OptimalConfig
plain-language theorem explainer
OptimalConfig packages a pair of positive radii whose combined J-cost is minimal over all alternatives while satisfying observability. Astrophysicists working on recognition-bounded stellar models cite it when extracting mass-to-light ratios from J-minimization. The structure directly encodes the universal minimization condition together with positivity and a simplified observability flag.
Claim. An optimal configuration consists of positive real numbers $r_m$ and $r_l$ such that $J(r_m,r_l) = J_m(r_m) + J_l(r_l)$ is minimal: $J(r_m,r_l) ≤ J(r_m',r_l')$ for every positive $r_m',r_l'$, with the configuration declared observable.
background
The module develops Strategy 3 for recognition-bounded observability. A stellar system is observable when photon flux exceeds the coherence energy divided by the fundamental tick and when mass assembly is limited by the recognition-length coherence volume. J_total is the sum of the separate J-mass and J-light costs; the structure OptimalConfig records the radii that achieve the global minimum of this sum under the observability constraint. Upstream, the Observable structure from RecognitionForcing supplies the cost interpretation of recognition events, while the scale definition from LargeScaleStructureFromRS supplies the phi-powered length ratios that later appear in the M/L derivation.
proof idea
The declaration is a bare structure definition with no proof body. It assembles four fields for the radii and their positivity, a trivial True flag for observability, and a single forall statement that directly expresses the minimization property over all positive alternatives.
why it matters
The structure supplies the formal carrier for the module's main claim that M/L belongs to the set of phi powers. It implements the J-cost minimization step that converts observability constraints into the phi-ladder relation, consistent with the Recognition Composition Law and the forced value of phi. The definition therefore sits between the general forcing chain (T5–T6) and the concrete astrophysical output that the sibling optimal_ratio_is_phi_power is expected to consume.
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