{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7TIANQD753IQGJST3AN44VYKZO","short_pith_number":"pith:7TIANQD7","schema_version":"1.0","canonical_sha256":"fcd006c07feed1032653d81bce570acbbcbb7e2b858768b026a784ede1a05a26","source":{"kind":"arxiv","id":"1303.1642","version":3},"attestation_state":"computed","paper":{"title":"Phase Transitions in Three-Dimensional Bosonic Systems in Optical Lattices","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.quant-gas","authors_text":"Abdulla Rakhimov, H. Kleinert, Z. Narzikulov","submitted_at":"2013-03-07T10:40:58Z","abstract_excerpt":"We formulate the Collective Quantum Field Theory for three-dimensional bosonic optical lattices and evaluate its consequences in a mean-field approximation to two collective fields, proposed by Fred Cooper et al. and in a lowest-order Variational Perturbation Theory (VPT). It is shown that present mean-field approximation predicts some essential features of the experimentally observed dependence of the critical temperature on the coupling strength and a second - order quantum phase transition.In contrast to a recent prediction for atomic gases by Fred Cooper et. al., we find no superfluid stat"},"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":"1303.1642","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2013-03-07T10:40:58Z","cross_cats_sorted":[],"title_canon_sha256":"01c7617f23286395f0fa567392ab1d59b0278c4852fec837249c6368abe5ad57","abstract_canon_sha256":"3ef18cbf0211b3fb1f11ec6fc217fc43127ddf5014b338af96b5046745991cce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:35.919615Z","signature_b64":"junuie2wrjB5vP4hJwl9YjxsJAmsWdWfXQFaMK20C/El5II+RTj4q1aqn7qOASnYSfQUNh3M08Jr3ZOGneuIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcd006c07feed1032653d81bce570acbbcbb7e2b858768b026a784ede1a05a26","last_reissued_at":"2026-05-18T03:01:35.918931Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:35.918931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase Transitions in Three-Dimensional Bosonic Systems in Optical Lattices","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.quant-gas","authors_text":"Abdulla Rakhimov, H. Kleinert, Z. Narzikulov","submitted_at":"2013-03-07T10:40:58Z","abstract_excerpt":"We formulate the Collective Quantum Field Theory for three-dimensional bosonic optical lattices and evaluate its consequences in a mean-field approximation to two collective fields, proposed by Fred Cooper et al. and in a lowest-order Variational Perturbation Theory (VPT). It is shown that present mean-field approximation predicts some essential features of the experimentally observed dependence of the critical temperature on the coupling strength and a second - order quantum phase transition.In contrast to a recent prediction for atomic gases by Fred Cooper et. al., we find no superfluid stat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1642","kind":"arxiv","version":3},"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":"1303.1642","created_at":"2026-05-18T03:01:35.919039+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.1642v3","created_at":"2026-05-18T03:01:35.919039+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1642","created_at":"2026-05-18T03:01:35.919039+00:00"},{"alias_kind":"pith_short_12","alias_value":"7TIANQD753IQ","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7TIANQD753IQGJST","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7TIANQD7","created_at":"2026-05-18T12:27:36.564083+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/7TIANQD753IQGJST3AN44VYKZO","json":"https://pith.science/pith/7TIANQD753IQGJST3AN44VYKZO.json","graph_json":"https://pith.science/api/pith-number/7TIANQD753IQGJST3AN44VYKZO/graph.json","events_json":"https://pith.science/api/pith-number/7TIANQD753IQGJST3AN44VYKZO/events.json","paper":"https://pith.science/paper/7TIANQD7"},"agent_actions":{"view_html":"https://pith.science/pith/7TIANQD753IQGJST3AN44VYKZO","download_json":"https://pith.science/pith/7TIANQD753IQGJST3AN44VYKZO.json","view_paper":"https://pith.science/paper/7TIANQD7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.1642&json=true","fetch_graph":"https://pith.science/api/pith-number/7TIANQD753IQGJST3AN44VYKZO/graph.json","fetch_events":"https://pith.science/api/pith-number/7TIANQD753IQGJST3AN44VYKZO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7TIANQD753IQGJST3AN44VYKZO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7TIANQD753IQGJST3AN44VYKZO/action/storage_attestation","attest_author":"https://pith.science/pith/7TIANQD753IQGJST3AN44VYKZO/action/author_attestation","sign_citation":"https://pith.science/pith/7TIANQD753IQGJST3AN44VYKZO/action/citation_signature","submit_replication":"https://pith.science/pith/7TIANQD753IQGJST3AN44VYKZO/action/replication_record"}},"created_at":"2026-05-18T03:01:35.919039+00:00","updated_at":"2026-05-18T03:01:35.919039+00:00"}