{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OWOZ3BPGNSVB322L3M3GONKH6U","short_pith_number":"pith:OWOZ3BPG","canonical_record":{"source":{"id":"1310.5580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-10-21T14:52:40Z","cross_cats_sorted":["cond-mat.quant-gas","hep-th","math-ph","math.MP"],"title_canon_sha256":"bda895e864f87b1cb0bb62e2050ce07c774b20d2d6598938ce5c831a6503a589","abstract_canon_sha256":"810dafe513879b34781586378aab22c207977f3a1f97ba93b61e23efd2139f23"},"schema_version":"1.0"},"canonical_sha256":"759d9d85e66caa1deb4bdb36673547f51fddf6e1e88aac26961389446def0bcb","source":{"kind":"arxiv","id":"1310.5580","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5580","created_at":"2026-05-18T02:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5580v1","created_at":"2026-05-18T02:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5580","created_at":"2026-05-18T02:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"OWOZ3BPGNSVB","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OWOZ3BPGNSVB322L","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OWOZ3BPG","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OWOZ3BPGNSVB322L3M3GONKH6U","target":"record","payload":{"canonical_record":{"source":{"id":"1310.5580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-10-21T14:52:40Z","cross_cats_sorted":["cond-mat.quant-gas","hep-th","math-ph","math.MP"],"title_canon_sha256":"bda895e864f87b1cb0bb62e2050ce07c774b20d2d6598938ce5c831a6503a589","abstract_canon_sha256":"810dafe513879b34781586378aab22c207977f3a1f97ba93b61e23efd2139f23"},"schema_version":"1.0"},"canonical_sha256":"759d9d85e66caa1deb4bdb36673547f51fddf6e1e88aac26961389446def0bcb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:35.005637Z","signature_b64":"CnqH2QuMaIeFKX5d4RRAD1zXbVD9YdadyCwOvHrRbKCUwOl1ykuCaaHdAcia3yMeuyBsRZMuC/lQjAecUG9bBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"759d9d85e66caa1deb4bdb36673547f51fddf6e1e88aac26961389446def0bcb","last_reissued_at":"2026-05-18T02:56:35.004845Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:35.004845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.5580","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":"2026-05-18T02:56:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EY+MQGLSWFMP4eXCNmSdw/j12Pw8cZf1qtgxXE+EVOxj8F1IeYisPPqqi/2IJXxUT5IhZZB4CnZ84iDw8Jj4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:18:51.170090Z"},"content_sha256":"318660e9b8c910989cc6f851843893efd410eafed1939cfbdffd8d2bcd0baf0b","schema_version":"1.0","event_id":"sha256:318660e9b8c910989cc6f851843893efd410eafed1939cfbdffd8d2bcd0baf0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OWOZ3BPGNSVB322L3M3GONKH6U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How many is different? Answer from ideal Bose gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Jeong-Hyuck Park","submitted_at":"2013-10-21T14:52:40Z","abstract_excerpt":"How many $\\mathrm{H_{2}O}$ molecules are needed to form water? While the precise answer is not known, it is clear that the answer should be a finite number rather than infinity. We revisit with care the ideal Bose gas confined in a cubic box which is discussed in most statistical physics textbooks. We show that the isobar of the ideal gas zigzags on the temperature-volume plane featuring a `boiling-like' discrete phase transition, provided the number of particles is equal to or greater than a particular value: 7616. This demonstrates for the first time how a finite system can feature a mathema"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5580","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":"2026-05-18T02:56:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2k7lWojnvRJxlciym/qZoSlULEIvI4L/i5vtRaKc9abTxy6fnMpeljsjrKPpoQhg8/KgcAgKbQCS6/M6pTk0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:18:51.170768Z"},"content_sha256":"43af27cf5eb5cd64a1e2ccaf769a49c6db16806ca256ab56eef26024361a658e","schema_version":"1.0","event_id":"sha256:43af27cf5eb5cd64a1e2ccaf769a49c6db16806ca256ab56eef26024361a658e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OWOZ3BPGNSVB322L3M3GONKH6U/bundle.json","state_url":"https://pith