referenceRate
referenceRate defines the base core-vocabulary replacement rate as the real number 1 in RS-native units. Linguists extending Pagel et al. (2007) decay estimates within the Recognition Science phi-ladder model would cite this constant to scale rates across rungs. The definition is a direct constant assignment with no further computation.
claimThe reference core-vocabulary replacement rate satisfies $r_0 = 1$ in RS-native units.
background
The Swadesh-List Decay Rate module places core vocabulary at rung 0 on the phi-ladder, with replacement rates increasing by successive factors of phi for environmental nouns (rung 1) and verbal periphery (rung 2). This structure reproduces the observed peripheral-to-core ratio of roughly 5-10 over two steps, since phi squared is approximately 2.618. Upstream rung definitions in RSBridge.Anchor and Masses.AnchorPolicy assign integer levels to categories such as fermions or ore classes, supplying the discrete steps used throughout the framework.
proof idea
The declaration is a one-line constant definition that directly assigns the real number 1.
why it matters in Recognition Science
It supplies the base value for rateAtRung, which defines the replacement rate at rung k as referenceRate multiplied by phi to the power k, and for the positivity theorem rateAtRung_pos. This anchors the linguistic application of the phi self-similar fixed point (T6) and the eight-tick octave structure, allowing decay predictions to sit on the same ladder used for mass and particle assignments.
scope and limits
- Does not derive the value 1 from empirical calibration.
- Does not convert the rate to calendar or physical time units.
- Does not apply to non-core or non-Swadesh vocabulary.
- Does not prove monotonicity or other rate properties.
Lean usage
def rateAtRung (k : ℕ) : ℝ := referenceRate * phi ^ kformal statement (Lean)
37def referenceRate : ℝ := 1
proof body
Definition body.
38
39/-- Replacement rate at φ-ladder rung `k` (higher rung = faster). -/