Exact Counterexamples and Interface Gaps in Quantum Oracle Sketching
Version 2 of a version-specific mathematical audit of arXiv:2604.07639v1, submitted on 8 April 2026. The manuscript examines whether the Appendix-D quantum-oracle-sketching arguments establish the reversible, controlled, repeated-use, sparse-access, block-encoding, and state-preparation interfaces invoked downstream. Version 2 preserves the exact counterexample to Theorem D.16 / Eq. D.99, the allowed-boundary counterexample to Eq. D.185, and the fixed-channel obstruction for the canonical full-domain clean completion analyzed for D.24. It adds the D.183 square-root-of-R to R arithmetic finding, a positive 4k-wise moment-transfer lemma under a fixed-matrix condition, and a reassessment of conditional channel composition, QSVT robustness, padded row-slot access, and the standard adjoint-Gram construction. The results concern only arXiv:2604.07639v1. They do not claim that quantum oracle sketching is impossible, do not assess a later source revision, and do not challenge the IID core, the classical lower-bound program, or every result of the source paper. The record contains the Version-2 main manuscript, technical supplement, changelog, corresponding Markdown source files, a release README, and SHA-256 checksums.
Authors
- Carmelo Vellón Gascón (ORCID: https://orcid.org/0009-0006-4923-1151)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-07-30
- DOI
- https://doi.org/10.5281/zenodo.21704142
- Primary Topic
- Quantum Computing Algorithms and Architecture
- Type
- preprint