What was already known
Global support was standard for full-rank finite-dimensional states, but was not established for degenerate boundary states.
AI involvement
Holevo and Shirokov credit Claude Fable 5 with finding the decisive state. They supplied the criterion, calculation and higher-dimensional extension. Song and Zong’s later classification is separate human work.
The model supplied the decisive explicit state, while the authors supplied the criterion, proof, and broader results.
- Supporting source (arxiv.org) — Submission history: only v1 as of 18 October 2026
- Supporting source (arxiv.org) — Submission history: follow-up v1 25 September, v2 11 October 2026
Importance
Provides an explicit counterexample to an assumption used for boundary-state entanglement of formation.
Limitations
The authors developed the support criterion and proof; Claude found the state. Song and Zong later independently derived its concurrence within a broader classification, without auditing the original proof.
Technical verification
The original paper supplies an analytic proof, and Song–Zong later independently derive the same state’s concurrence formula and square-root behavior within a larger family. This corroborates the specific state and formula, but no explicit completed check of the original argument is documented. The later replacement proof is not counted as a human check of that argument.
Human understanding
Holevo and Shirokov explain the Lipschitz criterion and Wootters-based square-root cusp; Song and Zong further explain the tangent-support geometry. The latter explanation is separately credited and does not transfer authorship of the original state.
Correction and publication history
Provides an explicit counterexample to an assumption used for boundary-state entanglement of formation.
Read this published revision