream structure as encodes the Laplacian action on a simplicial complex via the identification (1/2) Σ w_ij (ε_i − ε_j)² = (1/κ) Σ δ_h A_h.

proof idea

The proof is a one-line term proof that applies norm_num to discharge the rational inequality.

why it matters

The result supplies a basic inequality anchor inside the RS constants collection, supporting derivations that involve the prime 37 and related factorizations such as those appearing in the eight-tick octave. It contributes to the stable arithmetic base that later bridge lemmas rely on, consistent with the module's role of avoiding re-proofs of the same small facts.

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