Records Amplify Hysteresis

This note proves the formal lemma underlying the S₃ stabilization signature: when accumulated records shift a system's switching thresholds, a closed constraint sweep produces a hysteresis loop whose area grows with the accumulated record state. For a binary-state hysteron whose thresholds are shifted by record state R, a closed major sweep of the constraint yields absolute loop area A(R) = 4θ₀ + 4αR, where θ₀ is the intrinsic threshold gap and α the record-threshold coupling. Loop area is therefore strictly increasing in R whenever α > 0.

The lemma's sharpest point is what it denies: records do not create hysteresis from nothing — at α = 0 the loop area is the intrinsic 4θ₀ — they amplify it. The note proves this self-contained as a geometric major-loop calculation and identifies the cross-domain empirical signature it predicts: loop area scaling as A ≈ A₀ + cR against an independently audited record proxy. Preisach superposition, return-point memory, and avalanche regimes are noted as scope-limited extensions, not claims established here. Its operational pair, Methods-S₃, turns the lemma into a deployable loop-scaling audit.

What acceptance commits you to. Acceptance of this note commits the reader only to the conditional lemma under its single-hysteron, quasi-static, major-loop assumptions — not to Universal Collapse Theory, and not to the claim that any particular real-world path dependence is record-driven. That is what the paired audit tests, separating record-driven hysteresis from rate lag and other confounds.

Keywords: hysteresis; loop area; record state; hysteron; S₃ signature.