Asserted Zeros: When a Valid Guarantee Certifies an Unmeasured Quantity
Abstract
A distribution-free guarantee certifies whatever score it is handed, including one that was never measured. We call this a measurement-integrity failure, and document one in a pipeline whose two LLM judges grade spoken answers. It stored option probabilities to five decimals, so anything below 5e-6 became exactly 0.0, and rescaling what survived to sum to one pushed the one remaining option (usually the correct one) to 1.0. A record's score is one minus the true answer's stored probability, so on 90.6% of graded records that score was exactly 0.0: a certainty no judge expressed. Those scores became the held-out set that fixes the release threshold, as conformal prediction does. You sort them, take the one sitting at a position your error budget picks, and release an option whose score falls at or below it. With nine in ten at the manufactured 0.0, that position lands among them, so the threshold is 0.0 and the gate admits exactly the options a judge rounded up to 1.0. It now turns on whether the two judges rounded up to the same option, not on the evidence beneath them. A pre-registered probe found every grading decision we checked unchanged. On the recordings this system actually ran, the gate released nothing at all, with or without the defect. Re-imposed at that resolution on correctly measured scores, the rounding makes the gate release more than measurement does in 36 cases of 42 and fewer in none, certifying answers honest measurement would have withheld. The repair is dull: measure every option or refuse. Five questions about how probabilities are recorded catch this before calibration.