Every PPT channel has finite entanglement-breaking index
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. The OpenAI math release (September 2026) claims a counterexample to the PPT-squared conjecture: a PPT channel on 21x21 matrices whose square is not entanglement breaking; see ppt-squared-conjecture.
Exact FrontierDelta
Scope and record
Occurred: Oct 29, 2026
Delta type: REGISTRY REVISION
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-assisted. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Every PPT channel has finite entanglement-breaking index · Finite EB index for PPT channels
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
ChatGPT-5.6 Sol
model · ai model contributor · OpenAI
Sang-Jun Park
human · human collaborator
Lineage and corrections
Corrects Every PPT channel has finite entanglement-breaking index →
Supersedes Every PPT channel has finite entanglement-breaking index →
Every PPT channel has finite entanglement-breaking index evidence for this event
Stronger result in the OpenAI math release evidence for this event
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. The OpenAI math release (September 2026) claims a counterexample to the PPT-squared conjecture: a PPT channel on 21x21 matrices whose square is not entanglement breaking; see ppt-squared-conjecture. parent of this event
VibeMathed record: Every PPT channel has finite entanglement-breaking index evidence for this event
This event attributed to ChatGPT-5.6 Sol
Every PPT channel has finite entanglement-breaking index parent of this event
This event attributed to Sang-Jun Park
Act on this frontier