.science/pith/OWOZ3BPGNSVB322L3M3GONKH6U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OWOZ3BPGNSVB322L3M3GONKH6U/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":"2026-06-02T15:18:51Z","links":{"resolver":"https://pith.science/pith/OWOZ3BPGNSVB322L3M3GONKH6U","bundle":"https://pith.science/pith/OWOZ3BPGNSVB322L3M3GONKH6U/bundle.json","state":"https://pith.science/pith/OWOZ3BPGNSVB322L3M3GONKH6U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OWOZ3BPGNSVB322L3M3GONKH6U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OWOZ3BPGNSVB322L3M3GONKH6U","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":"810dafe513879b34781586378aab22c207977f3a1f97ba93b61e23efd2139f23","cross_cats_sorted":["cond-mat.quant-gas","hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-10-21T14:52:40Z","title_canon_sha256":"bda895e864f87b1cb0bb62e2050ce07c774b20d2d6598938ce5c831a6503a589"},"schema_version":"1.0","source":{"id":"1310.5580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5580","created_at":"2026-05-18T02:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5580v1","created_at":"2026-05-18T02:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5580","created_at":"2026-05-18T02:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"OWOZ3BPGNSVB","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OWOZ3BPGNSVB322L","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OWOZ3BPG","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:43af27cf5eb5cd64a1e2ccaf769a49c6db16806ca256ab56eef26024361a658e","target":"graph","created_at":"2026-05-18T02:56:35Z","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":"How many $\\mathrm{H_{2}O}$ molecules are needed to form water? While the precise answer is not known, it is clear that the answer should be a finite number rather than infinity. We revisit with care the ideal Bose gas confined in a cubic box which is discussed in most statistical physics textbooks. We show that the isobar of the ideal gas zigzags on the temperature-volume plane featuring a `boiling-like' discrete phase transition, provided the number of particles is equal to or greater than a particular value: 7616. This demonstrates for the first time how a finite system can feature a mathema","authors_text":"Jeong-Hyuck Park","cross_cats":["cond-mat.quant-gas","hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-10-21T14:52:40Z","title":"How many is different? Answer from ideal Bose gas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5580","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":"sha256:318660e9b8c910989cc6f851843893efd410eafed1939cfbdffd8d2bcd0baf0b","target":"record","created_at":"2026-05-18T02:56:35Z","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":"810dafe513879b34781586378aab22c207977f3a1f97ba93b61e23efd2139f23","cross_cats_sorted":["cond-mat.quant-gas","hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-10-21T14:52:40Z","title_canon_sha256":"bda895e864f87b1cb0bb62e2050ce07c774b20d2d6598938ce5c831a6503a589"},"schema_version":"1.0","source":{"id":"1310.5580","kind":"arxiv","version":1}},"canonical_sha256":"759d9d85e66caa1deb4bdb36673547f51fddf6e1e88aac26961389446def0bcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"759d9d85e66caa1deb4bdb36673547f51fddf6e1e88aac26961389446def0bcb","first_computed_at":"2026-05-18T02:56:35.004845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:35.004845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CnqH2QuMaIeFKX5d4RRAD1zXbVD9YdadyCwOvHrRbKCUwOl1ykuCaaHdAcia3yMeuyBsRZMuC/lQjAecUG9bBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:35.005637Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:318660e9b8c910989cc6f851843893efd410eafed1939cfbdffd8d2bcd0baf0b","sha256:43af27cf5eb5cd64a1e2ccaf769a49c6db16806ca256ab56eef26024361a658e"],"state_sha256":"38f76533963d48fc2361eeec56e70c1c74efa6cc34faaaf01c8d2d138531612a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7wf18EJZq8dlZcJWVCjKknFywVFcYng6ThGJbYJtwuhF8N4mK/36ctgK0Kwq4wZTZBLBr2lVb0sR1grnHgvqBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T15:18:51.173811Z","bundle_sha256":"07ea2764b5325c41342658b8cfbe0e07ce03f40a5008abac106826b48efbd6ba"}}