{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:HECYXOEZCNU7WIJANWFSNCEUI3","short_pith_number":"pith:HECYXOEZ","canonical_record":{"source":{"id":"0906.3777","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-06-20T04:06:09Z","cross_cats_sorted":[],"title_canon_sha256":"6e4815539e4065ad73b10c43c728c869778e84eee6d53193039ddd13660152dd","abstract_canon_sha256":"616ef87a43990115ccf35904c49c1a0782decfa597a3b4ac9febcada5767d961"},"schema_version":"1.0"},"canonical_sha256":"39058bb8991369fb21206d8b26889446dbd5452bfc81de723351c8592ac85eab","source":{"kind":"arxiv","id":"0906.3777","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.3777","created_at":"2026-05-18T02:13:13Z"},{"alias_kind":"arxiv_version","alias_value":"0906.3777v1","created_at":"2026-05-18T02:13:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3777","created_at":"2026-05-18T02:13:13Z"},{"alias_kind":"pith_short_12","alias_value":"HECYXOEZCNU7","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"HECYXOEZCNU7WIJA","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"HECYXOEZ","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:HECYXOEZCNU7WIJANWFSNCEUI3","target":"record","payload":{"canonical_record":{"source":{"id":"0906.3777","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-06-20T04:06:09Z","cross_cats_sorted":[],"title_canon_sha256":"6e4815539e4065ad73b10c43c728c869778e84eee6d53193039ddd13660152dd","abstract_canon_sha256":"616ef87a43990115ccf35904c49c1a0782decfa597a3b4ac9febcada5767d961"},"schema_version":"1.0"},"canonical_sha256":"39058bb8991369fb21206d8b26889446dbd5452bfc81de723351c8592ac85eab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:13.602614Z","signature_b64":"o+VjdaiAnDRM6g+HDYUSjwOdNcL04Lhd5bKc9NfspMfIZgcifH2wlt4YsGmC1kDGtziMl6GV3NK6Rb+2QjKkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39058bb8991369fb21206d8b26889446dbd5452bfc81de723351c8592ac85eab","last_reissued_at":"2026-05-18T02:13:13.602245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:13.602245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.3777","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:13:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jMEK1+wTXA9Avzm2R7vc2y+vvrc9ACq8Va5eQGtnaPtqIx2OPNQqwKl66gQINH9k6cUxi0TZnbvck3OXFfLgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:37:22.169388Z"},"content_sha256":"ce30ce65a5bd7e4e0faf561a303db7f800261bcbad1e9cd48aafcbda9e93437f","schema_version":"1.0","event_id":"sha256:ce30ce65a5bd7e4e0faf561a303db7f800261bcbad1e9cd48aafcbda9e93437f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:HECYXOEZCNU7WIJANWFSNCEUI3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Do bosons obey Bose-Einstein distribution: two iterated limits of Gentile distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Mi Xie, Wu-Sheng Dai","submitted_at":"2009-06-20T04:06:09Z","abstract_excerpt":"It is a common impression that by only setting the maximum occupation number to infinity, which is the demand of the indistinguishability of bosons, one can achieve the statistical distribution that bosons obey -- the Bose-Einstein distribution. In this letter, however, we show that only with an infinite maximum occupation number one cannot uniquely achieve the Bose-Einstein distribution, since in the derivation of the Bose-Einstein distribution, the problem of iterated limit is encountered. For achieving the Bose-Einstein distribution, one needs to take both the maximum occupation number and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3777","kind":"arxiv","version":1},"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":"2026-05-18T02:13:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0KDo/1t5BiKg25kokMsv2+t3siwx/b/N+1MiVWUR745GsMvHAzkYKr+HqjxExdb66w4gU2gVwfGTlw0dJeViAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:37:22.170079Z"},"content_sha256":"ccead6c7e2614c488dab56964049bb9665311b984eaa8d215453ed948be3b85a","schema_version":"1.0","event_id":"sha256:ccead6c7e2614c488dab56964049bb9665311b984eaa8d215453ed948be3b85a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HECYXOEZCNU7WIJANWFSNCEUI3/bundle.json","state_url":"https://pith.science