Reasoning-Constraint Elasticity under Dynamic Feasible Sets

Alignment interventions can improve policy adherence and harm mitigation while also inducing over-refusal and benign capability regressions. In many deployments, base checkpoints or matched base logs are unavailable; therefore base-relative restriction magnitude is not identifiable from present observables.

We develop a reference-free alternative: Reasoning–Constraint Elasticity (RCE) over dynamic feasible sets. Capability is represented as simultaneous satisfaction of observable inequality families with context/time-varying thresholds; feasibility is summarized by minimum slack. Primary objects are finite-difference elasticities (e.g., Δ𝑅/Δ𝑀𝑔, −Δ𝐶/Δ𝑀𝑔), robust to non-smooth regime transitions.
The framework is strengthened in fourteen directions. (i) Predictable thresholds: non-anticipative, replayable threshold processes. (ii) Slack decomposition: observed slack movement is decomposed into frozen-threshold movement plus bounded threshold-drift contribution, with explicit active-constraint switching residuals. (iii) Auxiliary-witness falsification: independently specified witness inequalities provide a falsifiable disagreement channel with non-redundancy certificates. (iv) Goodhart/gaming resistance: public-vs-audit evaluator split with delayed audit selection, transfer-gap certification, and all-channel fail-closed gating. (v) Attack resistance: append-only transcript commitments with quorum-signed roots and split-view incompatibility conditions. (vi) Contamination robustness: 𝜀-contamination margins and ratio domains are corrected by adversarial-budget terms. (vii) Tail evidence preservation (TEPP): tail candidates are first committed as immutable evidence objects before value judgment. (viii) Delayed opportunity: immediate and horizon-𝐻 opportunity signals are unified through delayed re-evaluation with doubly robust correction. (ix) Certified tail chance: rare contexts are counted as measurable chance only when net upside, reserve sufficiency, and depletion severity are jointly certified. (x) Dual-layer tail-positive gate: hard fail-closed ruin guard plus bounded fail-open discovery guard. (xi) Safe niche search: context is an optimizable variable under explicit viability constraints. (xii) Cryptographic replay/reveal: replayable leaf schemas, delayed reveal transcripts, and VRF-based audit selectors. (xiii) Barbell portfolio control: dual-gate architecture is formalized as a ruin-bounded convex-opportunity portfolio with explicit exploration allocation, budget constraints, and skin-in-the-game agency symmetry. (xiv) The Convexity Principle in Safety (CPS), referred to as the Shinkidan Principle: maximize bounded convex upside only under hard ruin constraints, with preserve-before-judge evidence discipline.

Results are observable-only and auditable. They define falsifiable measurement and reporting rules under declared assumptions, without reliance on inaccessible internal narratives. Although motivated by AI alignment, the formalism is system-level and applies to any adaptive decision process where only externally observable traces are admissible.