EnduranceThreshold
plain-language theorem explainer
EnduranceThreshold defines the fatigue endurance limit as the J-cost evaluated at the golden ratio phi. Materials researchers modeling S-N curves or Basquin's law under cyclic loading would cite this constant to mark the transition between infinite-life and finite-life regimes. The declaration is a direct one-line abbreviation that applies the Jcost evaluator from the core Cost quantity to phi.
Claim. The endurance threshold is defined by $EnduranceThreshold := Jcost(phi)$, where $Jcost$ is the recognition cost function on the dimensionless stress ratio and $phi$ is the golden ratio.
background
In the Recognition Science treatment of materials fatigue, cyclic loading is modeled via the dimensionless stress ratio $r :=$ observed stress over yield stress. The recognition cost $J(r)$ vanishes at $r=1$ and is strictly positive for $r<1$, accumulating per cycle. The endurance limit is identified with the golden-section value $J(phi)$ lying in the interval $(0.11,0.13)$ that separates infinite-life from finite-life behavior.
proof idea
This is a one-line definition that directly applies the Jcost evaluator from the Cost quantity to the constant phi.
why it matters
The definition supplies the canonical threshold referenced by the endurance_threshold_band theorem that certifies the interval $0.11 < EnduranceThreshold < 0.13$ and by the FatigueThresholdCert structure that collects yield-zero, reciprocal symmetry, and non-negativity properties. It places materials fatigue on the same footing as other RS-governed processes such as plaque vulnerability and magnetic reconnection, consistent with the J-uniqueness and phi fixed-point steps of the forcing chain. The module doc notes the shared quantum across pathology, combustion, and plasma.
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