{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EDDEYEFLM2VMTVJUIFWSXDUOTF","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":"2488748bd5711d06ec177408f200b39c98cea1a9ba5ff28c01069034929daa6f","cross_cats_sorted":["cond-mat.mes-hall","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-10-28T06:59:01Z","title_canon_sha256":"d4b6caee4b11b6a1ae6297d79eddb42e0341e8213ae741b49f56913ee156adb4"},"schema_version":"1.0","source":{"id":"1110.6264","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6264","created_at":"2026-05-18T04:09:57Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6264v1","created_at":"2026-05-18T04:09:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6264","created_at":"2026-05-18T04:09:57Z"},{"alias_kind":"pith_short_12","alias_value":"EDDEYEFLM2VM","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"EDDEYEFLM2VMTVJU","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"EDDEYEFL","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:2c8d93f0182b73df1416e79df64173e8a01bcf6ead5b910d5d793d9c407daaed","target":"graph","created_at":"2026-05-18T04:09:57Z","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 consider equilibrium level occupation numbers in a Fermi gas with a fixed number of particles, n, and finite level spacing. Using the method of generating functions and the cumulant expansion we derive a recurrence relation for canonical partition function and an explicit formula for occupation numbers in terms of single-particle partition function at n different temperatures. We apply this result to a model with equidistant non-degenerate spectrum and obtain close-form expressions in terms of q-polynomials and Rogers-Ramanujan partial theta function. Deviations from the standard Fermi-Dira","authors_text":"Vyacheslavs Kashcheyevs","cross_cats":["cond-mat.mes-hall","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-10-28T06:59:01Z","title":"Exact canonical occupation numbers in a Fermi gas with finite level spacing and a q-analog of Fermi-Dirac distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6264","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":"sha256:63db0cfd2777db61038351c60e3995d855263d6699a4cb8843531aa77ead32d2","target":"record","created_at":"2026-05-18T04:09:57Z","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":"2488748bd5711d06ec177408f200b39c98cea1a9ba5ff28c01069034929daa6f","cross_cats_sorted":["cond-mat.mes-hall","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-10-28T06:59:01Z","title_canon_sha256":"d4b6caee4b11b6a1ae6297d79eddb42e0341e8213ae741b49f56913ee156adb4"},"schema_version":"1.0","source":{"id":"1110.6264","kind":"arxiv","version":1}},"canonical_sha256":"20c64c10ab66aac9d534416d2b8e8e99761ff21c9779d2e5f22cc160561702db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20c64c10ab66aac9d534416d2b8e8e99761ff21c9779d2e5f22cc160561702db","first_computed_at":"2026-05-18T04:09:57.232423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:57.232423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yF8fKaokiEcNIffMFvIAj/TMCOu0c5tRnnEZc3qsnPr7hS5/HKzBv2QQwUdmCoVgON/NyxKI7JxPSZ6Skp01AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:57.233282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6264","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63db0cfd2777db61038351c60e3995d855263d6699a4cb8843531aa77ead32d2","sha256:2c8d93f0182b73df1416e79df64173e8a01bcf6ead5b910d5d793d9c407daaed"],"state_sha256":"1b10c24edc90a55540ae4b11f288aa7b5b50a35b3580bed4fbd56af6633d6e7e"}