Finite-Copy Distillability of NPT States in the DiVincenzo Family
partialconfidence 70%
VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Whether negative-partial-transpose states undistillable from one copy become distillable from finitely many copies is a basic open problem in entanglement theory. In the canonical two-parameter DiVincenzo family used as its symmetry-reduced testbed, a distinguished one-copy-undistillable state is shown to be two-copy distillable in every local dimension d >= 3, disproving the conjecture that the family's whole one-copy-undistillable region stays undistillable for arbitrarily many copies.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement
fidelity, correctness, priority, or novelty.
What AI did
GPT-5.6 Thinking
The disclosure lists the specific work: "GNMT acknowledges substantial assistance from OpenAI's ChatGPT, using the GPT-5.6 Thinking model, in the discovery and development of this work. The tool helped with scientific reasoning, the numerical filter search, the derivation of exact two-copy and three-copy certificates, and the organization of the arguments. The interaction was initiated and directed by GNMT." An appendix gives a fuller account of the AI-assisted discovery process.
A preprint days old. The witnesses are explicit Schmidt-rank-two certificates that the authors independently reconstructed and verified, but no outside party has checked them.
Partial deliberately: the NPT bound entanglement problem itself is untouched. What falls is the conjecture about the canonical family, and the paper is explicit that a substantial neighbouring region remains unresolved while another is known two-copy undistillable.
Known method families
construction (source-reported)
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.