step
plain-language theorem explainer
Atomic one-step act in the RS→RL bridge: take a 14-coefficient virtue action, project it onto the σ=0 feasible set by least-action completion, then audit the projected action against the current moral state. Anyone building a Recognition-native control or RL loop cites this as the environment transition. The body is a two-line compose of the environment projector and lexicographic selector.
Claim. Given an RS environment (initial moral state, LACompletion projector, lexicographic selector, Gibbs policy), a moral state $s$, and a virtue action $a$ (14 real coefficients on the virtue generators), return the audit result of first projecting $a$ onto the $\sigma=0$ feasible set, then evaluating that projected action at $s$. The audit records post-action skew, max harm, value $V$, spectral gap, and $\varphi$-tier.
background
The module casts Recognition Science as control theory for RL: states are lightweight moral states (reciprocity skew $\sigma$, energy budget, value $V=\kappa\cdot I(A;E)-C_{J^*}$, max harm, spectral gap); actions are coefficient vectors on the 14 virtue generators (DREAM: complete minimal admissible set). Hard physics is enforced by LACompletion, a propose-then-project map that sends an unconstrained virtue direction onto the $\sigma=0$ manifold while minimizing added $J$-cost.
RSEnvironment bundles initial state, that projector, a lexicographic multi-objective selector (feasible → harm-minimax → value → robustness), and a Gibbs policy $p(a|s)\propto\exp(-J(s,a)/T_R)$. Evaluation returns an AuditResult packing the quantities the selector ranks. Cadence is undiscounted eight-tick windows (T6/T7), not an arbitrary discount factor.
Upstream, the name step also appears in the primitive recognition calculus as one-step trace extension by $\delta$; here it is the RL-facing analogue: apply one admissible (projected) act and read the audit.
proof idea
Definition, not a proof. Bind projected := env.projector.project a (LACompletion onto the feasible set), then return env.selector.evaluate s projected. No lemmas; pure composition of the two environment fields named in the doc-comment (project, then audit).
why it matters
This is the environment step that separates creativity from physics in the RS→RL design: the policy may propose any virtue coefficients; LACompletion enforces $\sigma=0$; the selector scores the feasible act. It operationalizes the module's claim that RS is already a specified control theory (state, admissible generators, hard constraints, multi-objective order, thermodynamic exploration).
It sits under the eight-tick cadence forced by T6/T7 and under the DREAM completeness of the 14 virtues. Downstream training loops, Gibbs sampling of actions, and lexicographic selection all route through this transition. Graph used_by edges into unrelated physics lemmas are name-collision noise; the real consumers are the RStoRL policy and audit machinery built on RSEnvironment.
Open surface: LACompletion.preserves_feasibility is still a placeholder True, so the step assumes projection semantics that the formal dynamics have not yet discharged.
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