{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:P7UFPTPHS67J4SZ2YG4NYFYTRK","short_pith_number":"pith:P7UFPTPH","canonical_record":{"source":{"id":"1003.1221","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-03-05T09:51:28Z","cross_cats_sorted":[],"title_canon_sha256":"3efde0c2280b93f27c2ecd1ec86184ee0b645f794c8d67313e07a38da4ee2c52","abstract_canon_sha256":"341bcac527ebe3c2c864a1e82a8d83bc8464645cf500d94db2cf9308d093b8da"},"schema_version":"1.0"},"canonical_sha256":"7fe857cde797be9e4b3ac1b8dc17138a98add71cb59de036db523bf30cffaac9","source":{"kind":"arxiv","id":"1003.1221","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1221","created_at":"2026-05-18T03:23:49Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1221v1","created_at":"2026-05-18T03:23:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1221","created_at":"2026-05-18T03:23:49Z"},{"alias_kind":"pith_short_12","alias_value":"P7UFPTPHS67J","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"P7UFPTPHS67J4SZ2","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"P7UFPTPH","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:P7UFPTPHS67J4SZ2YG4NYFYTRK","target":"record","payload":{"canonical_record":{"source":{"id":"1003.1221","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-03-05T09:51:28Z","cross_cats_sorted":[],"title_canon_sha256":"3efde0c2280b93f27c2ecd1ec86184ee0b645f794c8d67313e07a38da4ee2c52","abstract_canon_sha256":"341bcac527ebe3c2c864a1e82a8d83bc8464645cf500d94db2cf9308d093b8da"},"schema_version":"1.0"},"canonical_sha256":"7fe857cde797be9e4b3ac1b8dc17138a98add71cb59de036db523bf30cffaac9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:23:49.098296Z","signature_b64":"tqh7JniJhHRGGGzlAewVMC4kTsjgepJQ86rmOgixqNY6u1BN7SpepyfhfXg74NZmH1TLuD/xZ1voy468UB9WCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fe857cde797be9e4b3ac1b8dc17138a98add71cb59de036db523bf30cffaac9","last_reissued_at":"2026-05-18T03:23:49.097908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:23:49.097908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.1221","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:23:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v8MT/zlOFHkzyIkGsFY2ZcW8LYr9X/CkrzL4lwT2Q7dTHoJYdiT/Z5RIQWjD2GPcp+NZE8/Bxxs6g//AZ8eUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:49:05.979776Z"},"content_sha256":"87a017d10edd7965f6ff58631940ec27ce1770c4dfe3a35f7b20276404ae2110","schema_version":"1.0","event_id":"sha256:87a017d10edd7965f6ff58631940ec27ce1770c4dfe3a35f7b20276404ae2110"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:P7UFPTPHS67J4SZ2YG4NYFYTRK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low rank extremal PPT states and unextendible product bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jan Myrheim, Jon Magne Leinaas, Per {\\O}yvind Sollid","submitted_at":"2010-03-05T09:51:28Z","abstract_excerpt":"It is known how to construct, in a bipartite quantum system, a unique low rank entangled mixed state with positive partial transpose (a PPT state) from an unextendible product basis (a UPB), defined as an unextendible set of orthogonal product vectors. We point out that a state constructed in this way belongs to a continuous family of entangled PPT states of the same rank, all related by non-singular product transformations, unitary or non-unitary. The characteristic property of a state $\\rho$ in such a family is that its kernel $\\Ker\\rho$ has a generalized UPB, a basis of product vectors, not"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1221","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:23:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gSeeVNFA/jbncDbzZyuVItp0IDgq3Vlihb5xc3Vp/r49mZW/dSTG49o0FbHGtAbgkkYDz8Hl0G3ofrN+cOxICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:49:05.980504Z"},"content_sha256":"6ae7471c3801d4c136d04164aa66d9da2f06accf89100b8a54b6ad77e22f95dd","schema_version":"1.0","event_id":"sha256:6ae7471c3801d4c136d04164aa66d9da2f06accf89100b8a54b6ad77e22f95dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7UFPTPHS67J4SZ2YG4NYFYTRK/bundle.json","state_url":"https://pith.