What was already known
DiVincenzo and coauthors proved one-copy undistillability in the BCGK region and conjectured it at every copy number. Later Werner-state and triangle-BGK results did not cover point C.
AI involvement
GPT-5.6 Thinking helped design and implement the qutrit search, extract an exact certificate and develop the all-dimensional construction. Tabia directed the work and chose the general form; Tabia, Chen and Hsieh reconstructed and checked the calculations. Claude Opus 5.5 cross-checked formulas as a checker.
The model found the qutrit filters and assisted the exact and uniform constructions under Tabia’s direction; the human-selected all-dimensional form is separately credited.
Importance
Refutes the all-copy undistillability claim for this family in every local dimension d≥3.
Limitations
The result does not settle whether NPT bound entanglement exists generally. Finite-cell certificates and three-copy examples are separate results.
Technical verification
The authors explicitly say they independently reconstructed and verified all calculations and exact certificates, covering the explicit witness for every d>=3. This is source-reported complete human checking. Claude’s numerical and symbolic cross-checks are additional partial review, not a proof assistant.
Formal checking
Independent human reconstruction and verification of exact witness calculations and certificates
- Checker
- Gelo Noel M. Tabia, Kai-Siang Chen, and Min-Hsiu Hsieh, paper authors
- Scope
- Theorem 1 point-C two-copy distillability witness for every d>=3 and one-copy contrast
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain how opposite local copy parity gives favorable coherent terms and the equal-norm frame minimizes the remaining positive diagonal term.
Correction and publication history
Refutes the all-copy undistillability claim for this family in every local dimension d≥3.
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