{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:65TUXWJH5KWRDTE7PHXZI5MLPH","short_pith_number":"pith:65TUXWJH","schema_version":"1.0","canonical_sha256":"f7674bd927eaad11cc9f79ef94758b79fe315f313190a10eca64d15ebb4476db","source":{"kind":"arxiv","id":"0909.5553","version":2},"attestation_state":"computed","paper":{"title":"Off-diagonal Long-Range Order and Supersolidity in a Quantum Solid with Vacancies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.other","authors_text":"Shao-Ming Fei, Yin Yang, Yu Shi","submitted_at":"2009-09-30T09:31:24Z","abstract_excerpt":"We consider a lattice of bosonic atoms, whose number N may be smaller than the number of lattice sites M. We study the Hartree-Fock wave function built up from localized wave functios w(\\mathbf{r}) of single atoms, with nearest neighboring overlap. The zero-momentum particle number is expressed in terms of permanents of matrices. In one dimension, it is analytically calculated to be \\alpha*N(M-N+1)/M, with \\alpha=|\\int w(\\mathbf{r})d\\Omega|^2/[(1+2a)l], where a is the nearest-neighboring overlap, l is the lattice constant. \\alpha is of the order of 1. The result indicates that the condensate f"},"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":"0909.5553","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.other","submitted_at":"2009-09-30T09:31:24Z","cross_cats_sorted":[],"title_canon_sha256":"6fbe6b4664d3d24f0da2c62b3433b8e1eaea764367216591fe444836febcc924","abstract_canon_sha256":"a514be04d8b5301cec312940e743266ea96d890a6d4074dc7877bf16b00db872"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:03.427290Z","signature_b64":"iYy9vOIpbjvUy6YS01dMaWIpOqoFKa/rAO31ZFo6+MofmIvrQaJDs5nt6kXnofMVgZZd2dbgqzN30UX913OeDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7674bd927eaad11cc9f79ef94758b79fe315f313190a10eca64d15ebb4476db","last_reissued_at":"2026-05-18T04:42:03.426862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:03.426862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Off-diagonal Long-Range Order and Supersolidity in a Quantum Solid with Vacancies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.other","authors_text":"Shao-Ming Fei, Yin Yang, Yu Shi","submitted_at":"2009-09-30T09:31:24Z","abstract_excerpt":"We consider a lattice of bosonic atoms, whose number N may be smaller than the number of lattice sites M. We study the Hartree-Fock wave function built up from localized wave functios w(\\mathbf{r}) of single atoms, with nearest neighboring overlap. The zero-momentum particle number is expressed in terms of permanents of matrices. In one dimension, it is analytically calculated to be \\alpha*N(M-N+1)/M, with \\alpha=|\\int w(\\mathbf{r})d\\Omega|^2/[(1+2a)l], where a is the nearest-neighboring overlap, l is the lattice constant. \\alpha is of the order of 1. The result indicates that the condensate f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.5553","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0909.5553","created_at":"2026-05-18T04:42:03.426926+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.5553v2","created_at":"2026-05-18T04:42:03.426926+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.5553","created_at":"2026-05-18T04:42:03.426926+00:00"},{"alias_kind":"pith_short_12","alias_value":"65TUXWJH5KWR","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"65TUXWJH5KWRDTE7","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"65TUXWJH","created_at":"2026-05-18T12:25:58.837520+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/65TUXWJH5KWRDTE7PHXZI5MLPH","json":"https://pith.science/pith/65TUXWJH5KWRDTE7PHXZI5MLPH.json","graph_json":"https://pith.science/api/pith-number/65TUXWJH5KWRDTE7PHXZI5MLPH/graph.json","events_json":"https://pith.science/api/pith-number/65TUXWJH5KWRDTE7PHXZI5MLPH/events.json","paper":"https://pith.science/paper/65TUXWJH"},"agent_actions":{"view_html":"https://pith.science/pith/65TUXWJH5KWRDTE7PHXZI5MLPH","download_json":"https://pith.science/pith/65TUXWJH5KWRDTE7PHXZI5MLPH.json","view_paper":"https://pith.science/paper/65TUXWJH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.5553&json=true","fetch_graph":"https://pith.science/api/pith-number/65TUXWJH5KWRDTE7PHXZI5MLPH/graph.json","fetch_events":"https://pith.science/api/pith-number/65TUXWJH5KWRDTE7PHXZI5MLPH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/65TUXWJH5KWRDTE7PHXZI5MLPH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/65TUXWJH5KWRDTE7PHXZI5MLPH/action/storage_attestation","attest_author":"https://pith.science/pith/65TUXWJH5KWRDTE7PHXZI5MLPH/action/author_attestation","sign_citation":"https://pith.science/pith/65TUXWJH5KWRDTE7PHXZI5MLPH/action/citation_signature","submit_replication":"https://pith.science/pith/65TUXWJH5KWRDTE7PHXZI5MLPH/action/replication_record"}},"created_at":"2026-05-18T04:42:03.426926+00:00","updated_at":"2026-05-18T04:42:03.426926+00:00"}