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

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
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preprint

Exact Counterexamples and Interface Gaps in Quantum Oracle Sketching

Carmelo Vellón Gascón
Zenodo (CERN European Organization for Nuclear Research)
Quantum Computing Algorithms and Architecture
preprint

Exact Counterexamples and Interface Gaps in Quantum Oracle Sketching

Carmelo Vellón Gascón
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Quantum Computing Algorithms and Architecture
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