{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HNYIG5CAOTUMCGXYDDXJGGH4ZP","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":"f83eb5c987b29faec5f83d17ebff6e01cc56077543271afc614d7c53a297f8ee","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2010-11-30T08:25:04Z","title_canon_sha256":"e7259ced51a580ac701cdacf62c026da54abeda1b4cbfa88b388eae07feaf15a"},"schema_version":"1.0","source":{"id":"1011.6477","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.6477","created_at":"2026-05-17T23:49:34Z"},{"alias_kind":"arxiv_version","alias_value":"1011.6477v2","created_at":"2026-05-17T23:49:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6477","created_at":"2026-05-17T23:49:34Z"},{"alias_kind":"pith_short_12","alias_value":"HNYIG5CAOTUM","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HNYIG5CAOTUMCGXY","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HNYIG5CA","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:2f611112674544c6273669104680fe16e5eab6e243e2be09ad5ca02a99417332","target":"graph","created_at":"2026-05-17T23:49:34Z","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":"Bose-Einstein condensation (BEC) of an ideal gas is investigated, beyond the thermodynamic limit, for a finite number $N$ of particles trapped in a generic three-dimensional power-law potential. We derive an analytical expression for the condensation temperature $T_c$ in terms of a power series in $x_0=\\epsilon_0/k_BT_c$, where $\\epsilon_0$ denotes the zero-point energy of the trapping potential. This expression, which applies in cartesian, cylindrical and spherical power-law traps, is given analytically at infinite order. It is also given numerically for specific potential shapes as an expans","authors_text":"Amine Jaouadi (ISMO, CNSTN), Eric Charron (ISMO), LSAMA), Mourad Telmini (LSAMA","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2010-11-30T08:25:04Z","title":"Bose-Einstein condensation with a finite number of particles in a power-law trap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6477","kind":"arxiv","version":2},"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:fdc9192e53dd9ebe6d645d32492d753837a10dc0a371d48226d9e3d7991af07e","target":"record","created_at":"2026-05-17T23:49:34Z","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":"f83eb5c987b29faec5f83d17ebff6e01cc56077543271afc614d7c53a297f8ee","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2010-11-30T08:25:04Z","title_canon_sha256":"e7259ced51a580ac701cdacf62c026da54abeda1b4cbfa88b388eae07feaf15a"},"schema_version":"1.0","source":{"id":"1011.6477","kind":"arxiv","version":2}},"canonical_sha256":"3b7083744074e8c11af818ee9318fccbddc76ca6b0189ba068e395ee787c6146","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b7083744074e8c11af818ee9318fccbddc76ca6b0189ba068e395ee787c6146","first_computed_at":"2026-05-17T23:49:34.172744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:34.172744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JrosOy5mTvUu4zbr4HKk7PCvmykKwilgaxwhO1i/2nnY4H49Y5o3kJR+Cxe4Qw9EjqoFbb5nsiZzjl6H+jqbCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:34.173234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.6477","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdc9192e53dd9ebe6d645d32492d753837a10dc0a371d48226d9e3d7991af07e","sha256:2f611112674544c6273669104680fe16e5eab6e243e2be09ad5ca02a99417332"],"state_sha256":"9c92256e603ccd69bbaad1d37680f43223ef654f07ae9f61f2dab4c436005ade"}