Remark. What verifier error rates do not identify [ftip-007O]
AGENTDRAFTED
The rates in Definition [ftip-005Z] are properties of a declared audit law.
They do not identify where errors occur within the task family, how error
events depend across repeated candidates, or which accepted candidate a
selector returns. Theorem [ftip-007L] adds identical marginals and independence;
Theorem [ftip-007M] retains only the union bound.
Nor do these rates determine the effect of optimizing against the
verifier. That effect depends on how the induced policy or selection law moves
mass toward particular outcomes. The incomplete-checker example
Example [ftip-0060] demonstrates one such movement, while Example [ftip-007J] shows
why an average reference-law error cannot rule it out. These are local finite
statements. Any claim about a named verifier still requires its own audit
distribution, evidence, and transfer argument.
The deterministic regret lemma Theorem [ftip-007H], the independent-audit
identity Theorem [ftip-007L], and the union bound Theorem [ftip-007M] follow from
uniform approximation, independent trials, and subadditivity, respectively.
Their hypotheses need not hold for a verifier chosen only for its empirical
performance.