warm
plain-language theorem explainer
Constructs a high-temperature Gibbs policy on moral states and virtue actions: temperature fixed above 1, cost equal to the action energy cost. Anyone wiring RS thermodynamic exploration (soft actor-critic style) into the RS→RL bridge cites this as the warm/Hope regime. The body is a structure instance: assign temperature, discharge positivity by linear arithmetic, and plug in the energy-cost functional.
Claim. For every real $t>1$, there is a Gibbs policy with recognition temperature $T_R=t$ and cost $J(s,a)$ equal to the energy cost of the virtue-action $a$ (independent of state $s$). Temperature positivity holds automatically from $t>1$.
background
The RS→RL bridge treats Recognition Science as control theory: states are moral ledgers (bonds, skew, energy), actions are 14-coefficient combinations of virtue generators, and hard feasibility is enforced by projection onto the $\sigma=0$ set. Learning is thermodynamic rather than ad hoc: a Gibbs policy samples $p(a\mid s)\propto\exp(-J(s,a)/T_R)$.
A Gibbs policy package is three pieces: a positive recognition temperature $T_R$, the positivity witness, and a cost $J$ on (moral state, virtue action) pairs. High $T_R$ flattens the distribution and raises exploration mass; low $T_R$ concentrates on low-cost actions. The module ties the warm regime to the virtue Hope: nonzero support for exploratory moves.
Upstream constants fix the RS time quantum (one tick) and the eight-tick octave forced by T6 ledger closure; those set the cadence on which policies are evaluated, but the warm constructor itself only needs the Gibbs structure and the energy-cost map on virtue actions.
proof idea
Definitional structure instance, not a deep proof. Set temp_R to the supplied $t$. Discharge temp_pos ($0<T_R$) from the hypothesis $t>1$ by linarith. Set the cost field to the pure function that ignores the moral state and returns VirtueAction.energyCost of the action. No lemmas beyond arithmetic positivity are required.
why it matters
Gives the concrete high-temperature endpoint of the RS thermodynamic policy family inside the RS→RL bridge. Together with the Gibbs structure (soft-max / maximum-entropy form grounded in the RS cost $J$), it operationalizes exploration as Hope: support stays positive on non-greedy virtue actions when $T_R>1$.
It sits beside the eight-tick cadence section (undiscounted 8-tick windows from T6 minimality) and the lexicographic selector (feasible → harm-minimax → value → robustness). Downstream consumers that need a ready-made exploratory policy can instantiate warm t ht rather than hand-building Gibbs fields. No used-by edges are recorded yet; the declaration is infrastructure for later policy theorems and audits in the RecognitionStabilityAudit stack.
Framework landmarks: thermodynamic form $p\propto e^{-J/T_R}$ is the RS analogue of soft actor-critic; temperature is a strictness parameter, not a free RL hyperparameter invented outside the theory.
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