cool
plain-language theorem explainer
Constructs a cool Gibbs policy at recognition temperature t in (0,1], biasing the thermodynamic action law toward exploitation. Anyone wiring RS virtue costs into soft-max RL cites this factory. The body is a three-field structure fill-in: temperature t, positivity from the hypothesis, and cost equal to virtue energy cost.
Claim. Given $t\in\mathbb{R}$ with $0<t\le 1$, the cool policy is the Gibbs policy with recognition temperature $T_R=t$ and cost $J(s,a)$ equal to the energy cost of the virtue-action $a$.
background
The RS→RL bridge treats Recognition Science as control theory: moral states, fourteen virtue generators as admissible actions, σ=0 feasibility via propose-then-project, and thermodynamic selection. The Gibbs policy is the RS form $p(a|s)\propto\exp(-J(s,a)/T_R)$, the same soft-max law as maximum-entropy RL but with the RS cost $J$ rather than an engineered reward.
Recognition temperature $T_R$ is the strictness parameter. Low $T_R$ concentrates mass on low-cost actions (exploitation); high $T_R$ flattens the distribution (exploration). The cost field here is the in-module virtue energy cost on (MoralState, VirtueAction) pairs, tying the policy to the ledger/bond energy already used by the moral-state machinery.
Upstream cost notions (observer J-cost on recognition events, multiplicative-recognizer derived cost, rung-coarsen totals) all instantiate the same J-family; this definition simply plugs the virtue-level energy cost into the Gibbs structure.
proof idea
Definitional constructor, not a proof. The three structure fields of a Gibbs policy are filled directly: temp_R is the supplied $t$, positivity is the hypothesis $0<t$, and the cost map ignores the state argument and returns the virtue-action energy cost. No lemmas are invoked.
why it matters
Gives the low-temperature endpoint of the RS thermodynamic learning stack in this module: cool policies exploit the virtue basis under the energy cost, complementary to the warm (high-$T_R$) policy that keeps exploration support (Hope). That pair operationalizes the module's Gibbs layer beside LACompletion and the lexicographic selector.
Downstream, gravity-candidate geometry (Searl geometric resonance) references entropic cooling as an RS falsifier for devices that must shed heat while ordering; the cool-policy constructor is the control-side counterpart of that cooling language. Framework landmarks: the eight-tick cadence (T6/T7) still governs evaluation windows; this definition only sets the temperature and cost of the Gibbs kernel, not the cadence itself.
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