Definition. Costed consultation with observable certification [ftip-00OE]

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Fix the shared task, checker, evaluation law and endowments from the lineage specification. Preparation of the contributor population and recipient costs at most \(S\geq 0\) in one declared additive resource unit. For a fixed integer \(k\geq 1\), a causal protocol makes at most \(k\) attempts, each with hard cost at most \(c\geq 0\). Each attempt includes selection of a contributor, communication, recipient learning, validation, and any reset. Retention, final selection and evaluation are also charged within these caps. All remaining resource coordinates require a feasible schedule.

An attempt either returns an observable certificate with a frozen recipient artifact or reports failure. The protocol returns the first certified artifact, continuing after each failure until certification or \(k\) failures; in the latter case it returns a declared fallback. Contributor access is removed for fresh evaluation. Let \(Z\in [0,1]\) be the resulting score. Assume \(0<q\leq 1\) and \(0<\beta \leq 1\) such that:

1. At every prior failure history reached with positive probability, the conditional probability of certification on the next attempt is at least \(q\). For general history spaces this condition holds almost surely.
2. For every possible selected certificate history, the conditional expected fresh-evaluation score of that retained artifact is at least \(\beta \), again almost surely.

The second premise is a soundness requirement for acquired capability, including any effect of selection. A proof checked on an observed task or a finite validation score need not imply it. Establishing such soundness, affordable contributor access and the first probability bound remains a substantive obligation for an application. Independent attempts are not required.