{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:BE2ZA4VGQPLHPHS2KAPMKITWNF","short_pith_number":"pith:BE2ZA4VG","canonical_record":{"source":{"id":"cond-mat/9909184","kind":"arxiv","version":5},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-09-13T15:06:26Z","cross_cats_sorted":["cond-mat.mes-hall"],"title_canon_sha256":"e86d749d5b815719b78068a60d489bc9de7f91839db3bc27ec60484326cc9657","abstract_canon_sha256":"c03fa096c874397ed028d7d93c1c5e258e8f1a4da384c8f52bbf5210a55e3433"},"schema_version":"1.0"},"canonical_sha256":"09359072a683d6779e5a501ec522766959c024456c3f601333bac54f1e347167","source":{"kind":"arxiv","id":"cond-mat/9909184","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9909184","created_at":"2026-07-04T16:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9909184v5","created_at":"2026-07-04T16:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9909184","created_at":"2026-07-04T16:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"BE2ZA4VGQPLH","created_at":"2026-07-04T16:13:16Z"},{"alias_kind":"pith_short_16","alias_value":"BE2ZA4VGQPLHPHS2","created_at":"2026-07-04T16:13:16Z"},{"alias_kind":"pith_short_8","alias_value":"BE2ZA4VG","created_at":"2026-07-04T16:13:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:BE2ZA4VGQPLHPHS2KAPMKITWNF","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/9909184","kind":"arxiv","version":5},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-09-13T15:06:26Z","cross_cats_sorted":["cond-mat.mes-hall"],"title_canon_sha256":"e86d749d5b815719b78068a60d489bc9de7f91839db3bc27ec60484326cc9657","abstract_canon_sha256":"c03fa096c874397ed028d7d93c1c5e258e8f1a4da384c8f52bbf5210a55e3433"},"schema_version":"1.0"},"canonical_sha256":"09359072a683d6779e5a501ec522766959c024456c3f601333bac54f1e347167","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:13:16.181727Z","signature_b64":"cugsvXpA9BsRaevwnx473+7w7f0N4B/u8GpgH6G70jGnx3Xro5d4d/a6P8SepwfngCi/zeEQj4zcUqLbDPi1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09359072a683d6779e5a501ec522766959c024456c3f601333bac54f1e347167","last_reissued_at":"2026-07-04T16:13:16.181263Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:13:16.181263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/9909184","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:13:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+7LyWj9BPBpR/g/26y9ThDGPt4WzLPT6t6hiruYwoYiC65AOs6e0eZBixf081EOA0yhq+nuwQlnIBKz2aY0WBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T12:55:21.639327Z"},"content_sha256":"0b0958f469a1f3950402f6bd64afb84b45471d64cc693b01508b1543e3fb05d1","schema_version":"1.0","event_id":"sha256:0b0958f469a1f3950402f6bd64afb84b45471d64cc693b01508b1543e3fb05d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:BE2ZA4VGQPLHPHS2KAPMKITWNF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of phase transitions in small systems","license":"","headline":"","cross_cats":["cond-mat.mes-hall"],"primary_cat":"cond-mat.stat-mech","authors_text":"Jens Harting, Oliver Muelken, Peter Borrmann","submitted_at":"1999-09-13T15:06:26Z","abstract_excerpt":"We present a classification scheme for phase transitions in finite systems like atomic and molecular clusters based on the Lee-Yang zeros in the complex temperature plane. In the limit of infinite particle numbers the scheme reduces to the Ehrenfest definition of phase transitions and gives the right critical indices. We apply this classification scheme to Bose-Einstein condensates in a harmonic trap as an example of a higher order phase transitions in a finite system and to small Ar clusters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9909184","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cond-mat/9909184/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:13:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/yNh55u5Sdtlf/r1TjsermUftvo5si7SGBY2xGgnKqH66Dw+2XFaSkz4Wk7+eBCqoJBxS3kvtMszc5ha1ZPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T12:55:21.639834Z"},"content_sha256":"02f464302d4cd386ad9445844a8f8a8abb67bf5e3110be44dfb23378e0475767","schema_version":"1.0","event_id":"sha256:02f464302d4cd386ad9445844a8f8a8abb67bf5e3110be44dfb23378e0475767"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BE