{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:ANC7ORTO4L3PFYZJGVON7CHK76","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":"7652648054fa0eaa270080c7837b2ebd98236991d96b77bb4f0bfd4d39f6bdba","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat","submitted_at":"1998-03-13T16:50:26Z","title_canon_sha256":"3e45b7b67f52b5589f9f70e2b23dbc84da87a2be1057e531fca5c128ea15eba8"},"schema_version":"1.0","source":{"id":"cond-mat/9803174","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9803174","created_at":"2026-05-18T01:39:30Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9803174v1","created_at":"2026-05-18T01:39:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9803174","created_at":"2026-05-18T01:39:30Z"},{"alias_kind":"pith_short_12","alias_value":"ANC7ORTO4L3P","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"ANC7ORTO4L3PFYZJ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"ANC7ORTO","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:6f711c7b70020e1373c8522a424503d776122e7f78edeae190197c7996aa0ccb","target":"graph","created_at":"2026-05-18T01:39:30Z","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 investigate the stability of the Bose-Einstein condensate (BEC) the case of atoms with negative scattering lengths at zero temperature using the Ginzburg-Pitaevskii-Gross (GPG) stationary theory. We have found a new exact equation for determining the upper bound of the critical numbers $N_{cr}$ of atoms for a metastable state to exist. Our calculated value of $N_{cr}$ for Bose-Einstein condensation of lithium atoms based on our new equation is in agreement with those observed in a agreement with those observed in a recent experiment.","authors_text":"Alexander L. Zubarev (Department of Physics, Purdue University), Yeong E. Kim","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat","submitted_at":"1998-03-13T16:50:26Z","title":"Stability of Solution of the Nonlinear Schr\\\"odinger Equation for the Bose-Einstein Condensation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9803174","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":"sha256:5e416a6bd35d3502649e688f12698f32d02e945a6e54e9b862b05398b24de829","target":"record","created_at":"2026-05-18T01:39:30Z","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":"7652648054fa0eaa270080c7837b2ebd98236991d96b77bb4f0bfd4d39f6bdba","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat","submitted_at":"1998-03-13T16:50:26Z","title_canon_sha256":"3e45b7b67f52b5589f9f70e2b23dbc84da87a2be1057e531fca5c128ea15eba8"},"schema_version":"1.0","source":{"id":"cond-mat/9803174","kind":"arxiv","version":1}},"canonical_sha256":"0345f7466ee2f6f2e329355cdf88eaff91a037ea718081a429176fa7f3f65a70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0345f7466ee2f6f2e329355cdf88eaff91a037ea718081a429176fa7f3f65a70","first_computed_at":"2026-05-18T01:39:30.975307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:30.975307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MdkLwTB1yIReissP9B2JrsqP7jG+a+euOUMLeahGgCnfiqA1CothbYbkprfJIjrJPGv5RwdKQBqax7RHKVNhCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:30.975853Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9803174","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e416a6bd35d3502649e688f12698f32d02e945a6e54e9b862b05398b24de829","sha256:6f711c7b70020e1373c8522a424503d776122e7f78edeae190197c7996aa0ccb"],"state_sha256":"d7ea671ad2e1172cf59455ea319ce9806bd8eb0aadf650a612fd8705ac95a721"}