{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GDDSQKUGHXLCTSJTUNIRYVCEUM","short_pith_number":"pith:GDDSQKUG","canonical_record":{"source":{"id":"1305.2264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-05-10T06:23:24Z","cross_cats_sorted":[],"title_canon_sha256":"bbc443a1a01217cb6c0edf1b136f94ea8488de449ac612ff8e512c83e197227f","abstract_canon_sha256":"af47210c98e9a9428da35b73ea34e9b5ec21bc6401fee1bdd1aca487aa9c54e7"},"schema_version":"1.0"},"canonical_sha256":"30c7282a863dd629c933a3511c5444a33f6579483f5025f9797f82f55a5098a3","source":{"kind":"arxiv","id":"1305.2264","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2264","created_at":"2026-05-18T00:37:21Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2264v1","created_at":"2026-05-18T00:37:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2264","created_at":"2026-05-18T00:37:21Z"},{"alias_kind":"pith_short_12","alias_value":"GDDSQKUGHXLC","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GDDSQKUGHXLCTSJT","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GDDSQKUG","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GDDSQKUGHXLCTSJTUNIRYVCEUM","target":"record","payload":{"canonical_record":{"source":{"id":"1305.2264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-05-10T06:23:24Z","cross_cats_sorted":[],"title_canon_sha256":"bbc443a1a01217cb6c0edf1b136f94ea8488de449ac612ff8e512c83e197227f","abstract_canon_sha256":"af47210c98e9a9428da35b73ea34e9b5ec21bc6401fee1bdd1aca487aa9c54e7"},"schema_version":"1.0"},"canonical_sha256":"30c7282a863dd629c933a3511c5444a33f6579483f5025f9797f82f55a5098a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:21.667886Z","signature_b64":"XFrJiCChsI3fqP2vKmupd/pL1Imxxb8sPx7nNBbwQvEmBwMB0VWaHZ0J9F5CdLAJjk89T0ACyK/CZ7SCMngqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30c7282a863dd629c933a3511c5444a33f6579483f5025f9797f82f55a5098a3","last_reissued_at":"2026-05-18T00:37:21.667141Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:21.667141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.2264","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":"2026-05-18T00:37:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0R0D0sTD0rVktRyNhs2bPSxOFeCPlxcX648YY7KbdrJhJjUxAo7z4edgh3+9cP3ooXWp+YQPH1NwZUjnrTOaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:44:01.679893Z"},"content_sha256":"92a83134c3dd51f8cc9d376cfc417ba40837eef4bb103f3657103c9d3ea4e0aa","schema_version":"1.0","event_id":"sha256:92a83134c3dd51f8cc9d376cfc417ba40837eef4bb103f3657103c9d3ea4e0aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GDDSQKUGHXLCTSJTUNIRYVCEUM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three-tangle and Three-\\pi\\ for a class of tripartite mixed states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Shao-Ming Fei, Teng Ma","submitted_at":"2013-05-10T06:23:24Z","abstract_excerpt":"We study the tripartite entanglement for a class of mixed states defined by the mixture of GHZ and W states, \\rho=p|GHZ><GHZ|+(1-p)|W><W|. Based on the Caratheodory theorem and the periodicity assumption, the possible optimal decomposition of the states has been derived, which is not independent on the detailed measure of entanglement. We find that, according to p, there are two different decompositions containing 3 or 4 quantum states in the decomposition respectively. When the decomposition contains 3 quantum states, the tripartite entanglement of the mixed state is simply the entanglement o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2264","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":"2026-05-18T00:37:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"juha+vw4QA/ODQPN9eVgtiPVDJedBynAgqO+B/8WjnPmbc3w1CQi3cNR8EsQACrdyQu2+DlCBEih5jw3h62hDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:44:01.680243Z"},"content_sha256":"2ad3f318ead0460b59b9ddd2a826dfb91339d6c65c69ef620099d2c6955b0233","schema_version":"1.0","event_id":"sha256:2ad3f318ead0460b59b9ddd2a826dfb91339d6c65c69ef620099d2c6955b0233"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GDDSQKUGHXLCTSJTUNIRYVCEUM/bundle.json","state_url":"https://pith.science