Persistent Carrier Non-Identifiability under Averaged and Singleton Holevo Information, with Certified Pairwise Separation

Fragment-size-averaged Holevo-information curves omit the identities of environmental fragments. We construct a restricted four-qubit example in which two equal-prior orthogonal pure-branch ensembles have exactly the same fragment-size-averaged Holevo curve (0, 1/6, 1/2, 1) and all four labeled singleton Holevo values equal to zero, while their minimum pure-common-rest carrier sizes differ (2 versus 4). Subject to the correctness of a reduced entropy formula and validated directed interval arithmetic, this coincidence persists for every choice of six raw amplitude coordinates in an explicit product box, with a unique two-coordinate correction inside a common root box. The solution family is open in the six free coordinates, not in the full coefficient or observational space. Analytic exact-rational sign bounds show that the two ensembles are separated by the pattern of labeled two-site fragment information (one positive pair versus three). Combining quantum Pinsker's inequality and an exact-rational simplex bound yields a permutation-invariant second-moment gap larger than 0.6128 bit², conditional on the existence certificate. The release includes the manuscript source, exact reports, four frozen phase source packages, original figure data, checksums, code, and AI-assistance disclosure. This is an unreviewed preprint, not a theorem about general carrier estimation, operational quantum data hiding, local indistinguishability, or finite-shot measurements. Independent priority assessment and comprehensive external peer review remain outstanding.