IndisputableMonolith.Linguistics.LexicalDecayFromPhiLadder
The module supplies definitions for lexical decay in Recognition Science linguistics, grounding half-lives and decay ratios in the phi ladder. It certifies decay via bounds on phi^5 together with a predicate LexicalDecayCert. Quantitative linguists modeling vocabulary evolution would cite these objects. The module is a pure definition block that imports the base constants module and declares the halfLife family without proofs.
claim$halfLife : Nat → Real$, $halfLifeRatio : Real$, $phi^5 > 10$, $phi^5 < 12$, and $LexicalDecayCert$ a predicate asserting that lexical frequency decay follows the phi-ladder scale with half-life proportional to $phi^5 τ_0$.
background
The module lives in the linguistics domain and imports the fundamental RS time quantum $τ_0 = 1$ tick from IndisputableMonolith.Constants. It introduces halfLife as the characteristic time for lexical item frequency to drop by a factor of two and halfLifeRatio as the corresponding scaling factor derived from the phi ladder. The sibling declarations phi5_gt_10 and phi5_lt_12 supply the numerical bounds that place $phi^5$ inside (10,12), mirroring the Z_cf interval used elsewhere in the framework for self-similar scaling.
proof idea
This is a definition module, no proofs. It declares the halfLife and halfLifeRatio functions, the two phi^5 inequalities, and the LexicalDecayCert predicate that packages them into a single certification object.
why it matters in Recognition Science
The module extends the phi-ladder machinery (T6 fixed-point and mass-formula yardstick) into linguistics, supplying the lexical-decay objects that later results in the domain would cite. It closes the gap between the core constants and domain-specific decay rates without introducing new hypotheses.
scope and limits
- Does not derive the phi^5 bounds from the forcing chain.
- Does not compute numerical half-lives for concrete languages.
- Does not address semantic change beyond frequency decay.
- Does not connect to the RCL or J-cost functions.