{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:I54VUDSKE3F5OUYEM2FIQJDFJ4","short_pith_number":"pith:I54VUDSK","canonical_record":{"source":{"id":"1210.1088","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-03T12:38:49Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"18acc99ea9392784599f090a65e41bd69f3a6c73e35b3a6af1eb51a3b4df6854","abstract_canon_sha256":"361847c967200eecc3b9cd363793beec4a1f61c6caa71dd9ccc8bcee5e6564de"},"schema_version":"1.0"},"canonical_sha256":"47795a0e4a26cbd75304668a8824654f00c2fc17d6e12d7c5913d3c8c55ad0f4","source":{"kind":"arxiv","id":"1210.1088","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1088","created_at":"2026-05-18T02:47:16Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1088v5","created_at":"2026-05-18T02:47:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1088","created_at":"2026-05-18T02:47:16Z"},{"alias_kind":"pith_short_12","alias_value":"I54VUDSKE3F5","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I54VUDSKE3F5OUYE","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I54VUDSK","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:I54VUDSKE3F5OUYEM2FIQJDFJ4","target":"record","payload":{"canonical_record":{"source":{"id":"1210.1088","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-03T12:38:49Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"18acc99ea9392784599f090a65e41bd69f3a6c73e35b3a6af1eb51a3b4df6854","abstract_canon_sha256":"361847c967200eecc3b9cd363793beec4a1f61c6caa71dd9ccc8bcee5e6564de"},"schema_version":"1.0"},"canonical_sha256":"47795a0e4a26cbd75304668a8824654f00c2fc17d6e12d7c5913d3c8c55ad0f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:16.281969Z","signature_b64":"DMZDIWvEOfHxemqEJq4p2MPIleaylX/NqJtycZuVp/8UXtem/n9Ce5xL0lLgIYImCH+d+pX3JSy//I2QSJM5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47795a0e4a26cbd75304668a8824654f00c2fc17d6e12d7c5913d3c8c55ad0f4","last_reissued_at":"2026-05-18T02:47:16.281551Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:16.281551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.1088","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qFEgVDJMqoDlDwvvhNxQ0CGjH6YaJkcFJfqwiXoAtbAwb4+VILSMAzw3I27JkyLp+dnfayx0f4pva076sTspAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:14:56.066628Z"},"content_sha256":"2cfa8b764ea7f545d44c01311d6bcc72b5f3a258df08a4e88f0f2a5f8beee507","schema_version":"1.0","event_id":"sha256:2cfa8b764ea7f545d44c01311d6bcc72b5f3a258df08a4e88f0f2a5f8beee507"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:I54VUDSKE3F5OUYEM2FIQJDFJ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Separable states with unique decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"quant-ph","authors_text":"Kil-Chan Ha, Seung-Hyeok Kye","submitted_at":"2012-10-03T12:38:49Z","abstract_excerpt":"We search for faces of the convex set consisting of all separable states, which are affinely isomorphic to simplices, to get separable states with unique decompositions. In the two-qutrit case, we found that six product vectors spanning a five dimensional space give rise to a face isomorphic to the 5-dimensional simplex with six vertices, under suitable linear independence assumption.\n  If the partial conjugates of six product vectors also span a 5-dimensional space, then this face is inscribed in the face for PPT states whose boundary shares the fifteen 3-simplices on the boundary of the 5-si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1088","kind":"arxiv","version":5},"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":"2026-05-18T02:47:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTjHtKHQQn+e38OsOPX9ZfrLVyXP1BS530Hik8mnyPuzBVCPe2JaGSjH5gD5G00pUuNQXYz1p+aZleOV4xenDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:14:56.067273Z"},"content_sha256":"9d9a258b15249306974c39d4a412275cd9474614d7fcb282c174ace159f8cd50","schema_version":"1.0","event_id":"sha256:9d9a258b15249306974c39d4a412275cd9474614d7fcb282c174ace159f8cd50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I54VUDSKE3F5OUYEM2FIQJDFJ4/bundle.json","state_url":"https://pith.science/pith/I54VUDSKE3F5OUYEM2FIQJDFJ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I54VUDSKE3F5OUYEM2FIQJDFJ4/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":"2026-05-25T17:14:56Z","links":{"resolver":"https://pith.science/pith/I54VUDSKE3F5OUYEM2FIQJDFJ4","bundle":"https://pith.science/pith/I54VUDSKE3F5OUYEM2FIQJDFJ4/bundle.json","state":"https://pith.science/pith/I54VUDSKE3F5OUYEM2FIQJDFJ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I54VUDSKE3F5OUYEM2FIQJDFJ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:I54VUDSKE3F5OUYEM2FIQJDFJ4","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":"361847c967200eecc3b9cd363793beec4a1f61c6caa71dd9ccc8bcee5e6564de","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-03T12:38:49Z","title_canon_sha256":"18acc99ea9392784599f090a65e41bd69f3a6c73e35b3a6af1eb51a3b4df6854"},"schema_version":"1.0","source":{"id":"1210.1088","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1088","created_at":"2026-05-18T02:47:16Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1088v5","created_at":"2026-05-18T02:47:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1088","created_at":"2026-05-18T02:47:16Z"},{"alias_kind":"pith_short_12","alias_value":"I54VUDSKE3F5","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I54VUDSKE3F5OUYE","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I54VUDSK","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:9d9a258b15249306974c39d4a412275cd9474614d7fcb282c174ace159f8cd50","target":"graph","created_at":"2026-05-18T02:47:16Z","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":"We search for faces of the convex set consisting of all separable states, which are affinely isomorphic to simplices, to get separable states with unique decompositions. In the two-qutrit case, we found that six product vectors spanning a five dimensional space give rise to a face isomorphic to the 5-dimensional simplex with six vertices, under suitable linear independence assumption.\n  If the partial conjugates of six product vectors also span a 5-dimensional space, then this face is inscribed in the face for PPT states whose boundary shares the fifteen 3-simplices on the boundary of the 5-si","authors_text":"Kil-Chan Ha, Seung-Hyeok Kye","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-03T12:38:49Z","title":"Separable states with unique decompositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1088","kind":"arxiv","version":5},"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":"sha256:2cfa8b764ea7f545d44c01311d6bcc72b5f3a258df08a4e88f0f2a5f8beee507","target":"record","created_at":"2026-05-18T02:47:16Z","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":"361847c967200eecc3b9cd363793beec4a1f61c6caa71dd9ccc8bcee5e6564de","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-03T12:38:49Z","title_canon_sha256":"18acc99ea9392784599f090a65e41bd69f3a6c73e35b3a6af1eb51a3b4df6854"},"schema_version":"1.0","source":{"id":"1210.1088","kind":"arxiv","version":5}},"canonical_sha256":"47795a0e4a26cbd75304668a8824654f00c2fc17d6e12d7c5913d3c8c55ad0f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47795a0e4a26cbd75304668a8824654f00c2fc17d6e12d7c5913d3c8c55ad0f4","first_computed_at":"2026-05-18T02:47:16.281551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:16.281551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DMZDIWvEOfHxemqEJq4p2MPIleaylX/NqJtycZuVp/8UXtem/n9Ce5xL0lLgIYImCH+d+pX3JSy//I2QSJM5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:16.281969Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.1088","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cfa8b764ea7f545d44c01311d6bcc72b5f3a258df08a4e88f0f2a5f8beee507","sha256:9d9a258b15249306974c39d4a412275cd9474614d7fcb282c174ace159f8cd50"],"state_sha256":"e873d5c57b5344d011316947fac9c5af4a2746c1443e2d3712a788893f24c5d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qPHwQKU/PGrK90LDlFg6+VTY/a//MFXb9B/XfUv6EQewf8vTl5eyCKBHZqUitX8mG9QHuZpm50F2hIKt1MIODA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:14:56.070761Z","bundle_sha256":"794f75b135d81273b0810f8c662d5efb47e1644a40b4eb164967be3cd7589d6d"}}