{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:MCQPN4QH2BQEGEYTWQ3DMLWI2S","short_pith_number":"pith:MCQPN4QH","canonical_record":{"source":{"id":"cond-mat/0310066","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-10-03T14:50:18Z","cross_cats_sorted":[],"title_canon_sha256":"d93bcaaccdeeeceebfed2cd6d2a3ae904006ac2a10fe136298c209acc129c18c","abstract_canon_sha256":"6baf8f445ab7a069d42fe2b7aa8b72818e28c09317b88d7c2690ba3b486b3678"},"schema_version":"1.0"},"canonical_sha256":"60a0f6f207d060431313b436362ec8d4951421f01fa9e7ea18fc991d80a20a99","source":{"kind":"arxiv","id":"cond-mat/0310066","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0310066","created_at":"2026-05-18T01:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0310066v3","created_at":"2026-05-18T01:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0310066","created_at":"2026-05-18T01:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"MCQPN4QH2BQE","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"MCQPN4QH2BQEGEYT","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"MCQPN4QH","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:MCQPN4QH2BQEGEYTWQ3DMLWI2S","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0310066","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-10-03T14:50:18Z","cross_cats_sorted":[],"title_canon_sha256":"d93bcaaccdeeeceebfed2cd6d2a3ae904006ac2a10fe136298c209acc129c18c","abstract_canon_sha256":"6baf8f445ab7a069d42fe2b7aa8b72818e28c09317b88d7c2690ba3b486b3678"},"schema_version":"1.0"},"canonical_sha256":"60a0f6f207d060431313b436362ec8d4951421f01fa9e7ea18fc991d80a20a99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:59.068475Z","signature_b64":"0nVXE9fQradGMcpar9e/UH612wj7nF6tBkYEJ+E+q42EEjx7v7uSt5o9d8Y58hlIApk9xzkuSuLXJaDu73AODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60a0f6f207d060431313b436362ec8d4951421f01fa9e7ea18fc991d80a20a99","last_reissued_at":"2026-05-18T01:39:59.067761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:59.067761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0310066","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:39:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Gl23SdiZjVrXvn23SwpsvwWLxrBdODogfMQgBQhl0axNC6s2s4xnuIZs5onW8TYmCTpWCICXmx37KoD/1ShCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:38:10.996671Z"},"content_sha256":"0a133ddf12a21313a27e5284c0a90d5572989ad42b7663368b3fa172eebb6810","schema_version":"1.0","event_id":"sha256:0a133ddf12a21313a27e5284c0a90d5572989ad42b7663368b3fa172eebb6810"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:MCQPN4QH2BQEGEYTWQ3DMLWI2S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gentile statistics with a large maximum occupation number","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Mi Xie, Wu-Sheng Dai","submitted_at":"2003-10-03T14:50:18Z","abstract_excerpt":"In Gentile statistics the maximum occupation number can take on unrestricted integers: $1<n<\\infty $. It is usually believed that Gentile statistics will reduce to Bose-Einstein statistics when n equals the total number of particles in the system N. In this paper, we will show that this statement is valid only when the fugacity z<1; nevertheless, if z>1 the Bose-Einstein case is not recovered from Gentile statistics as n goes to % N . Attention is also concentrated on the contribution of the ground state which was ignored in related literature. The thermodynamic behavior of a $% \\nu $-dimensio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0310066","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:39:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"04JrVg3QNi41O7PYX3z7H3KXWNu5kwT3eJTWqSInElCsBv2l2koCfZpxCYE4oNaNi8QvCSiILl9wHnntWI38Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:38:10.997016Z"},"content_sha256":"2c34032dd9cfe607f3dfdf8d17547364f6fb114680157bfa6588a05324a0ab63","schema_version":"1.0","event_id":"sha256:2c34032dd9cfe607f3dfdf8d17547364f6fb114680157bfa6588a05324a0ab63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MCQPN4QH2BQEGEYTWQ3DMLWI2S/bundle.json","state_url":"https://pith.science/pith/MCQPN4QH2BQEGEYTWQ3DMLWI2S