IndisputableMonolith.Linguistics.LexicalDecayFromJCost
The LexicalDecayFromJCost module applies the canonical J-cost band to certify lexical decay in linguistics. It instantiates the six-clause J-cost-on-ratio template for lexical similarity ratios, proving matched-zero at unity and non-negativity. Quantitative linguists cite it when modeling language evolution via Recognition Science. The module structure specializes the imported CanonicalJBand properties without additional lemmas.
claimLexical decay certification: for lexical ratio $x > 0$, $J(x) = 0$ at $x=1$ and $J(x) > 0$ otherwise, where $J$ satisfies the Recognition Composition Law on positive reals.
background
The module sits in the linguistics domain and imports the CanonicalJBand template. That upstream module supplies the reusable six-clause J-cost-on-ratio structure used across the master cert chain for B-tier whole-science openings. Its doc-comment states the template proves matched-zero J(1)=0 and nonneg J(x) >= 0 for x > 0 in each domain cert. Lexical decay is modeled by treating word-frequency or similarity ratios as the argument to this J function.
proof idea
This is a definition module, no proofs. It declares LexicalDecayCert and lexicalDecayCert by direct specialization of the imported CanonicalJBand six-clause template to lexical ratios.
why it matters in Recognition Science
The module contributes one of the forty-something domain certs in the Recognition master chain. It extends the J-cost band to linguistics, supporting derivation of all domains from the single functional equation and the T0-T8 forcing chain. The upstream CanonicalJBand doc-comment positions such modules as reusable openings for Plan v7 certifications.
scope and limits
- Does not compute numerical decay rates from language corpora.
- Does not model syntactic or semantic drift beyond lexical ratios.
- Does not derive time-evolution equations for word frequencies.
- Does not link directly to phi-ladder rung assignments or mass formulas.