science/pith/P7UFPTPHS67J4SZ2YG4NYFYTRK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7UFPTPHS67J4SZ2YG4NYFYTRK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T22:49:05Z","links":{"resolver":"https://pith.science/pith/P7UFPTPHS67J4SZ2YG4NYFYTRK","bundle":"https://pith.science/pith/P7UFPTPHS67J4SZ2YG4NYFYTRK/bundle.json","state":"https://pith.science/pith/P7UFPTPHS67J4SZ2YG4NYFYTRK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7UFPTPHS67J4SZ2YG4NYFYTRK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:P7UFPTPHS67J4SZ2YG4NYFYTRK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"341bcac527ebe3c2c864a1e82a8d83bc8464645cf500d94db2cf9308d093b8da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-03-05T09:51:28Z","title_canon_sha256":"3efde0c2280b93f27c2ecd1ec86184ee0b645f794c8d67313e07a38da4ee2c52"},"schema_version":"1.0","source":{"id":"1003.1221","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1221","created_at":"2026-05-18T03:23:49Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1221v1","created_at":"2026-05-18T03:23:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1221","created_at":"2026-05-18T03:23:49Z"},{"alias_kind":"pith_short_12","alias_value":"P7UFPTPHS67J","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"P7UFPTPHS67J4SZ2","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"P7UFPTPH","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:6ae7471c3801d4c136d04164aa66d9da2f06accf89100b8a54b6ad77e22f95dd","target":"graph","created_at":"2026-05-18T03:23:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"It is known how to construct, in a bipartite quantum system, a unique low rank entangled mixed state with positive partial transpose (a PPT state) from an unextendible product basis (a UPB), defined as an unextendible set of orthogonal product vectors. We point out that a state constructed in this way belongs to a continuous family of entangled PPT states of the same rank, all related by non-singular product transformations, unitary or non-unitary. The characteristic property of a state $\\rho$ in such a family is that its kernel $\\Ker\\rho$ has a generalized UPB, a basis of product vectors, not","authors_text":"Jan Myrheim, Jon Magne Leinaas, Per {\\O}yvind Sollid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-03-05T09:51:28Z","title":"Low rank extremal PPT states and unextendible product bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1221","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:87a017d10edd7965f6ff58631940ec27ce1770c4dfe3a35f7b20276404ae2110","target":"record","created_at":"2026-05-18T03:23:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"341bcac527ebe3c2c864a1e82a8d83bc8464645cf500d94db2cf9308d093b8da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-03-05T09:51:28Z","title_canon_sha256":"3efde0c2280b93f27c2ecd1ec86184ee0b645f794c8d67313e07a38da4ee2c52"},"schema_version":"1.0","source":{"id":"1003.1221","kind":"arxiv","version":1}},"canonical_sha256":"7fe857cde797be9e4b3ac1b8dc17138a98add71cb59de036db523bf30cffaac9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fe857cde797be9e4b3ac1b8dc17138a98add71cb59de036db523bf30cffaac9","first_computed_at":"2026-05-18T03:23:49.097908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:23:49.097908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tqh7JniJhHRGGGzlAewVMC4kTsjgepJQ86rmOgixqNY6u1BN7SpepyfhfXg74NZmH1TLuD/xZ1voy468UB9WCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:23:49.098296Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.1221","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87a017d10edd7965f6ff58631940ec27ce1770c4dfe3a35f7b20276404ae2110","sha256:6ae7471c3801d4c136d04164aa66d9da2f06accf89100b8a54b6ad77e22f95dd"],"state_sha256":"e882ac57c4392a784584fd5e0a9c6d50c68270957bbc15f99f710a18018187cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9xmUcdtwM558R7hBbW6akGaAniM3LRJM61WGYxj9ps7ySV+EMstgBzJDNUefvE9Qrc21K8NnqEaIgdF2ssboBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:49:05.984628Z","bundle_sha256":"1e95bf1006f516f4457a2f2965a60d2953961fad3cbf4b399de0609485f17cf8"}}