/pith/HECYXOEZCNU7WIJANWFSNCEUI3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HECYXOEZCNU7WIJANWFSNCEUI3/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":"2026-06-07T02:37:22Z","links":{"resolver":"https://pith.science/pith/HECYXOEZCNU7WIJANWFSNCEUI3","bundle":"https://pith.science/pith/HECYXOEZCNU7WIJANWFSNCEUI3/bundle.json","state":"https://pith.science/pith/HECYXOEZCNU7WIJANWFSNCEUI3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HECYXOEZCNU7WIJANWFSNCEUI3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:HECYXOEZCNU7WIJANWFSNCEUI3","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":"616ef87a43990115ccf35904c49c1a0782decfa597a3b4ac9febcada5767d961","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-06-20T04:06:09Z","title_canon_sha256":"6e4815539e4065ad73b10c43c728c869778e84eee6d53193039ddd13660152dd"},"schema_version":"1.0","source":{"id":"0906.3777","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.3777","created_at":"2026-05-18T02:13:13Z"},{"alias_kind":"arxiv_version","alias_value":"0906.3777v1","created_at":"2026-05-18T02:13:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3777","created_at":"2026-05-18T02:13:13Z"},{"alias_kind":"pith_short_12","alias_value":"HECYXOEZCNU7","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"HECYXOEZCNU7WIJA","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"HECYXOEZ","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:ccead6c7e2614c488dab56964049bb9665311b984eaa8d215453ed948be3b85a","target":"graph","created_at":"2026-05-18T02:13:13Z","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":"It is a common impression that by only setting the maximum occupation number to infinity, which is the demand of the indistinguishability of bosons, one can achieve the statistical distribution that bosons obey -- the Bose-Einstein distribution. In this letter, however, we show that only with an infinite maximum occupation number one cannot uniquely achieve the Bose-Einstein distribution, since in the derivation of the Bose-Einstein distribution, the problem of iterated limit is encountered. For achieving the Bose-Einstein distribution, one needs to take both the maximum occupation number and ","authors_text":"Mi Xie, Wu-Sheng Dai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-06-20T04:06:09Z","title":"Do bosons obey Bose-Einstein distribution: two iterated limits of Gentile distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3777","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:ce30ce65a5bd7e4e0faf561a303db7f800261bcbad1e9cd48aafcbda9e93437f","target":"record","created_at":"2026-05-18T02:13:13Z","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":"616ef87a43990115ccf35904c49c1a0782decfa597a3b4ac9febcada5767d961","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-06-20T04:06:09Z","title_canon_sha256":"6e4815539e4065ad73b10c43c728c869778e84eee6d53193039ddd13660152dd"},"schema_version":"1.0","source":{"id":"0906.3777","kind":"arxiv","version":1}},"canonical_sha256":"39058bb8991369fb21206d8b26889446dbd5452bfc81de723351c8592ac85eab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39058bb8991369fb21206d8b26889446dbd5452bfc81de723351c8592ac85eab","first_computed_at":"2026-05-18T02:13:13.602245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:13.602245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o+VjdaiAnDRM6g+HDYUSjwOdNcL04Lhd5bKc9NfspMfIZgcifH2wlt4YsGmC1kDGtziMl6GV3NK6Rb+2QjKkBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:13.602614Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.3777","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce30ce65a5bd7e4e0faf561a303db7f800261bcbad1e9cd48aafcbda9e93437f","sha256:ccead6c7e2614c488dab56964049bb9665311b984eaa8d215453ed948be3b85a"],"state_sha256":"25bf211e1c756244fd7b66d4027c6366e79816f57d130382431303054bdfc060"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZXt/jkHAlVbpm4cg6/QLlcCdLL2+AwcvFIR7ReVVoJeC4kw6UI67U9VMOjYEurdeDZO/TR/c7mVglMe+1C0KDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:37:22.173577Z","bundle_sha256":"34379a6a39a5dc9b9fb9153a47782a735092f1569f60531e640935d7bd0b5e14"}}