{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:CAWZ7UTOOXPLZFB6REYGDIHUTI","short_pith_number":"pith:CAWZ7UTO","schema_version":"1.0","canonical_sha256":"102d9fd26e75debc943e893061a0f49a3137c5a690f42f0a4abf91497575e95d","source":{"kind":"arxiv","id":"1012.2850","version":3},"attestation_state":"computed","paper":{"title":"Generalized Bose-Einstein Condensation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","cond-mat.stat-mech"],"primary_cat":"quant-ph","authors_text":"Asaad R. Sakhel, William J. Mullin","submitted_at":"2010-12-13T20:21:43Z","abstract_excerpt":"Generalized Bose-Einstein condensation (GBEC) involves condensates appearing simultaneously in multiple states. We review examples of the three types in an ideal Bose gas with different geometries. In Type I there is a discrete number of quantum states each having macroscopic occupation; Type II has condensation into a continuous band of states, with each state having macroscopic occupation; in Type III each state is microscopically occupied while the entire condensate band is macroscopically occupied. We begin by discussing Type I or \"normal\" BEC into a single state for an isotropic harmonic "},"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":"1012.2850","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-13T20:21:43Z","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech"],"title_canon_sha256":"3addf92a1de2f2635daf851272d3b0676ba7de777908e22e2c8c2087bb4de0b8","abstract_canon_sha256":"9582218f94002544106c6c5f727a94150316468675ac8922acfc19ccdbdac7f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:25.487277Z","signature_b64":"0AOjpEoX63kzD26LEUWf4yLsn/4EOwcK91zo/DoJqKzMLtjsKT5Y7EUrfBPRhlCxMHHERmbXRXAB6oFw4NjZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"102d9fd26e75debc943e893061a0f49a3137c5a690f42f0a4abf91497575e95d","last_reissued_at":"2026-05-18T02:04:25.486630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:25.486630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Bose-Einstein Condensation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","cond-mat.stat-mech"],"primary_cat":"quant-ph","authors_text":"Asaad R. Sakhel, William J. Mullin","submitted_at":"2010-12-13T20:21:43Z","abstract_excerpt":"Generalized Bose-Einstein condensation (GBEC) involves condensates appearing simultaneously in multiple states. We review examples of the three types in an ideal Bose gas with different geometries. In Type I there is a discrete number of quantum states each having macroscopic occupation; Type II has condensation into a continuous band of states, with each state having macroscopic occupation; in Type III each state is microscopically occupied while the entire condensate band is macroscopically occupied. We begin by discussing Type I or \"normal\" BEC into a single state for an isotropic harmonic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2850","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":"1012.2850","created_at":"2026-05-18T02:04:25.486727+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.2850v3","created_at":"2026-05-18T02:04:25.486727+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2850","created_at":"2026-05-18T02:04:25.486727+00:00"},{"alias_kind":"pith_short_12","alias_value":"CAWZ7UTOOXPL","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CAWZ7UTOOXPLZFB6","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CAWZ7UTO","created_at":"2026-05-18T12:26:05.355336+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/CAWZ7UTOOXPLZFB6REYGDIHUTI","json":"https://pith.science/pith/CAWZ7UTOOXPLZFB6REYGDIHUTI.json","graph_json":"https://pith.science/api/pith-number/CAWZ7UTOOXPLZFB6REYGDIHUTI/graph.json","events_json":"https://pith.science/api/pith-number/CAWZ7UTOOXPLZFB6REYGDIHUTI/events.json","paper":"https://pith.science/paper/CAWZ7UTO"},"agent_actions":{"view_html":"https://pith.science/pith/CAWZ7UTOOXPLZFB6REYGDIHUTI","download_json":"https://pith.science/pith/CAWZ7UTOOXPLZFB6REYGDIHUTI.json","view_paper":"https://pith.science/paper/CAWZ7UTO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.2850&json=true","fetch_graph":"https://pith.science/api/pith-number/CAWZ7UTOOXPLZFB6REYGDIHUTI/graph.json","fetch_events":"https://pith.science/api/pith-number/CAWZ7UTOOXPLZFB6REYGDIHUTI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CAWZ7UTOOXPLZFB6REYGDIHUTI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CAWZ7UTOOXPLZFB6REYGDIHUTI/action/storage_attestation","attest_author":"https://pith.science/pith/CAWZ7UTOOXPLZFB6REYGDIHUTI/action/author_attestation","sign_citation":"https://pith.science/pith/CAWZ7UTOOXPLZFB6REYGDIHUTI/action/citation_signature","submit_replication":"https://pith.science/pith/CAWZ7UTOOXPLZFB6REYGDIHUTI/action/replication_record"}},"created_at":"2026-05-18T02:04:25.486727+00:00","updated_at":"2026-05-18T02:04:25.486727+00:00"}