{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:77AJ5LOEMEMJESGFX2I5DIF67F","short_pith_number":"pith:77AJ5LOE","schema_version":"1.0","canonical_sha256":"ffc09eadc461189248c5be91d1a0bef961f27e0391668ed94ed6dbc6e801dd5f","source":{"kind":"arxiv","id":"1210.1609","version":1},"attestation_state":"computed","paper":{"title":"On Nonlocal Gross-Pitaevskii Equations with Periodic Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Christopher W. Curtis","submitted_at":"2012-10-04T23:02:34Z","abstract_excerpt":"The Gross-Pitaevskii equation is a widely used model in physics, in particular in the context of Bose-Einstein condensates. However, it only takes into account local interactions between particles. This paper demonstrates the validity of using a nonlocal formulation as a generalization of the local model. In particular, the paper demonstrates that the solution of the nonlocal model approaches in norm the solution of the local model as the nonlocal model approaches the local model. The nonlocality and potential used for the Gross-Pitaevskii equation are quite general, thus this paper shows that"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.1609","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-04T23:02:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"cd10a42a8b09545a5dd6beffba5de052c5bc129e80f12d7a22edcd74f01920e2","abstract_canon_sha256":"e53aeb3bc4c073aa597f4adca0c840341795d12b6396af30a66d9843ca97fa0e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:06.122106Z","signature_b64":"TKd/RkZFZ7IoGMpa94la4/vDuIC/E+R036kKd1Vv/mPu35qzXc/O/wIK2T7v9VjiZZ8uwAeiP9T1hagFwrjDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffc09eadc461189248c5be91d1a0bef961f27e0391668ed94ed6dbc6e801dd5f","last_reissued_at":"2026-05-18T03:39:06.121271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:06.121271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Nonlocal Gross-Pitaevskii Equations with Periodic Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Christopher W. Curtis","submitted_at":"2012-10-04T23:02:34Z","abstract_excerpt":"The Gross-Pitaevskii equation is a widely used model in physics, in particular in the context of Bose-Einstein condensates. However, it only takes into account local interactions between particles. This paper demonstrates the validity of using a nonlocal formulation as a generalization of the local model. In particular, the paper demonstrates that the solution of the nonlocal model approaches in norm the solution of the local model as the nonlocal model approaches the local model. The nonlocality and potential used for the Gross-Pitaevskii equation are quite general, thus this paper shows that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1609","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.1609","created_at":"2026-05-18T03:39:06.121428+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.1609v1","created_at":"2026-05-18T03:39:06.121428+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1609","created_at":"2026-05-18T03:39:06.121428+00:00"},{"alias_kind":"pith_short_12","alias_value":"77AJ5LOEMEMJ","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"77AJ5LOEMEMJESGF","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"77AJ5LOE","created_at":"2026-05-18T12:26:56.085431+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/77AJ5LOEMEMJESGFX2I5DIF67F","json":"https://pith.science/pith/77AJ5LOEMEMJESGFX2I5DIF67F.json","graph_json":"https://pith.science/api/pith-number/77AJ5LOEMEMJESGFX2I5DIF67F/graph.json","events_json":"https://pith.science/api/pith-number/77AJ5LOEMEMJESGFX2I5DIF67F/events.json","paper":"https://pith.science/paper/77AJ5LOE"},"agent_actions":{"view_html":"https://pith.science/pith/77AJ5LOEMEMJESGFX2I5DIF67F","download_json":"https://pith.science/pith/77AJ5LOEMEMJESGFX2I5DIF67F.json","view_paper":"https://pith.science/paper/77AJ5LOE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.1609&json=true","fetch_graph":"https://pith.science/api/pith-number/77AJ5LOEMEMJESGFX2I5DIF67F/graph.json","fetch_events":"https://pith.science/api/pith-number/77AJ5LOEMEMJESGFX2I5DIF67F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/77AJ5LOEMEMJESGFX2I5DIF67F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/77AJ5LOEMEMJESGFX2I5DIF67F/action/storage_attestation","attest_author":"https://pith.science/pith/77AJ5LOEMEMJESGFX2I5DIF67F/action/author_attestation","sign_citation":"https://pith.science/pith/77AJ5LOEMEMJESGFX2I5DIF67F/action/citation_signature","submit_replication":"https://pith.science/pith/77AJ5LOEMEMJESGFX2I5DIF67F/action/replication_record"}},"created_at":"2026-05-18T03:39:06.121428+00:00","updated_at":"2026-05-18T03:39:06.121428+00:00"}