{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DBOWUZXIDAY6ZD7RNA75PUZXLT","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":"5d94c5e0caf2681145ce73fe32148ad3c3866f7ee3d09035729a332f3deb45a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-18T16:11:43Z","title_canon_sha256":"077ed9bf863aa6ae6624620419038ba5db24590b026d7b8bf60958e26ee3996b"},"schema_version":"1.0","source":{"id":"1604.05228","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05228","created_at":"2026-05-18T01:16:12Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05228v1","created_at":"2026-05-18T01:16:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05228","created_at":"2026-05-18T01:16:12Z"},{"alias_kind":"pith_short_12","alias_value":"DBOWUZXIDAY6","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"DBOWUZXIDAY6ZD7R","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"DBOWUZXI","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:9d1b905e521c3d3582fa437969e7320b5d1576f718b74cb2686e9cec6f1f7f17","target":"graph","created_at":"2026-05-18T01:16:12Z","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":"In this paper, we propose a computable error estimate of the Gross-Pitaevskii equation for ground state solution of Bose-Einstein condensates by general conforming finite element methods on general meshes. Based on the proposed error estimate, asymptotic lower bounds of the smallest eigenvalue and ground state energy can be obtained. Several numerical examples are presented to validate our theoretical results in this paper.","authors_text":"Hehu Xie, Manting Xie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-18T16:11:43Z","title":"Computable Error Estimates for Ground State Solution of Bose-Einstein Condensates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05228","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":"sha256:7333b73e3c403aaa2a2d778d69d2fec7e70437a2d785fe0d27b6b51a4d433aef","target":"record","created_at":"2026-05-18T01:16:12Z","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":"5d94c5e0caf2681145ce73fe32148ad3c3866f7ee3d09035729a332f3deb45a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-18T16:11:43Z","title_canon_sha256":"077ed9bf863aa6ae6624620419038ba5db24590b026d7b8bf60958e26ee3996b"},"schema_version":"1.0","source":{"id":"1604.05228","kind":"arxiv","version":1}},"canonical_sha256":"185d6a66e81831ec8ff1683fd7d3375ce68f4b61bc5e271ed42b80d496464e5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"185d6a66e81831ec8ff1683fd7d3375ce68f4b61bc5e271ed42b80d496464e5a","first_computed_at":"2026-05-18T01:16:12.732820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:12.732820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6m+5UFpmnUUqZJRL7hpy6oojL5RNes5AUbLCdPT2RLRB1vG3gwc0RmkcUS/tOzaemNcljhaccN8G9mChb6LTDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:12.733590Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.05228","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7333b73e3c403aaa2a2d778d69d2fec7e70437a2d785fe0d27b6b51a4d433aef","sha256:9d1b905e521c3d3582fa437969e7320b5d1576f718b74cb2686e9cec6f1f7f17"],"state_sha256":"c75099077c8d2f70477735465fa8e0434a95b4d7ab60322e7382890bf455ef0b"}