The Root of the Demand: What Bounded Verdict Agreement Is, What It Is Not, and Why Boundedness, Answerability and Co-Declaration Do Not Entail It

Abstract What makes a demand for bounded verdict agreement satisfiable, and what premises entail it? This paper distinguishes a declared standard from the outcomes evaluators can actually return. Boundedness, answerability, and answerability together with co-declaration do not, by themselves, entail determinate agreement. For a declared verification task, the paper proves an exact characterization: every admitted run returns a determinate verdict and all requested comparisons agree if and only if, within each class of the equivalence generated by those comparisons, the union of possible outcomes is a singleton contained in the determinate verdict set. The result assumes nonempty procedure and outcome families and interprets agreement robustly over all possible outcomes, including same-case comparisons. Requested comparisons admit a corresponding kernel characterization. Agreement, correctness, and substantive decision are separate properties. Evaluators can agree uniformly on an incorrect answer, while agreement on UNDEFINED can satisfy the demand without deciding any substantive case. The paper distinguishes prescribed evaluation from robust pointwise, uniform, and universal correctness, and proves that the latter three coincide under determinate agreement. It also characterizes zero-error decoding through observation fibers and gives a finite-family diagonal separation between per-case availability of a correct procedure and the existence of one listed procedure correct everywhere. These results identify what agreement requires without treating declaration as execution, agreement as correctness, or an observed successful run as certification of all possible outcomes. The paper supplies explicit countermodels, records corrections to predecessor claims, and includes reproducibility checks with declared finite scope. It establishes no specification-floor implication; such an implication requires a separate theorem with explicit premises.