{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:IJAXT3OXH3JBR7REMTYBWJKUVF","short_pith_number":"pith:IJAXT3OX","canonical_record":{"source":{"id":"cond-mat/0701764","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.other","submitted_at":"2007-01-31T02:28:02Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"693aa82f970cf157cf87d61aa844aaef141ddebb60317d23b8edf08136b24155","abstract_canon_sha256":"cfb7f51cf756362db49695d4c76f6bee97e90ce345f38b25410685627cc2f63b"},"schema_version":"1.0"},"canonical_sha256":"424179edd73ed218fe2464f01b2554a95ef42c9e746c38fa54a86b9517daa75f","source":{"kind":"arxiv","id":"cond-mat/0701764","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0701764","created_at":"2026-05-18T01:09:20Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0701764v2","created_at":"2026-05-18T01:09:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0701764","created_at":"2026-05-18T01:09:20Z"},{"alias_kind":"pith_short_12","alias_value":"IJAXT3OXH3JB","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"IJAXT3OXH3JBR7RE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"IJAXT3OX","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:IJAXT3OXH3JBR7REMTYBWJKUVF","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0701764","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.other","submitted_at":"2007-01-31T02:28:02Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"693aa82f970cf157cf87d61aa844aaef141ddebb60317d23b8edf08136b24155","abstract_canon_sha256":"cfb7f51cf756362db49695d4c76f6bee97e90ce345f38b25410685627cc2f63b"},"schema_version":"1.0"},"canonical_sha256":"424179edd73ed218fe2464f01b2554a95ef42c9e746c38fa54a86b9517daa75f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:20.962183Z","signature_b64":"U6SvN5VQR0rCMvMCi9xbwdMImMAHkktFgemr65zXxPNnCKvwYeji0Rb9l3WoFQA1FKXuWZEK3utd4MWsW60zCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"424179edd73ed218fe2464f01b2554a95ef42c9e746c38fa54a86b9517daa75f","last_reissued_at":"2026-05-18T01:09:20.961559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:20.961559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0701764","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":"2026-05-18T01:09:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kYHVSHi87SetN+2mXQR2FSs01Qsl55jykrNSMona/z+Kj/q9P1Clm7MqZAm1asN+V/OJ/Fl4TvT3mAhoyeRLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:12:36.455239Z"},"content_sha256":"80f859186099834b668af9ecf08f2dd517ad5f2543d17f540c619285aa0c55a8","schema_version":"1.0","event_id":"sha256:80f859186099834b668af9ecf08f2dd517ad5f2543d17f540c619285aa0c55a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:IJAXT3OXH3JBR7REMTYBWJKUVF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ground-state properties of trapped Bose-Einstein condensates: Extension of the Thomas-Fermi approximation","license":"","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.other","authors_text":"A. Mu\\~noz Mateo, V. Delgado (Univ. La Laguna)","submitted_at":"2007-01-31T02:28:02Z","abstract_excerpt":"We derive general approximate formulas that provide with remarkable accuracy the ground-state properties of any mean-field scalar Bose-Einstein condensate with short-range repulsive interatomic interactions, confined in arbitrary cylindrically symmetric harmonic traps. Our formulation is even applicable for condensates containing a multiply quantized axisymmetric vortex. We have checked the validity of our formulas by numerically solving the 3D Gross-Pitaevskii equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0701764","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":"2026-05-18T01:09:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7rBFuHu58nZLlP/YJ+iDmDrk4JkjvwikFq7gBma07b8Uj5ZRxT2qyjXaz5roYOtSm/RqVyZGJ2c09g6aqkQmAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:12:36.455593Z"},"content_sha256":"bcff7c75e27004e67cb7aeb90c607aed9fbef2e4b832cf7dc60ddaad1d99f799","schema_version":"1.0","event_id":"sha256:bcff7c75e27004e67cb7aeb90c607aed9fbef2e4b832cf7dc60ddaad1d99f799"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IJAXT3OXH3JBR7REMTYBWJKUVF/bundle.json","state_url":"https://pith.science/pith/IJAXT3OXH3JBR7REMTYBWJKUVF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IJAXT3OXH3JBR7REMTYBWJKUVF/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":"2026-06-26T02:12:36Z","links":{"resolver":"https://pith.science/pith/IJAXT3OXH3JBR7REMTYBWJKUVF","bundle":"https://pith.science/pith/IJAXT3OXH3JBR7REMTYBWJKUVF/bundle.json","state":"https://pith.science/pith/IJAXT3OXH3JBR7REMTYBWJKUVF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IJAXT3OXH3JBR7REMTYBWJKUVF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:IJAXT3OXH3JBR7REMTYBWJKUVF","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":"cfb7f51cf756362db49695d4c76f6bee97e90ce345f38b25410685627cc2f63b","cross_cats_sorted":["quant-ph"],"license":"","primary_cat":"cond-mat.other","submitted_at":"2007-01-31T02:28:02Z","title_canon_sha256":"693aa82f970cf157cf87d61aa844aaef141ddebb60317d23b8edf08136b24155"},"schema_version":"1.0","source":{"id":"cond-mat/0701764","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0701764","created_at":"2026-05-18T01:09:20Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0701764v2","created_at":"2026-05-18T01:09:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0701764","created_at":"2026-05-18T01:09:20Z"},{"alias_kind":"pith_short_12","alias_value":"IJAXT3OXH3JB","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"IJAXT3OXH3JBR7RE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"IJAXT3OX","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:bcff7c75e27004e67cb7aeb90c607aed9fbef2e4b832cf7dc60ddaad1d99f799","target":"graph","created_at":"2026-05-18T01:09:20Z","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 derive general approximate formulas that provide with remarkable accuracy the ground-state properties of any mean-field scalar Bose-Einstein condensate with short-range repulsive interatomic interactions, confined in arbitrary cylindrically symmetric harmonic traps. Our formulation is even applicable for condensates containing a multiply quantized axisymmetric vortex. We have checked the validity of our formulas by numerically solving the 3D Gross-Pitaevskii equation.","authors_text":"A. Mu\\~noz Mateo, V. Delgado (Univ. La Laguna)","cross_cats":["quant-ph"],"headline":"","license":"","primary_cat":"cond-mat.other","submitted_at":"2007-01-31T02:28:02Z","title":"Ground-state properties of trapped Bose-Einstein condensates: Extension of the Thomas-Fermi approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0701764","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":"sha256:80f859186099834b668af9ecf08f2dd517ad5f2543d17f540c619285aa0c55a8","target":"record","created_at":"2026-05-18T01:09:20Z","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":"cfb7f51cf756362db49695d4c76f6bee97e90ce345f38b25410685627cc2f63b","cross_cats_sorted":["quant-ph"],"license":"","primary_cat":"cond-mat.other","submitted_at":"2007-01-31T02:28:02Z","title_canon_sha256":"693aa82f970cf157cf87d61aa844aaef141ddebb60317d23b8edf08136b24155"},"schema_version":"1.0","source":{"id":"cond-mat/0701764","kind":"arxiv","version":2}},"canonical_sha256":"424179edd73ed218fe2464f01b2554a95ef42c9e746c38fa54a86b9517daa75f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"424179edd73ed218fe2464f01b2554a95ef42c9e746c38fa54a86b9517daa75f","first_computed_at":"2026-05-18T01:09:20.961559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:20.961559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U6SvN5VQR0rCMvMCi9xbwdMImMAHkktFgemr65zXxPNnCKvwYeji0Rb9l3WoFQA1FKXuWZEK3utd4MWsW60zCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:20.962183Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0701764","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80f859186099834b668af9ecf08f2dd517ad5f2543d17f540c619285aa0c55a8","sha256:bcff7c75e27004e67cb7aeb90c607aed9fbef2e4b832cf7dc60ddaad1d99f799"],"state_sha256":"e595fa2adf38f3e1b98512a2cd9315f3ce65edbc9e3f47768ae99911639917f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BYNsKefUaO8KyL68ZNqF6PZuyqS3yBb0m07gYdvVndHr6wUZFAVF1BOjVclVq7ezLkha5nRLwn3qoH1Ch64IAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T02:12:36.457528Z","bundle_sha256":"16fe96ee5ecbaec388b4d89e253ef59eb1e3481edad947f53e48dc6f01f65741"}}