injuryTipPoint_gt_one
plain-language theorem explainer
The tip point for injury risk in the J-cost workload model lies strictly above one. Sports physiologists applying Recognition Science to acute-chronic workload ratios would cite this to confirm the departure from the balanced state. The proof reduces directly to the known inequality for the golden ratio via a single term application.
Claim. Let $τ$ be the acute-to-chronic workload ratio at which J-cost equals the canonical recognition quantum. Then $1 < τ$.
background
The module models athletic injury risk via J-cost on the acute:chronic workload ratio. J-cost is the derived cost of a multiplicative recognizer on positive ratios, equivalently the cost of any recognition event. The canonical arithmetic object supplies the initial Peano structure for any realization. Upstream, the lemma one_lt_phi establishes the inequality 1 < phi, while cost definitions appear in the observer forcing and multiplicative recognizer layers.
proof idea
The proof is a one-line term wrapper that applies the lemma one_lt_phi.
why it matters
This theorem supplies the tip_gt_one field to the InjuryRiskCert definition. It anchors the RS prediction that the injury threshold occurs at phi, consistent with the forcing chain from T5 J-uniqueness through T8 and the recognition composition law. The module doc identifies the falsifier as any large-N cohort study placing the ACWR inflection outside (1.4, 1.9).
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