IndisputableMonolith.Linguistics.SwadeshListDecayRate
This module defines the reference core-vocabulary replacement rate in RS-native units along with rung-dependent scalings and a decay certificate. Historical linguists working in the Recognition Science framework would cite it to quantify Swadesh list evolution rates. It is a pure definition module that introduces referenceRate, rateAtRung and SwadeshDecayCert without any proof obligations.
claimThe module supplies the reference replacement rate $r_0$ (RS-native) and the rung-dependent rate $r(n)$ together with the certificate SwadeshDecayCert for core-vocabulary decay.
background
The module imports the RS time quantum from Constants, where τ₀ equals one tick. It introduces referenceRate as the base core-vocabulary replacement rate expressed in these native units. Further definitions include rateAtRung, which scales the reference by position on the phi-ladder, together with positivity and monotonicity statements rateAtRung_pos and rateAtRung_strictly_increasing. The SwadeshDecayCert type packages these rates into a certified decay model.
proof idea
This is a definition module, no proofs. The structure proceeds by declaring referenceRate, then defining rateAtRung and its adjacent-ratio and strictly-increasing properties, and finally packaging the results into the SwadeshDecayCert and its constructor swadeshDecayCert.
why it matters in Recognition Science
The module supplies the RS-native rate constants required for any linguistic application of the Recognition framework. It extends the same phi-ladder and time-quantum structure used in the T0-T8 forcing chain to language data, providing the base for SwadeshDecayCert. No downstream theorems are recorded yet, but the definitions close the interface between the Constants module and future linguistics results.
scope and limits
- Does not incorporate empirical word-frequency data.
- Does not model borrowing or language contact.
- Does not address non-core vocabulary.
- Does not calibrate rates against historical corpora.