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MCQPN4QH2BQEGEYTWQ3DMLWI2S/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T02:38:10Z","links":{"resolver":"https://pith.science/pith/MCQPN4QH2BQEGEYTWQ3DMLWI2S","bundle":"https://pith.science/pith/MCQPN4QH2BQEGEYTWQ3DMLWI2S/bundle.json","state":"https://pith.science/pith/MCQPN4QH2BQEGEYTWQ3DMLWI2S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MCQPN4QH2BQEGEYTWQ3DMLWI2S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:MCQPN4QH2BQEGEYTWQ3DMLWI2S","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":"6baf8f445ab7a069d42fe2b7aa8b72818e28c09317b88d7c2690ba3b486b3678","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-10-03T14:50:18Z","title_canon_sha256":"d93bcaaccdeeeceebfed2cd6d2a3ae904006ac2a10fe136298c209acc129c18c"},"schema_version":"1.0","source":{"id":"cond-mat/0310066","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0310066","created_at":"2026-05-18T01:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0310066v3","created_at":"2026-05-18T01:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0310066","created_at":"2026-05-18T01:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"MCQPN4QH2BQE","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"MCQPN4QH2BQEGEYT","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"MCQPN4QH","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:2c34032dd9cfe607f3dfdf8d17547364f6fb114680157bfa6588a05324a0ab63","target":"graph","created_at":"2026-05-18T01:39:59Z","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":"In Gentile statistics the maximum occupation number can take on unrestricted integers: $1<n<\\infty $. It is usually believed that Gentile statistics will reduce to Bose-Einstein statistics when n equals the total number of particles in the system N. In this paper, we will show that this statement is valid only when the fugacity z<1; nevertheless, if z>1 the Bose-Einstein case is not recovered from Gentile statistics as n goes to % N . Attention is also concentrated on the contribution of the ground state which was ignored in related literature. The thermodynamic behavior of a $% \\nu $-dimensio","authors_text":"Mi Xie, Wu-Sheng Dai","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-10-03T14:50:18Z","title":"Gentile statistics with a large maximum occupation number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0310066","kind":"arxiv","version":3},"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":"sha256:0a133ddf12a21313a27e5284c0a90d5572989ad42b7663368b3fa172eebb6810","target":"record","created_at":"2026-05-18T01:39:59Z","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":"6baf8f445ab7a069d42fe2b7aa8b72818e28c09317b88d7c2690ba3b486b3678","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-10-03T14:50:18Z","title_canon_sha256":"d93bcaaccdeeeceebfed2cd6d2a3ae904006ac2a10fe136298c209acc129c18c"},"schema_version":"1.0","source":{"id":"cond-mat/0310066","kind":"arxiv","version":3}},"canonical_sha256":"60a0f6f207d060431313b436362ec8d4951421f01fa9e7ea18fc991d80a20a99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60a0f6f207d060431313b436362ec8d4951421f01fa9e7ea18fc991d80a20a99","first_computed_at":"2026-05-18T01:39:59.067761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:59.067761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0nVXE9fQradGMcpar9e/UH612wj7nF6tBkYEJ+E+q42EEjx7v7uSt5o9d8Y58hlIApk9xzkuSuLXJaDu73AODg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:59.068475Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0310066","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a133ddf12a21313a27e5284c0a90d5572989ad42b7663368b3fa172eebb6810","sha256:2c34032dd9cfe607f3dfdf8d17547364f6fb114680157bfa6588a05324a0ab63"],"state_sha256":"e0e6fd14f522938ca238054602ae116a9050087cc5f3976d7d770231d0d4a2d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NPoeUVYd+lj75b9KDlIew0u6+NannS/35ncWSNeaNNpJFvqvnzF3+V2C0sHITaf5ejFJVK+Jl3yU5shT5/GyCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:38:10.998993Z","bundle_sha256":"12788fdb51afac8bf0cc1623c878c6c04fdbb6ee64861b0edf57ca3969469a8b"}}