IndisputableMonolith.Skeleton.Cost
Skeleton packaging for the Recognition cost layer: T5 J-uniqueness helpers plus the d'Alembert factorization gate that forces affine combiners. Anyone tracing cost uniqueness into B2 algebraic closure cites this layer. It is an import-aggregation module, not a theorem body.
claimThe cost skeleton assembles the $J$-cost functional-equation toolkit for T5 uniqueness together with the factorization-and-associativity gate: factorization plus three-way compatibility imply the combiner is affine in its second argument.
background
Recognition Science forces the cost functional $J$ uniquely (forcing step T5): $J(x)=(x+x^{-1})/2-1$, equivalently $\cosh(\log x)-1$, via the Recognition Composition Law $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$. The imported FunctionalEquation module supplies the lemma surface used in that uniqueness argument.
Separately, the B2 closure program needs an algebraic gate: once a combiner factors and satisfies three-way compatibility, it must respond affinely in its second argument; remaining forcing is then pure algebra. FactorizationForcing formalizes that gate.
Skeleton.Cost sits in the Skeleton domain and wires these two upstream modules into one cost-facing entry point for downstream skeleton constructions.
proof idea
This is a module shell, not a proof. It imports Cost.FunctionalEquation (T5 helper lemmas) and Foundation.DAlembert.FactorizationForcing (factorization-to-affine gate). No local theorems or sorry stubs are declared at the module boundary; argument structure lives in the imported files.
why it matters in Recognition Science
Gives the Skeleton layer a single cost handle tying T5 J-uniqueness to the B2 factorization/associativity program. Downstream skeleton developments that need either the cost functional equation surface or the affine-combiner forcing can depend here rather than reaching into Foundation and Cost separately. Lands on the forcing chain at T5 and on the hard analytic-to-algebraic step of B2 closure described in FactorizationForcing: once affinity is forced, the rest is algebra. No direct used_by edges are recorded at this module node.
scope and limits
- Does not prove T5 J-uniqueness; that lives in the FunctionalEquation and forcing-chain developments.
- Does not itself derive affinity of the combiner; it only imports FactorizationForcing.
- Does not fix numerical constants (c, hbar, G, alpha) or mass-ladder formulae.
- Does not assert D=3, eight-tick structure, or phi fixed-point results (T6–T8).
- Does not expose a single canonical theorem API at the module boundary.