IndisputableMonolith.Linguistics.SwadeshListDecayRate
This module defines the reference core-vocabulary replacement rate and rung-dependent variants for Swadesh lists in RS-native units. Linguists modeling language evolution under Recognition Science cite these objects when tying decay rates to the time quantum and phi-ladder. It supplies referenceRate together with rateAtRung, positivity, monotonicity, and ratio lemmas. The module consists entirely of definitions and elementary properties.
claimLet $\tau_0 = 1$ tick be the fundamental time quantum. The reference core-vocabulary replacement rate $r_{\rm ref}$ is defined in RS-native units; the rung-dependent rate is the function $r(r)$ that scales $r_{\rm ref}$ according to position on the phi-ladder, with adjacent ratios and strict increase established as basic properties.
background
The module sits in the linguistics domain of Recognition Science and imports only Constants. Constants supplies the single primitive $\tau_0 = 1$ tick, the RS-native time quantum. The module then introduces referenceRate as the baseline replacement rate for core Swadesh vocabulary together with rateAtRung(r) and the supporting facts rateAtRung_pos, rateAtRung_succ_ratio, rateAtRung_strictly_increasing, and rate_adjacent_ratio.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The rate objects defined here supply the quantitative foundation for SwadeshDecayCert and swadeshDecayCert inside the same module. They connect linguistic decay directly to the time quantum from Constants, allowing later integration with the phi-ladder and forcing-chain results of the broader framework.
scope and limits
- Does not calibrate rates against observed language data.
- Does not treat non-core vocabulary or syntax decay.
- Does not derive the reference rate from the J-function or RCL.
- Does not address cross-linguistic variation beyond the RS-native definition.