intensityAtRung
plain-language theorem explainer
The definition sets intensity at phi-ladder rung k to the unit reference scaled by phi to the power of negative k. Strength-training researchers cite it when mapping 5x5 or 3x3 schemes to integer steps on the Recognition Science ladder. It is a direct abbreviation that encodes geometric decay from the self-similar fixed point.
Claim. The intensity at rung $k$ on the phi-ladder is $I(k) = phi^{-k}$, where rung 0 corresponds to one-repetition maximum and the reference intensity equals the dimensionless unit 1.
background
The module develops a program-design layer on top of the phi-ladder, where intensities form a geometric sequence anchored at one-repetition maximum. Reference intensity is the RS-native dimensionless unit 1. Canonical schemes occupy specific rungs: rung 0 at 100 percent, rung 1 near 61.8 percent, rung 2 near 38.2 percent, and rung 3 near 23.6 percent.
proof idea
The declaration is a direct definition that multiplies the reference intensity by the real power phi to the negative k. No lemmas are invoked beyond the built-in exponentiation on the reals.
why it matters
This definition supplies the intensity function required by the LiftingProgramCert structure and its supporting theorems on positivity, strict decrease, and one-step ratio. It realizes the module's claim that classical 5x5 and 3x3 programs sit within half a rung of the phi-ladder anchors derived from the self-similar fixed point. The construction links the abstract ladder to concrete training protocols.
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