{
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  "problem_id": "vibemathed:every-ppt-channel-has-finite-entanglement-breaking-index",
  "title": "Every PPT channel has finite entanglement-breaking index",
  "canonical_statement": "We prove that every PPT linear map has finite entanglement-breaking index, thereby establishing the eventual entanglement-breaking property of PPT channels in full generality. Furthermore, by utilizing completely positive maps with low entanglement dimensionality, we show that a large family of PPT maps, which strictly containing the class of 2-superpositive maps, has entanglement-breaking index bounded above by 3, uniformly in the dimension. In particular, these results provide strong evidence that the PPT-cubed conjecture may hold in full generality.",
  "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "resolved",
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      "type": "proved",
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      "occurred_at": "2026-08-13T00:00:00.000Z",
      "title": "arXiv",
      "summary": "Establishes that every PPT channel is eventually entanglement-breaking (finite EB index), in full generality, and bounds the index by 3 uniformly in dimension for a family strictly containing the 2-superpositive maps. The PPT-squared conjecture itself - index at most 2 - remains open; the paper presents its results as strong evidence toward the cubed version.",
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      "model": "ChatGPT-5.6 Sol",
      "provider": "OpenAI",
      "attempted_at": "2026-08-13T00:00:00.000Z",
      "human_collaborators": [
        "Sang-Jun Park"
      ],
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          "url": "https://arxiv.org/abs/2608.13551",
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      "note": "Checked by this site on 17 August 2026 against the paper's LaTeX (arXiv:2608.13551, Park, 14 pages). The AI statement is verbatim as this entry describes: ChatGPT for language, LaTeX and exploratory mathematical discussions, with some ideas in the splitting section arising during interactions with GPT-5.6 Sol. That is a vague disclosure, and the site's rule takes the lower tier, so ai-assisted stands. The proof was not checked here. One-day-old preprint, no independent review.",
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