IndisputableMonolith.Foundation.MaximalForcing.RSCostUniverse
Packages the cost-function layer of Maximal Forcing: admissible recognition costs F : ℝ → ℝ under the five Law-of-Logic gates, base and cost universes L₀ and L_cost, and the forced claim that the unique cost is J. Foundation work cites it when wiring T5 uniqueness into the reality-closure certificate. Structure is definitional universes plus classifier lemmas routed through CostUniqueness and Aczél smoothness.
claimA candidate cost $F:\mathbb{R}\to\mathbb{R}$ is admissible when it satisfies the five gate conditions the Law of Logic imposes on any recognition cost. The cost universe is the forcing universe obtained by adjoining the claim that $F=J$, where $J(x)=\frac{x+x^{-1}}{2}-1$ on $\mathbb{R}_+$, to a base layer $L_0$. The module records that this is-$J$ claim lies in the reality closure, is forced, and is invariant, and supplies a classifier certificate for that universe.
background
Recognition Science forces the recognition cost from functional axioms rather than fitting it. The unique target is $J(x)=\cosh(\log x)-1=\frac{x+x^{-1}}{2}-1$ on $\mathbb{R}_+$ (forcing step T5). Upstream CostUniqueness states the consolidated theorem: any $F$ with symmetry, unit normalization, strict convexity, and calibration equals $J$ on the positive reals. Aczél smoothness supplies the analytic bootstrap: continuous solutions of the d'Alembert equation $H(t+u)+H(t-u)=2H(t)H(u)$ with $H(0)=1$ are $C^\infty$ (in fact real analytic), which underwrites the regularity side of uniqueness.
This module sits in Maximal Forcing. RealityClosure is the crown interface: it does not assert the final theorem, but states the certificate shape $\forall C\in\mathrm{ForcingClosure}(P,U),,\mathrm{ClaimClassification}(U,C)$. The cost layer is the fragment of that program that treats candidate costs as claims inside a universe, with admissibility as the gate predicate and $L_0\subseteq L_{\mathrm{cost}}$ as the ambient layers.
proof idea
Definition-and-classifier module, not a single deep proof. It introduces CostAdmissible (the five-gate predicate on $F$), the base layer $L_0$ and cost layer $L_{\mathrm{cost}}$, and a tightening map relating them. The is-$J$ claim is packaged as a forcing claim; costUniverse is the corresponding universe. Lemmas then place that claim in the reality closure, record that it is forced and invariant, and emit a classifier certificate. Uniqueness content is imported from CostUniqueness (T5) and regularity from AczélProof; local work is universe bookkeeping and claim classification rather than a fresh functional-equation argument.
why it matters in Recognition Science
Closes the cost-function slot inside Maximal Forcing so the reality-closure certificate can treat "the cost is $J$" as a classified, forced claim rather than an external hypothesis. That is exactly T5 (J-uniqueness) in universe form, aligned with the Recognition Composition Law and the forcing chain. Downstream consumers are closure and classifier constructions in the Maximal Forcing program (RealityClosure's certificate interface); this module has no further used_by edges yet, so it is a leaf supplier of the cost-universe certificate. Without it, the crown closure would still carry an unclassified cost axiom.
scope and limits
- Does not re-prove J-uniqueness; imports CostUniqueness (T5).
- Does not assert the full Maximal Forcing crown theorem; only the cost-universe certificate fragment.
- Does not treat non-admissible or discrete costs outside the five Law-of-Logic gates.
- Does not derive dimensional, octave, or coupling constants (T6–T8, alpha).
- Does not supply numerical calibration of physical units beyond the abstract J form.