LexicalDecayCert
plain-language theorem explainer
LexicalDecayCert is a structure that wraps a CanonicalCert to certify lexical decay rates derived from J-cost on word-frequency persistence ratios. Linguists modeling language evolution via Pagel et al. half-lives would cite it to anchor decay on the phi-ladder within the canonical J-band. The declaration is a minimal structure definition that reuses the six-clause CanonicalCert without additional clauses.
Claim. A lexical decay certificate is a structure containing a base CanonicalCert, where CanonicalCert asserts $J(1)=0$, $J(x)=J(1/x)$ for $x≠0$, $J(φ)>0$ with $0.11<J(φ)<0.13$, and $J(1/φ^2)>0$.
background
The module addresses F4 on lexical decay rate from J-cost on word-frequency persistence. Per-word J-cost is applied to the ratio r of observed frequency over expected frequency under Zipf, with lexical decay rate (half-life replacement) structurally permitted at the canonical band on the persistence ratio. It compounds with PhonemeInventoryBound and LexiconRatio modules. CanonicalCert from CanonicalJBand supplies the six-clause J-function certificate reused here: matched_zero J(1)=0, reciprocal symmetry, phi_pos J(phi)>0, phi_band bounds, and recovery_pos J(1/phi^2)>0. The upstream LexicalDecayCert from LexicalDecayFromPhiLadder adds phi_ratio halfLife(k+1)/halfLife(k)=phi together with phi^5 bounds in (10,12).
proof idea
The declaration is a one-line structure wrapper that requires only a base CanonicalCert from the CanonicalJBand module.
why it matters
This structure supplies the J-cost base for lexical decay certificates, feeding the lexicalDecayCert definition in the same module and the phi-ladder version in LexicalDecayFromPhiLadder. It fills the F4 step by connecting word-frequency persistence to the phi-ladder and J-uniqueness. It touches the open empirical question of validation against reconstructed proto-languages with measured Swadesh-list half-lives.
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