The claim
CASE-112’s normal form: ẇ = μw − w³ + h, with w the balance of authority between two regimes and h an input favouring one. For μ > 0 there are two basins, and the operative regime changes only when |h| exceeds h_c = 2μ^{3/2}/(3√3), where the occupied equilibrium meets the saddle and disappears. For 0 < |h| < h_c the equilibrium within the current basin shifts with h: the input has an effect, on w, and none on which regime operates. CASE-112, from A8 of the exchange of 2026-10-17: “An endorsement can be sincere and causally efficacious while remaining too weak to shift the system out of its current attractor basin. It may change the local balance without producing a behavioral transition.”
Two things follow that the record’s claims on efficacy do not say. CLAIM-047 separates possessing a regime from its being effective, and CLAIM-122 shows behaviour changing with the conditions while the attitudes stay fixed; this is the converse case, the attitude changing and the behaviour staying fixed, with the attitude still doing work. And, as this filing reads the normal form, because an input against the current regime shifts the equilibrium toward the saddle, a later change in μ or a further input can tip the regime sooner than it would have without the earlier one, so the earlier input is not idle even counterfactually. Which regime operates then depends on the path of h, which is the hysteresis CLAIM-463 states for a capacity’s maintenance.
What it does not say
- That any agent’s volitions behave so. CASE-112 is fictional by construction; reading h as a higher-order volition is the exchange’s interpretation.
- That a volition below threshold is as good as one above. It makes a difference to the balance, not to what is done.
- How to detect it. Behaviour alone cannot; an input’s subthreshold effect shows only under a further perturbation, as CLAIM-414’s method requires.