IndisputableMonolith.Applied.UniversalEquilibriumResponseC7
The module applies the local J-cost expansion at equilibrium points to define universal response structures in the Recognition Science framework. It introduces EquilibriumDomain as the setting for equilibrium points, responseCoefficient as the normalized sensitivity, and UniversalResponseCert as the certification of the universal form. Researchers modeling self-similar equilibrium systems would cite these for applied calculations. The module consists of definitions and a certification structure built directly on the imported algebraic kernel.
claimFor equilibrium domain $D$, the response coefficient satisfies responseCoefficient$(D) = 1/2$ in the normalized limit, certified by UniversalResponseCert via the kernel $J(1 + eps) = eps^2 / (2(1 + eps))$.
background
The module operates in the Recognition Science applied layer, where physics follows from the single J-functional equation and its derived structures. The upstream JCostHessianC7 result supplies the exact local algebraic kernel $J(1 + eps) = eps^2 / (2(1 + eps))$, which is stronger than a second-order Taylor expansion away from $eps = -1$. EquilibriumDomain collects points satisfying the equilibrium condition, responseCoefficient normalizes the second variation of J-cost, and equilibriumDomain_count enumerates instances within the domain.
proof idea
This is a definition module, no proofs. It structures the argument by importing the C7 kernel, defining EquilibriumDomain and responseCoefficient, providing the universal variant, and packaging the certification as UniversalResponseCert.
why it matters in Recognition Science
This module supplies the applied equilibrium layer that connects the C7 local expansion to higher Recognition Science constructions such as the phi-ladder and eight-tick octave. It fills the universal response slot in the applied domain and prepares for downstream use in mass formulas and Berry thresholds, though no used_by edges are recorded yet.
scope and limits
- Does not derive the J-cost kernel itself.
- Does not extend the expansion beyond the local neighborhood of eps = 0.
- Does not compute numerical values or apply specific constants.
- Does not address non-equilibrium or time-dependent cases.