IndisputableMonolith.Materials.Creep_Rate_RS
RS-native packaging of materials creep rate as a non-negative domain cost against a positive canonical threshold, with an inhabited certificate type. Materials theorists cite it when mapping continuum creep to the J-cost ledger. The module is mostly definitions and elementary positivity lemmas over Constants and Cost.
claimDefine a domain cost $C$ on the creep-rate parameter space, prove $C\ge 0$ and an evaluation identity, fix a canonical threshold $\theta>0$, and package a certificate $\mathrm{CreepRateCert}$ asserting the cost-threshold comparison in RS units.
background
Recognition Science measures mismatch by the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), imported here via the Cost module. Constants supplies the RS time quantum $\tau_0=1$ tick and the golden-ratio ladder used to nondimensionalize rates.
Creep is treated as a slow irreversible drift on that ladder: the module introduces a domain cost that scores how far a candidate creep rate sits from the self-similar fixed point, together with a single positive canonical threshold against which the cost is compared. The setting is continuum materials phenomenology rewritten in RS-native units ($c=1$, costs dimensionless on the $\phi$-ladder), not atomistic MD.
proof idea
Definition module with thin lemmas. domainCost is introduced and shown non-negative; domainCost_at_eq records the on-shell evaluation. canonicalThreshold is a positive constant (canonicalThreshold_pos). CreepRateCert bundles the cost-threshold inequality; cert and cert_inhabited supply a default witness. No deep forcing-chain argument; positivity and inhabitation are elementary from Cost and Constants.
why it matters in Recognition Science
Places ordinary creep-rate phenomenology on the same J-cost ledger as the T5 uniqueness and RCL identities, so materials claims can later attach to the eight-tick and $\phi$-ladder infrastructure. No downstream consumers are wired yet (used_by empty); the module is a materials-domain bridge waiting on continuum or experimental closure. It does not itself derive a numerical creep exponent from T0-T8.
scope and limits
- Does not derive a numerical creep exponent from the forcing chain T0-T8.
- Does not model atomistic mechanisms, dislocations, or temperature-activated barriers.
- Does not prove experimental agreement; only defines cost and certificate shape.
- Does not assert uniqueness of the canonical threshold beyond positivity.
- Does not connect yet to any downstream theorem (used_by is empty).