IndisputableMonolith.Materials.CreepFromPhiLadder
Materials module that packages creep as a phi-ladder cost phenomenon: a nonnegative domain cost vanishing at equilibrium, a positive canonical threshold, and an inhabited CreepCert bundle. Materials theorists in RS cite it when linking slow plastic flow to discrete rung hops rather than continuum viscosity. The file is mostly definitions and elementary positivity/equilibrium lemmas over the shared Cost and Constants imports.
claimIn RS-native units, a domain cost $C$ is a nonnegative real functional with $C=0$ at equilibrium; a canonical threshold $\theta>0$ marks the onset of creep; a creep certificate packages $(C,\theta)$ so that slow deformation is read as discrete $\varphi$-ladder hops once $C$ exceeds $\theta$.
background
Recognition Science treats materials response as ledger imbalance on the self-similar $\varphi$-ladder rather than as continuum rheology. The shared Cost import supplies the J-cost family (the unique symmetric generator forced by the Recognition Composition Law); Constants supplies the RS tick $\tau_0=1$. Within that setting, a "domain" is a coherent lattice region whose excess cost measures departure from equilibrium packing.
Creep is the slow, thermally assisted advance of that imbalance: when the domain cost sits above a positive threshold, discrete rung hops become available and macroscopic strain accumulates. The module therefore introduces a domain-cost functional, records that it is nonnegative and zero at equilibrium, fixes a canonical positive threshold, and wraps the pair into a CreepCert structure inhabited by a default certificate.
proof idea
Definition-heavy module, not a deep proof development. domainCost is introduced as a Cost-derived real; domainCost_nonneg and domainCost_at_equilibrium are elementary positivity and normalization facts. canonicalThreshold is a positive constant (canonicalThreshold_pos). CreepCert is a structure bundling cost and threshold; cert and cert_inhabited supply a default inhabited instance. No multi-step tactic chains; the argument is packaging plus nonnegativity.
why it matters in Recognition Science
Places materials creep inside the same phi-ladder and J-cost ledger used for masses and constants elsewhere in the monolith. Downstream materials or condensed-matter developments can assume an inhabited CreepCert rather than re-deriving threshold positivity. The module does not yet feed a named parent theorem in the graph (used_by is empty); it is a leaf interface for later strain-rate or activation-barrier results. It sits in the Materials domain and inherits the T5/T6 forcing of J and $\varphi$ only indirectly through Cost and Constants.
scope and limits
- Does not derive a continuum constitutive law or viscosity coefficient.
- Does not prove microscopic dislocation or vacancy kinetics.
- Does not fix numerical creep rates or activation energies beyond the threshold sign.
- Does not connect CreepCert to experimental stress-strain curves.
- Does not claim uniqueness of the canonical threshold among all possible cutoffs.