{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PYQGJZGNWBRFOOKEBBW2PA4EI4","short_pith_number":"pith:PYQGJZGN","canonical_record":{"source":{"id":"1104.3655","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-04-19T07:03:23Z","cross_cats_sorted":[],"title_canon_sha256":"744e879c2e39c3be2dc511b85a5b8726e466f7b4d94be4a32e4a50442021db37","abstract_canon_sha256":"b2d253f36a923dd308badd60fe13b4ae08493aae9231801dedc5de72f82449eb"},"schema_version":"1.0"},"canonical_sha256":"7e2064e4cdb062573944086da78384472692ed25548dde1cefb1b93d50f4a593","source":{"kind":"arxiv","id":"1104.3655","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3655","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3655v1","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3655","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"pith_short_12","alias_value":"PYQGJZGNWBRF","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PYQGJZGNWBRFOOKE","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PYQGJZGN","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PYQGJZGNWBRFOOKEBBW2PA4EI4","target":"record","payload":{"canonical_record":{"source":{"id":"1104.3655","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-04-19T07:03:23Z","cross_cats_sorted":[],"title_canon_sha256":"744e879c2e39c3be2dc511b85a5b8726e466f7b4d94be4a32e4a50442021db37","abstract_canon_sha256":"b2d253f36a923dd308badd60fe13b4ae08493aae9231801dedc5de72f82449eb"},"schema_version":"1.0"},"canonical_sha256":"7e2064e4cdb062573944086da78384472692ed25548dde1cefb1b93d50f4a593","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:55.856561Z","signature_b64":"bay5mF8vyffO/Jih/oydppAQYxrrcr5v0nndNmt0WJDekh9A58hpCH7z1Srue1b3Xhs80gfVgco/qcKJX2yyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e2064e4cdb062573944086da78384472692ed25548dde1cefb1b93d50f4a593","last_reissued_at":"2026-05-18T04:23:55.856161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:55.856161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.3655","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":"2026-05-18T04:23:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7+ngOGnCpkHtYE/+UnyJCZZZK4sZ5dsRkmxcWexR6Mt8zDb8lrsylVuQZRaFIsU8rpFWWQQPwEtfvog4bwECAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:45:14.611489Z"},"content_sha256":"5d1ef6900526b73b64e226d46db0c934881e91007804bd92d88338caf73318cb","schema_version":"1.0","event_id":"sha256:5d1ef6900526b73b64e226d46db0c934881e91007804bd92d88338caf73318cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PYQGJZGNWBRFOOKEBBW2PA4EI4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalised purity as an entanglement measure for two- and three-well Bose-Hubbard models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"C.V. Chianca, M.K. Olsen","submitted_at":"2011-04-19T07:03:23Z","abstract_excerpt":"The SU(2) and SU(3) Lie algebras lend themselves naturally to studies of two- and three-well Bose-Einstein condensates, with the group operators being expressed in terms of bosonic annihilation and creation operators at each site. The success of these representations has led to the purities associated with these algebras to be promoted as a measure of entanglement between the atomic modes in each well. In this report, we show that these purities do not provide an unambiguous measure, but instead give results which depend on the quantum statistical states of each atomic mode. Using the example "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3655","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":"2026-05-18T04:23:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UJ/8ET2VabTyji0zY41Q/fPyAQgkgq+/JAYFfa6Wi0+WbjEJuAk9agw8EvUw3b+G+rNtOrJeprUc4snCejH8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:45:14.611833Z"},"content_sha256":"a96b017d51388e027c3d367738355c2b94b21550f07a41dbb9b2a154ce2aef84","schema_version":"1.0","event_id":"sha256:a96b017d51388e027c3d367738355c2b94b21550f07a41dbb9b2a154ce2aef84"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PYQGJZGNWBRFOOKEBBW2PA4EI4/bundle.json","state_url":"https://pith.science/pith/PYQGJZGNWBRFOOKEBBW2PA4EI4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PYQGJZGNWBRFOOKEBBW2PA4EI4/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":"2026-06-26T07:45:14Z","links":{"resolver":"https://pith.science/pith/PYQGJZGNWBRFOOKEBBW2PA4EI4","bundle":"https://pith.science/pith/PYQGJZGNWBRFOOKEBBW2PA4EI4/bundle.json","state":"https://pith.science/pith/PYQGJZGNWBRFOOKEBBW2PA4EI4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PYQGJZGNWBRFOOKEBBW2PA4EI4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PYQGJZGNWBRFOOKEBBW2PA4EI4","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":"b2d253f36a923dd308badd60fe13b4ae08493aae9231801dedc5de72f82449eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-04-19T07:03:23Z","title_canon_sha256":"744e879c2e39c3be2dc511b85a5b8726e466f7b4d94be4a32e4a50442021db37"},"schema_version":"1.0","source":{"id":"1104.3655","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3655","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3655v1","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3655","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"pith_short_12","alias_value":"PYQGJZGNWBRF","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PYQGJZGNWBRFOOKE","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PYQGJZGN","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:a96b017d51388e027c3d367738355c2b94b21550f07a41dbb9b2a154ce2aef84","target":"graph","created_at":"2026-05-18T04:23:55Z","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":"The SU(2) and SU(3) Lie algebras lend themselves naturally to studies of two- and three-well Bose-Einstein condensates, with the group operators being expressed in terms of bosonic annihilation and creation operators at each site. The success of these representations has led to the purities associated with these algebras to be promoted as a measure of entanglement between the atomic modes in each well. In this report, we show that these purities do not provide an unambiguous measure, but instead give results which depend on the quantum statistical states of each atomic mode. Using the example ","authors_text":"C.V. Chianca, M.K. Olsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-04-19T07:03:23Z","title":"Generalised purity as an entanglement measure for two- and three-well Bose-Hubbard models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3655","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":"sha256:5d1ef6900526b73b64e226d46db0c934881e91007804bd92d88338caf73318cb","target":"record","created_at":"2026-05-18T04:23:55Z","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":"b2d253f36a923dd308badd60fe13b4ae08493aae9231801dedc5de72f82449eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-04-19T07:03:23Z","title_canon_sha256":"744e879c2e39c3be2dc511b85a5b8726e466f7b4d94be4a32e4a50442021db37"},"schema_version":"1.0","source":{"id":"1104.3655","kind":"arxiv","version":1}},"canonical_sha256":"7e2064e4cdb062573944086da78384472692ed25548dde1cefb1b93d50f4a593","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e2064e4cdb062573944086da78384472692ed25548dde1cefb1b93d50f4a593","first_computed_at":"2026-05-18T04:23:55.856161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:55.856161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bay5mF8vyffO/Jih/oydppAQYxrrcr5v0nndNmt0WJDekh9A58hpCH7z1Srue1b3Xhs80gfVgco/qcKJX2yyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:55.856561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3655","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d1ef6900526b73b64e226d46db0c934881e91007804bd92d88338caf73318cb","sha256:a96b017d51388e027c3d367738355c2b94b21550f07a41dbb9b2a154ce2aef84"],"state_sha256":"cf33144235d74ea55fe0ad92e1bc996920cdd5ca8854e14e3c825547dd804767"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A1vKqoi8P6Gz6tZnH/9IXfysTjB0JUfyIO+DZNomMJ7yKaMHSGg2UdDe6lLYPVSP/XarBXsdvaN0zhS/MU4MBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T07:45:14.613745Z","bundle_sha256":"136818a8f786d6b05ae0aefd2a7a05d5a9059b628942684673ff3b5ec942e69a"}}