Materials Creep Regimes From Config Dim Creep Regime Cert

Creep regime certificate

Materials under sustained stress slowly deform, a process called creep. Engineers divide this process into five canonical stages: primary (transient), secondary (steady-state), tertiary (accelerating), the ductile-brittle transition, and final fracture. The Recognition Science framework's ledger, a discrete record of events, models this progression with a formal certificate named CreepRegimeCert.

The certificate proves three facts. First, there are exactly five creep regimes, matching the classical engineering picture. Second, the characteristic strain rate of each regime sits one rung up a ladder where adjacent regimes differ by the golden ratio φ ≈ 1.618: strainRate(k+1)/strainRate(k) = φ. Third, strain rates are always positive, so the model never produces a physically impossible negative deformation rate.

The certificate is a machine-checked collection of formal theorems, meaning its three claims are verified by a computer kernel with no gaps and no added assumptions. It does not claim that real materials must follow this exact ratio, nor does it derive the five-stage classification from first principles. The five regimes are chosen as a model, and the golden-ratio spacing is a structural claim about that model, not a measured law of any specific alloy.

What the certificate does give engineers and materials scientists is a compact, provably consistent scaffold: five named stages, a fixed ratio between their rates, and a guarantee of positivity. It is a definitional tool for organizing creep data, not a prediction about any particular material's behavior.

theorem creepRegime_count : Fintype.card CreepRegime = 5 := by decide

theorem strainRate_ratio (k : ℕ) : strainRate (k + 1) / strainRate k = phi := by
  unfold strainRate
  have hpos : (0 : ℝ) < phi ^ k := pow_pos phi_pos k
  rw [div_eq_iff hpos.ne', pow_succ]
  ring

theorem strainRate_pos (k : ℕ) : 0 < strainRate k := pow_pos phi_pos k

What this page does not claim

The certificate does not claim that real materials must follow the golden-ratio spacing. It does not derive the five-stage classification from more basic principles. It makes no prediction about any specific alloy's creep behavior.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Materials/CreepRegimesFromConfigDim.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

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