IndisputableMonolith.Linguistics.LexicalDecayFromJCost
The module applies the J-cost band template to lexical decay in linguistics. Quantitative linguists modeling word frequency evolution via recognition cost would cite it. The structure reuses the six-clause matched-zero and nonnegativity template imported from CanonicalJBand.
claimLexical decay certificate: for all ratios $r > 0$, $J(r) = 0$ when $r = 1$ and $J(r) = (r + r^{-1})/2 - 1$ satisfies $J(r) >= 0$.
background
The module operates in the linguistics domain of Recognition Science. It imports the Canonical J-Cost Band, whose doc-comment states: 'The six-clause J-cost-on-ratio template is used across the master cert chain (B-tier whole-science openings, the Plan v7 forty-something domain certs).' Each domain cert proves matched-zero J(1)=0 and nonneg J(x)>=0 for x>0. The module specializes this template to lexical items by treating word ratios as the argument to J.
proof idea
This is a definition module, no proofs. It declares LexicalDecayCert and lexicalDecayCert by instantiating the imported six-clause template on the lexical decay ratio.
why it matters in Recognition Science
This module feeds the linguistics domain cert within the master cert chain. It fills one of the B-tier whole-science openings by deriving lexical decay from J-cost, connecting to T5 J-uniqueness and the Recognition Composition Law. The upstream doc-comment notes its reuse across the Plan v7 domain certs.
scope and limits
- Does not validate against language corpora or frequency data.
- Does not address syntax, semantics, or grammar beyond lexical items.
- Does not derive numerical decay exponents outside the J function.
- Does not treat cross-linguistic or diachronic variations.