This paper develops a certified local micro-theory for open-task participation in agent societies composed of humans, software agents, tool-using agents, and hybrids. Instead of assuming a fixed team, the paper studies a single reviewable task round in which authenticated participants may remain outside, act directly, assist a target, verify a target, continue an incumbent lease, withdraw while preserving identity continuity, or exit the episode. The theory is explicitly local and one-step: it does not claim a global equilibrium or full-horizon control law, but analyzes what can be justified, certified, and implemented on the margin of one reviewable task episode. The framework introduces a robust local benchmark for submitted profiles under certified posterior ambiguity, together with contributor-level attribution on linkage-consolidated submission bundles. This separation between submission-stage externalities and admission-stage value captures an important feature of open participation settings: a submitted claim can impose queue, information, coordination, or identity costs even if it is never admitted. The paper then develops an exact and constructive controller theory. The exact public object is an extended policy-risk functional defined on a common ambient action and loss model and restricted by state-feasible policies. On certified polyhedral posterior classes, the same controller can be recovered from a machine-readable certificate tuple rather than the full functional, and on factor-moment subclasses this further compresses to a polynomial-size operational sketch with exact linear optimization over certified moment envelopes. A third contribution is an audited implementation theory under limited public instruments. Participation decisions must be computed from certified projections of authenticated snapshots, stability must be reconstructible from public evidence, omitted deviations must be covered by auditable domination certificates, and implementability must be certified explicitly rather than assumed. The paper also gives a robust treatment of verification and corroboration. Verification is modeled as a portfolio problem under target-class posterior ambiguity rather than as a scalar reputation score, while corroboration is governed by valid public covariance certificates and observable separation guarantees. Finally, the paper derives a primitive-to-decision service-fault theory showing how certified faults in snapshot freshness, posterior widening, proxy or omission certificates, feasibility masks, verification ambiguity, and corroboration covariance degrade benchmark values, controller safety, implementable participation outcomes, and verification portfolios. Overall, the paper provides a mathematically explicit local theory for deciding when a local agent should act, assist, verify, withdraw, or exit in open-task environments with certified public coordination, identity linkage, provenance constraints, and auditable uncertainty.
K Takahashi (Fri,) studied this question.