LiftingProgramCert
plain-language theorem explainer
LiftingProgramCert packages the three axioms that any intensity sequence on the phi-ladder must satisfy to serve as a certified lifting program. Strength-training researchers would cite it when formalizing canonical schemes such as 5x5 or 3x3 as integer-rung steps. The definition is realized by a downstream one-line constructor that supplies the positivity, geometric-ratio, and strict-decrease lemmas already proved for intensityAtRung.
Claim. A structure whose fields require that the intensity function $I(k)$ on natural-number rungs satisfies $I(k)>0$ for all $k$, $I(k+1)=I(k)/phi$ for all $k$, and $I(k+1)<I(k)$ for all $k$, where $I(k)$ is the explicit geometric sequence $I_0 phi^{-k}$ anchored at 1RM.
background
The phi-ladder is introduced via the upstream definition intensityAtRung k := referenceIntensity * phi^(-k), with rung 0 fixed at 100% of 1RM. This yields the predicted sequence 100%, 61.8%, 38.2%, 23.6% at successive rungs, matching the classical zones for 1RM, 3x3, 5x5, and deload work. The module applies the Recognition Science self-similar fixed point phi to program design, treating documented strength protocols as discrete steps on this ladder.
proof idea
The declaration is a structure definition that simply collects three properties of intensityAtRung. No tactics are used; the fields are populated by the downstream constructor liftingProgramCert, which directly invokes the lemmas intensityAtRung_pos, intensityAtRung_succ_ratio, and intensityAtRung_strictly_decreasing.
why it matters
LiftingProgramCert supplies the type for the canonical certificate that realizes the phi-ladder predictions inside the Sport domain. It is instantiated by liftingProgramCert and supports the claim that peer-reviewed strength schemes lie within half a rung of the canonical anchors. In the Recognition Science setting it shows how the forced constant phi generates discrete intensity steps that align with empirical training data, extending the T6 fixed-point result into applied program design.
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