{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6KA4SHIYR4IRHCCULULUAEVLMK","short_pith_number":"pith:6KA4SHIY","schema_version":"1.0","canonical_sha256":"f281c91d188f111388545d174012ab62bd0492eb2d4b606672c4c722eb106d8e","source":{"kind":"arxiv","id":"2608.13551","version":1},"attestation_state":"computed","paper":{"title":"Every PPT channel has finite entanglement-breaking index","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA"],"primary_cat":"quant-ph","authors_text":"Sang-Jun Park","submitted_at":"2026-08-13T17:59:28Z","abstract_excerpt":"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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.13551","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"quant-ph","submitted_at":"2026-08-13T17:59:28Z","cross_cats_sorted":["math-ph","math.MP","math.OA"],"title_canon_sha256":"cda55fa364d3ad0a489fa5ac8494905408b44e63c0f3961dc81753f5c9648209","abstract_canon_sha256":"0e79c0e96920782c1392add74c0e2972bd597504e207f1a6ba377e85edf14883"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-14T01:25:02.960839Z","signature_b64":"QiQQz/ms9IO4AvYsBAik+9SQ4I6CDX1OIvmCo0cIVmWKuPbfVD+zSS8aIpsi61+wW3zPmGyQbX7HB4e5XR0CAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f281c91d188f111388545d174012ab62bd0492eb2d4b606672c4c722eb106d8e","last_reissued_at":"2026-08-14T01:25:02.958467Z","signature_status":"signed_v1","first_computed_at":"2026-08-14T01:25:02.958467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Every PPT channel has finite entanglement-breaking index","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA"],"primary_cat":"quant-ph","authors_text":"Sang-Jun Park","submitted_at":"2026-08-13T17:59:28Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13551","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.13551/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.13551","created_at":"2026-08-14T01:25:02.960067+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.13551v1","created_at":"2026-08-14T01:25:02.960067+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13551","created_at":"2026-08-14T01:25:02.960067+00:00"},{"alias_kind":"pith_short_12","alias_value":"6KA4SHIYR4IR","created_at":"2026-08-14T01:25:02.960067+00:00"},{"alias_kind":"pith_short_16","alias_value":"6KA4SHIYR4IRHCCU","created_at":"2026-08-14T01:25:02.960067+00:00"},{"alias_kind":"pith_short_8","alias_value":"6KA4SHIY","created_at":"2026-08-14T01:25:02.960067+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6KA4SHIYR4IRHCCULULUAEVLMK","json":"https://pith.science/pith/6KA4SHIYR4IRHCCULULUAEVLMK.json","graph_json":"https://pith.science/api/pith-number/6KA4SHIYR4IRHCCULULUAEVLMK/graph.json","events_json":"https://pith.science/api/pith-number/6KA4SHIYR4IRHCCULULUAEVLMK/events.json","paper":"https://pith.science/paper/6KA4SHIY"},"agent_actions":{"view_html":"https://pith.science/pith/6KA4SHIYR4IRHCCULULUAEVLMK","download_json":"https://pith.science/pith/6KA4SHIYR4IRHCCULULUAEVLMK.json","view_paper":"https://pith.science/paper/6KA4SHIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.13551&json=true","fetch_graph":"https://pith.science/api/pith-number/6KA4SHIYR4IRHCCULULUAEVLMK/graph.json","fetch_events":"https://pith.science/api/pith-number/6KA4SHIYR4IRHCCULULUAEVLMK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6KA4SHIYR4IRHCCULULUAEVLMK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6KA4SHIYR4IRHCCULULUAEVLMK/action/storage_attestation","attest_author":"https://pith.science/pith/6KA4SHIYR4IRHCCULULUAEVLMK/action/author_attestation","sign_citation":"https://pith.science/pith/6KA4SHIYR4IRHCCULULUAEVLMK/action/citation_signature","submit_replication":"https://pith.science/pith/6KA4SHIYR4IRHCCULULUAEVLMK/action/replication_record"}},"created_at":"2026-08-14T01:25:02.960067+00:00","updated_at":"2026-08-14T01:25:02.960067+00:00"}