log_15p83_lower_hypothesis
plain-language theorem explainer
This definition encodes the numerical hypothesis that log(1 + 24/φ) exceeds 2.7613 with φ approximated as 1.618034. Analysts establishing tight bounds on the structural residue gap(24) in the Recognition mass framework cite it to anchor the interval (5.737, 5.74). The declaration is a direct constant comparison with no lemmas or tactics applied.
Claim. The proposition asserts that $2.7613 < log(1 + 24/φ)$ where $φ ≈ 1.618034$.
background
The module supplies Lean-verified properties of the gap function gap(Z) = log(1 + Z/φ) / log φ, the zero-parameter Recognition-side residue f^Rec used in the mass ladder. This hypothesis supplies a concrete lower bound on log(1 + 24/φ) to support interval estimates for gap(24). It draws on the Hypothesis structure from ClassicalBridge.Fluids.CPM2D, which bundles constants and functionals enforcing projection-defect and energy-control inequalities for Galerkin models, and the for structure from UniversalForcingSelfReference that records meta-realization coherence properties.
proof idea
The declaration is a direct definition of the Prop as the stated real-number inequality; it applies no lemmas and requires no tactics.
why it matters
This hypothesis is invoked by the lemma gap_24_bounds to establish that 5.737 < gap(24) < 5.74. It contributes to verification of the phi-ladder mass formula by providing numerical control on the residue at Z=24, consistent with the eight-tick octave and D=3 dimensions from the forcing chain. The bound remains a numerical anchor rather than an algebraic identity derived from the Recognition Composition Law.
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