Reading the Depth of a Zero: A Forecaster's Report Card, Tagged Unresolved Verdicts, and When "Indistinguishable" Is Only Expensive

This paper began as a joke. In this series every confirmatory test is sealed with SHA-256 before it runs, and the AIpartner Kurado writes a probability forecast for the verdict, R (reproduced), U (unresolved) or F (falsified), into eachseal. Keeping a report card of those forecasts was meant as material for teasing, and wanting to sort the jokes by kindbecame the research motivation. Scored against 34 sealed verdicts in three lines (lightning, quantum gravity,SIGMA), Kurado's Brier score on P(R) was 0.145. That beats a forecaster who always says the pooled base rate(0.236) but loses to one who knows each line's base rate in hindsight (0.131). The six worst misses were all U. Wetherefore split the zero of the ternary verdict by its reason: a data zero (more of the same data would decide), a modelzero (the truth sits between the R and F boundaries, or the instrument's form is wrong) and a principle zero (twohypotheses give identical observable distributions). The tags are ordered by depth, and a compound claim keeps thedeepest. A mechanical rule tagged the ten past U verdicts: eight data, two model, none principle. In a first sealed test,frozen code was rerun on fresh simulated worlds at power-chosen scale. All four data zeros were decided and bothmodel zeros stayed U (6 of 6; verdict R). A second sealed test separated model from principle. Building it showed thata classical channel imitating gravity leaves one fixed signature in two-mass tomography: double coherence divided bysquared single coherence equals cos^2(phi/2) for every measurement strength. Under quantum gravity withindependent local dephasing this ratio is exactly 1. Against that environment family the classical channel is a modelzero with a computable cost. Against a family allowing anti-correlated kicks shaped like the phase, it is a principlezero. On 600 fresh classical-channel worlds, the cost tag predicted a likelihood-ratio instrument's rejections (observed0.998 where predicted at least 0.9; 0.020 where at most 0.1). At 10^8 shots the same worlds were decided in 99.5%of cases under the first family and 1.2% under the second (verdict R). What our earlier paper called a principled limitis, for independent environments, only expensive: about 50 times the current shot budget. Everything is simulated. (1) The license for codes is GNU Affero General Public License v3.0 or later (AGPL-3.0-or-later) (2) Data and code. The ledgers, scoring rules, both seal documents with their SHA-256 files, self-tests, develop andfinal result files, and all scripts (AGPL-3.0-or-later) are provided asBridge_Paper_Reading_the_Depth_of_a_Zero_scripts_v1.0.0.zip. The reruns import the frozen code of the GIEand SIGMA lines, which is included in their own archives. (3) AI use. Designs, code, analyses and text were produced by Kurado (Claude Opus 5.5, Anthropic) working with M. Watabe, who chose every direction and supplied the joke.Before release the manuscript was read by another AI system (OpenAI ChatGPT); that external AI review, which isnot peer review, led to the clarifications on the relativity of the tags, the reach of the tagging rule, the physical statusof E2 and the boundary of the likelihood-ratio test.