cooperatorThreshold
plain-language theorem explainer
cooperatorThreshold defines the minimum cooperator fraction for an evolutionarily stable strategy in a kin-selected population as the reciprocal of the golden ratio. Game theorists in the Recognition Science framework cite it when reframing Hamilton's rule as the condition cooperator_fraction ≥ 1/φ. The definition is a direct assignment drawing on the phi constant from the foundational layer.
Claim. The cooperator-fraction threshold for an evolutionarily stable strategy is given by $1/φ$, where $φ$ is the golden ratio.
background
The module on Evolutionarily Stable Strategies from σ-Conservation treats an ESS as a strategy that, once adopted by the majority, cannot be invaded by a rare mutant. cooperatorThreshold supplies the value 1/φ, while the sibling predicate isESS(cooperator_fraction) asserts that the fraction meets or exceeds this threshold. This setup reframes Hamilton's rule r > c/b as cooperator_fraction ≥ 1/φ in RS-native units.
proof idea
The declaration is a direct definition that assigns cooperatorThreshold to the reciprocal of phi. No lemmas or tactics are invoked beyond the assignment itself.
why it matters
This definition supplies the numerical threshold that appears in isESS and the master certificate ESSFromSigmaCert, which records that the all-cooperator strategy is ESS while the no-cooperator strategy is not. It anchors the game-theory module to the Recognition Science constant phi and feeds directly into cascadeThreshold and full_cooperation_cascades in the CooperationCascade module.
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