# Fixed-bank bounds with missing execution labels

Elementary partial-identification calculation, 6 October 2026 Pacific. Not a novel theorem, empirical result, confidence interval or frozen-H1 amendment.

Each label is known-correct, known-incorrect, or unknown. Each policy selects a fixed bank index or explicitly abstains (zero success). The formulas return sharp lower/upper bounds over every binary completion consistent with known labels, for bank coverage O, headroom O−B, and paired gain S−B. When both policies select the same candidate, their gain is exactly zero even if its label is unknown. Unknown is never converted to incorrect.

The headroom lower bound is one only if the baseline is known incorrect/abstains and a known correct candidate exists. Its upper bound is one only if the baseline could be incorrect and some other bank candidate could be correct. Coverage lower/upper bounds depend on known/possible correct candidates. Paired gain bounds use both selected outcomes, respecting shared selection identity. Average bounds are exact rational task averages. With no cross-task label restrictions, taskwise extrema can be attained independently, so average bounds are sharp too.

Run `python3 -B -m unittest discover -s .`, optionally with `-O`. Four tests enumerate all 2,550 banks/selection configurations with one through four candidates and compare against all compatible complete label assignments, plus input and average checks. Inputs contain authored Boolean values only; no task or candidate code is executed.

These bounds assume selections are fixed, outcomes refer to one declared suite, and unknown outcomes have no additional constraints. Adaptive policies whose choices change with unknown observations require a different analysis. A resource-constrained oracle also requires admissible action and cost evidence. Identification bounds are not sampling uncertainty; real task-cluster intervals and actual candidate execution remain separate requirements.

A separate AI agent reviewed the formulas and independently tested 8,748 five-candidate configurations. The returned intervals are individually sharp; they are not a Cartesian product of jointly attainable outcomes. Candidate identity is represented by one shared index. Duplicate bank entries representing the same underlying outcome require canonicalization or additional equality constraints; treating such outcomes as unrestricted can yield loose bounds.

This companion reports no empirical model result or confirmatory study. No model calls or external spending.