/pith/GDDSQKUGHXLCTSJTUNIRYVCEUM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GDDSQKUGHXLCTSJTUNIRYVCEUM/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":"2026-06-10T22:44:01Z","links":{"resolver":"https://pith.science/pith/GDDSQKUGHXLCTSJTUNIRYVCEUM","bundle":"https://pith.science/pith/GDDSQKUGHXLCTSJTUNIRYVCEUM/bundle.json","state":"https://pith.science/pith/GDDSQKUGHXLCTSJTUNIRYVCEUM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GDDSQKUGHXLCTSJTUNIRYVCEUM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GDDSQKUGHXLCTSJTUNIRYVCEUM","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":"af47210c98e9a9428da35b73ea34e9b5ec21bc6401fee1bdd1aca487aa9c54e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-05-10T06:23:24Z","title_canon_sha256":"bbc443a1a01217cb6c0edf1b136f94ea8488de449ac612ff8e512c83e197227f"},"schema_version":"1.0","source":{"id":"1305.2264","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2264","created_at":"2026-05-18T00:37:21Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2264v1","created_at":"2026-05-18T00:37:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2264","created_at":"2026-05-18T00:37:21Z"},{"alias_kind":"pith_short_12","alias_value":"GDDSQKUGHXLC","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GDDSQKUGHXLCTSJT","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GDDSQKUG","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:2ad3f318ead0460b59b9ddd2a826dfb91339d6c65c69ef620099d2c6955b0233","target":"graph","created_at":"2026-05-18T00:37:21Z","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 study the tripartite entanglement for a class of mixed states defined by the mixture of GHZ and W states, \\rho=p|GHZ><GHZ|+(1-p)|W><W|. Based on the Caratheodory theorem and the periodicity assumption, the possible optimal decomposition of the states has been derived, which is not independent on the detailed measure of entanglement. We find that, according to p, there are two different decompositions containing 3 or 4 quantum states in the decomposition respectively. When the decomposition contains 3 quantum states, the tripartite entanglement of the mixed state is simply the entanglement o","authors_text":"Shao-Ming Fei, Teng Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-05-10T06:23:24Z","title":"Three-tangle and Three-\\pi\\ for a class of tripartite mixed states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2264","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":"sha256:92a83134c3dd51f8cc9d376cfc417ba40837eef4bb103f3657103c9d3ea4e0aa","target":"record","created_at":"2026-05-18T00:37:21Z","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":"af47210c98e9a9428da35b73ea34e9b5ec21bc6401fee1bdd1aca487aa9c54e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-05-10T06:23:24Z","title_canon_sha256":"bbc443a1a01217cb6c0edf1b136f94ea8488de449ac612ff8e512c83e197227f"},"schema_version":"1.0","source":{"id":"1305.2264","kind":"arxiv","version":1}},"canonical_sha256":"30c7282a863dd629c933a3511c5444a33f6579483f5025f9797f82f55a5098a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30c7282a863dd629c933a3511c5444a33f6579483f5025f9797f82f55a5098a3","first_computed_at":"2026-05-18T00:37:21.667141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:21.667141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XFrJiCChsI3fqP2vKmupd/pL1Imxxb8sPx7nNBbwQvEmBwMB0VWaHZ0J9F5CdLAJjk89T0ACyK/CZ7SCMngqBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:21.667886Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.2264","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92a83134c3dd51f8cc9d376cfc417ba40837eef4bb103f3657103c9d3ea4e0aa","sha256:2ad3f318ead0460b59b9ddd2a826dfb91339d6c65c69ef620099d2c6955b0233"],"state_sha256":"e05696577ece4db1ab4edfac4ce76ddf62c325cbeaf338ca4496cef4e3cf9ed1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8gKkq7Qa5CY85PbQCfJrgtT6gGi+ukhJKR6XdF30o+2Ef2bZNbVmNnWsAgXG9D0nXlpH5V6duc5H8njkMLB3Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:44:01.682184Z","bundle_sha256":"56608cdd90aa8a4ac88763215462a07e059c6a5cd6c93c74e6acc13c0b932b8a"}}