{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:J2EI6LTYLV5JAZOMEX5WXZZJED","short_pith_number":"pith:J2EI6LTY","canonical_record":{"source":{"id":"1103.5096","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-25T23:33:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5bb6e29e6df80800d2e555f616c161eb9f58c779f4d55ce750f2e442b92494f3","abstract_canon_sha256":"0f1bd03aedab6a618dfdd19b2c7510dbde5dcde72d921ff5a89c02e5560208e2"},"schema_version":"1.0"},"canonical_sha256":"4e888f2e785d7a9065cc25fb6be72920fd63ab00dc2c690098345fc7367371aa","source":{"kind":"arxiv","id":"1103.5096","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.5096","created_at":"2026-05-18T04:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"1103.5096v2","created_at":"2026-05-18T04:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5096","created_at":"2026-05-18T04:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"J2EI6LTYLV5J","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J2EI6LTYLV5JAZOM","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J2EI6LTY","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:J2EI6LTYLV5JAZOMEX5WXZZJED","target":"record","payload":{"canonical_record":{"source":{"id":"1103.5096","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-25T23:33:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5bb6e29e6df80800d2e555f616c161eb9f58c779f4d55ce750f2e442b92494f3","abstract_canon_sha256":"0f1bd03aedab6a618dfdd19b2c7510dbde5dcde72d921ff5a89c02e5560208e2"},"schema_version":"1.0"},"canonical_sha256":"4e888f2e785d7a9065cc25fb6be72920fd63ab00dc2c690098345fc7367371aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:34.422976Z","signature_b64":"lYuf00wzPBDBSelBSivxsfmtR8WzwOzokm3g4IOPAsHRLQqEr2z3q11ia4fO41EMF55BEo/OrNfeU53zbV5xBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e888f2e785d7a9065cc25fb6be72920fd63ab00dc2c690098345fc7367371aa","last_reissued_at":"2026-05-18T04:18:34.422483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:34.422483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.5096","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F0yOWGvnP55mmHcyd/di4iU1b+s9vZ3qr4Gp+UBG1U48jULqdqYyBXVRuVocFMURp0Qmi+8+OkBA8PKwUsT8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:58:02.133898Z"},"content_sha256":"f5d121b274b0efe1429cdda55e63f90a781709fa4faa0c55aadba1e60e2e053e","schema_version":"1.0","event_id":"sha256:f5d121b274b0efe1429cdda55e63f90a781709fa4faa0c55aadba1e60e2e053e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:J2EI6LTYLV5JAZOMEX5WXZZJED","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Necessary and sufficient conditions for local manipulation of multipartite pure quantum states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Gilad Gour, Nolan R. Wallach","submitted_at":"2011-03-25T23:33:44Z","abstract_excerpt":"Suppose several parties jointly possess a pure multipartite state, |\\psi>. Using local operations on their respective systems and classical communication (i.e. LOCC) it may be possible for the parties to transform deterministically |\\psi> into another joint state |\\phi>. In the bipartite case, Nielsen majorization theorem gives the necessary and sufficient conditions for this process of entanglement transformation to be possible. In the multipartite case, such a deterministic local transformation is possible only if both the states in the same stochastic LOCC (SLOCC) class. Here we generalize "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5096","kind":"arxiv","version":2},"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":"2026-05-18T04:18:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KDpzudDCKmcDWfOTaUjx0WqlHsJtUlXtSbQfPvhNCPO5MMaWU80dev8nbTdPWfa9suELmcNi2lCbYu4CTFVhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:58:02.134728Z"},"content_sha256":"3058510c75ba5ed74060a18fc785dc33b321d4ed2140edc6169a88e5d156b081","schema_version":"1.0","event_id":"sha256:3058510c75ba5ed74060a18fc785dc33b321d4ed2140edc6169a88e5d156b081"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J2EI6LTYLV5JAZOMEX5WXZZJED/bundle.json","state_url":"https://pith.science/pith/J2EI6LTYLV5JAZOMEX5WXZZJED/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J2EI6LTYLV5JAZOMEX5WXZZJED/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":"2026-05-30T16:58:02Z","links":{"resolver":"https://pith.science/pith/J2EI6LTYLV5JAZOMEX5WXZZJED","bundle":"https://pith.science/pith/J2EI6LTYLV5JAZOMEX5WXZZJED/bundle.json","state":"https://pith.science/pith/J2EI6LTYLV5JAZOMEX5WXZZJED/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J2EI6LTYLV5JAZOMEX5WXZZJED/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:J2EI6LTYLV5JAZOMEX5WXZZJED","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":"0f1bd03aedab6a618dfdd19b2c7510dbde5dcde72d921ff5a89c02e5560208e2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-25T23:33:44Z","title_canon_sha256":"5bb6e29e6df80800d2e555f616c161eb9f58c779f4d55ce750f2e442b92494f3"},"schema_version":"1.0","source":{"id":"1103.5096","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.5096","created_at":"2026-05-18T04:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"1103.5096v2","created_at":"2026-05-18T04:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5096","created_at":"2026-05-18T04:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"J2EI6LTYLV5J","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J2EI6LTYLV5JAZOM","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J2EI6LTY","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:3058510c75ba5ed74060a18fc785dc33b321d4ed2140edc6169a88e5d156b081","target":"graph","created_at":"2026-05-18T04:18:34Z","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":"Suppose several parties jointly possess a pure multipartite state, |\\psi>. Using local operations on their respective systems and classical communication (i.e. LOCC) it may be possible for the parties to transform deterministically |\\psi> into another joint state |\\phi>. In the bipartite case, Nielsen majorization theorem gives the necessary and sufficient conditions for this process of entanglement transformation to be possible. In the multipartite case, such a deterministic local transformation is possible only if both the states in the same stochastic LOCC (SLOCC) class. Here we generalize ","authors_text":"Gilad Gour, Nolan R. Wallach","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-25T23:33:44Z","title":"Necessary and sufficient conditions for local manipulation of multipartite pure quantum states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5096","kind":"arxiv","version":2},"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:f5d121b274b0efe1429cdda55e63f90a781709fa4faa0c55aadba1e60e2e053e","target":"record","created_at":"2026-05-18T04:18:34Z","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":"0f1bd03aedab6a618dfdd19b2c7510dbde5dcde72d921ff5a89c02e5560208e2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-25T23:33:44Z","title_canon_sha256":"5bb6e29e6df80800d2e555f616c161eb9f58c779f4d55ce750f2e442b92494f3"},"schema_version":"1.0","source":{"id":"1103.5096","kind":"arxiv","version":2}},"canonical_sha256":"4e888f2e785d7a9065cc25fb6be72920fd63ab00dc2c690098345fc7367371aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e888f2e785d7a9065cc25fb6be72920fd63ab00dc2c690098345fc7367371aa","first_computed_at":"2026-05-18T04:18:34.422483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:34.422483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lYuf00wzPBDBSelBSivxsfmtR8WzwOzokm3g4IOPAsHRLQqEr2z3q11ia4fO41EMF55BEo/OrNfeU53zbV5xBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:34.422976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.5096","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5d121b274b0efe1429cdda55e63f90a781709fa4faa0c55aadba1e60e2e053e","sha256:3058510c75ba5ed74060a18fc785dc33b321d4ed2140edc6169a88e5d156b081"],"state_sha256":"19bf430934673255e934f433a4e249b97cb8531a669240ad77191b308951dabf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OKo7FBjaXEsFkqlGH7Hp3+b5qNxh8ssXTBwdaxl+Lropr7UtoCc4m8VQFdhEn+gzqyBD0lMyOSSM63kgk4PJBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:58:02.138361Z","bundle_sha256":"fb040cb98e80cc6211a79455d06a3bc055c8f64f101c731b323966e657b820d6"}}