IndisputableMonolith.Materials.Creep_Rate2FromJCost
Materials module that packages a second creep-rate certificate from the RS J-cost. It defines a nonnegative domain cost on the positive reals, a positive canonical threshold, and an inhabited CreepRate2Cert record tying those quantities together. Materials theorists working in the RS stack would cite it when they need a cost-derived creep bound rather than an empirical Arrhenius fit. The file is mostly definitions plus elementary nonnegativity and positivity lemmas.
claimOn the positive reals, a domain cost $C$ is defined from the RS $J$-cost, satisfying $C\ge 0$. A canonical threshold $\theta>0$ is fixed. The module assembles an inhabited certificate $\mathrm{CreepRate2Cert}$ asserting that the second creep-rate quantity is controlled by $C$ relative to $\theta$.
background
Recognition Science measures mismatch by the unique cost $J(x)=(x+x^{-1})/2-1$ on $x>0$, forced by the Recognition Composition Law and the T5 uniqueness step. The Cost import supplies that functional; Constants supplies the RS tick $\tau_0=1$ used as the native time unit in rate statements.
Creep is slow plastic flow under sustained load. In the RS materials layer the idea is to replace phenomenological rate laws by thresholds and costs built from $J$, so that activation and rate scales sit on the same $\phi$-ladder as the rest of the monolith.
This module introduces a domain cost (a $J$-derived nonnegative function on the positive reals), records its value at equality cases, proves nonnegativity, and fixes a strictly positive canonical threshold against which a second creep-rate certificate is stated.
proof idea
Definition-heavy module, not a deep derivation. domainCost is introduced from the Cost layer; domainCost_at_eq and domainCost_nonneg are short algebraic or order facts. canonicalThreshold is a positive constant definition; canonicalThreshold_pos is the positivity witness. CreepRate2Cert is a structure bundling those pieces; cert and cert_inhabited supply a concrete inhabitant so downstream code can treat the certificate as available data rather than an open Prop.
why it matters in Recognition Science
Places a second creep-rate certificate inside the Materials domain of the monolith, grounded in $J$-cost rather than fitted activation energies. No downstream used_by edges are recorded yet, so the module currently acts as a leaf certificate provider for materials arguments that want an RS-native rate bound. It sits downstream of Constants and Cost only, and does not itself close a T0–T8 forcing step; its role is applied: export a reusable CreepRate2Cert once the domain cost and threshold are fixed.
scope and limits
- Does not derive a continuum PDE or dislocation-dynamics model of creep.
- Does not claim numerical match to a specific alloy dataset.
- Does not force the threshold from T5–T8; threshold is module-canonical.
- Does not supply temperature or stress dependence beyond the J-cost packaging.
- Does not close any open forcing-chain or alpha-band obligation.