Small contracts, measurable limits: mathematical foundations for the MCRP seed release

Abstract

A protocol for solo researchers, collaborations, individual agents and agent teams should expose checkable boundary information without requiring participants to understand everyone else’s internal complexity. Four models identify what the offer–check–rely–amend interface can and cannot guarantee. Group-first sampling removes a representation-multiplicity incentive when the control map, feasible panels and group-level distribution are fixed. Selective completion can reverse offered-panel bounds; finite IID retries consume attention without repairing that selection bias. A common weighted repair envelope bounds expected cascades under changing regimes, while stable snapshots and finite mean work do not certify safe queues. One-shot auditing must satisfy effort incentives, participation and a specified funding constraint simultaneously. This revision distinguishes expected audit expenditure from a realized hard cap in separate propositions, with division-free conditions for degenerate cases. Exact sensitivity tables examine completion, cost, detection, false sanctions and enforceable loss, including infeasible cases and an analytically justified common feasible interval over a stipulated parameter box. A worked skill/conflict/capacity construction exercises representation invariance on a constrained panel family. Focused prior-work comparisons and qualified claim-ledger labels make the contribution and assumptions explicit. The results use established mathematical tools aligned with protocol records. The package retains exact calculations, finite enumerations, seeded stochastic checks and deliberate counterexamples. All new development and internal adversarial review were author-directed agent work. Synthetic sensitivity is not behavioral calibration, a confidence region, external scientific review or evidence of field efficacy. Identity authentication, institutional enforcement and actual reviewer behavior remain external obligations.

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