CreepRegime
plain-language theorem explainer
The CreepRegime inductive enumerates the five stages of material creep under Recognition Science, with each stage tied to a rung on the phi-ladder where adjacent strain-rate ratios equal phi. Materials modelers working from configDim = 5 would cite it when classifying failure sequences. The declaration is a direct inductive type with automatic Fintype derivation, enabling downstream cardinality and enumeration results.
Claim. An inductive type with five constructors corresponding to the transient, steady-state, accelerating, ductile-brittle transition, and fracture phases of creep, equipped with decidable equality and finite-type structure.
background
In this module creep is partitioned into five regimes that match configDim D = 5. Each regime receives a characteristic strain rate one rung higher on the phi-ladder, enforcing the adjacent-regime ratio phi. The module imports Constants to access phi and states the regimes directly as an inductive type. The module documentation records: 'Materials creep proceeds through five canonical regimes (= configDim D = 5): primary (transient), secondary (steady-state), tertiary (accelerating), ductile-brittle transition, and final fracture. Each regime's characteristic strain rate sits one rung up the φ-ladder: adjacent-regime rate ratio = φ.'
proof idea
The declaration is a direct inductive definition listing the five constructors, followed by deriving clauses for DecidableEq, Repr, BEq, and Fintype. No lemmas or tactics are invoked; the Fintype instance is generated automatically.
why it matters
This definition supplies the type for CreepRegimeCert, which asserts Fintype.card = 5 together with the phi-ratio property on strain rates. It realizes the configDim = 5 requirement in the materials section and supplies the enumeration needed for the counting theorem creepRegime_count. The construction sits inside the broader Recognition Science treatment that derives material behavior from the phi-ladder and the forcing chain.
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