2ZA4VGQPLHPHS2KAPMKITWNF/bundle.json","state_url":"https://pith.science/pith/BE2ZA4VGQPLHPHS2KAPMKITWNF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BE2ZA4VGQPLHPHS2KAPMKITWNF/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":"2026-08-04T12:55:21Z","links":{"resolver":"https://pith.science/pith/BE2ZA4VGQPLHPHS2KAPMKITWNF","bundle":"https://pith.science/pith/BE2ZA4VGQPLHPHS2KAPMKITWNF/bundle.json","state":"https://pith.science/pith/BE2ZA4VGQPLHPHS2KAPMKITWNF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BE2ZA4VGQPLHPHS2KAPMKITWNF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:BE2ZA4VGQPLHPHS2KAPMKITWNF","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":"c03fa096c874397ed028d7d93c1c5e258e8f1a4da384c8f52bbf5210a55e3433","cross_cats_sorted":["cond-mat.mes-hall"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-09-13T15:06:26Z","title_canon_sha256":"e86d749d5b815719b78068a60d489bc9de7f91839db3bc27ec60484326cc9657"},"schema_version":"1.0","source":{"id":"cond-mat/9909184","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9909184","created_at":"2026-07-04T16:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9909184v5","created_at":"2026-07-04T16:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9909184","created_at":"2026-07-04T16:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"BE2ZA4VGQPLH","created_at":"2026-07-04T16:13:16Z"},{"alias_kind":"pith_short_16","alias_value":"BE2ZA4VGQPLHPHS2","created_at":"2026-07-04T16:13:16Z"},{"alias_kind":"pith_short_8","alias_value":"BE2ZA4VG","created_at":"2026-07-04T16:13:16Z"}],"graph_snapshots":[{"event_id":"sha256:02f464302d4cd386ad9445844a8f8a8abb67bf5e3110be44dfb23378e0475767","target":"graph","created_at":"2026-07-04T16:13:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cond-mat/9909184/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a classification scheme for phase transitions in finite systems like atomic and molecular clusters based on the Lee-Yang zeros in the complex temperature plane. In the limit of infinite particle numbers the scheme reduces to the Ehrenfest definition of phase transitions and gives the right critical indices. We apply this classification scheme to Bose-Einstein condensates in a harmonic trap as an example of a higher order phase transitions in a finite system and to small Ar clusters.","authors_text":"Jens Harting, Oliver Muelken, Peter Borrmann","cross_cats":["cond-mat.mes-hall"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-09-13T15:06:26Z","title":"Classification of phase transitions in small systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9909184","kind":"arxiv","version":5},"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":"sha256:0b0958f469a1f3950402f6bd64afb84b45471d64cc693b01508b1543e3fb05d1","target":"record","created_at":"2026-07-04T16:13:16Z","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":"c03fa096c874397ed028d7d93c1c5e258e8f1a4da384c8f52bbf5210a55e3433","cross_cats_sorted":["cond-mat.mes-hall"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-09-13T15:06:26Z","title_canon_sha256":"e86d749d5b815719b78068a60d489bc9de7f91839db3bc27ec60484326cc9657"},"schema_version":"1.0","source":{"id":"cond-mat/9909184","kind":"arxiv","version":5}},"canonical_sha256":"09359072a683d6779e5a501ec522766959c024456c3f601333bac54f1e347167","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09359072a683d6779e5a501ec522766959c024456c3f601333bac54f1e347167","first_computed_at":"2026-07-04T16:13:16.181263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:13:16.181263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cugsvXpA9BsRaevwnx473+7w7f0N4B/u8GpgH6G70jGnx3Xro5d4d/a6P8SepwfngCi/zeEQj4zcUqLbDPi1Cw==","signature_status":"signed_v1","signed_at":"2026-07-04T16:13:16.181727Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9909184","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b0958f469a1f3950402f6bd64afb84b45471d64cc693b01508b1543e3fb05d1","sha256:02f464302d4cd386ad9445844a8f8a8abb67bf5e3110be44dfb23378e0475767"],"state_sha256":"aededab7f74e184a7b8641d882dd925e280d4b806998962425ba719f0a09d436"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RF7wdKIRLer4pMiyJJ5ZXmkyLlikbwUIZItFX+r2pOSfpENWiYv5tasYueGq31j1xkcQKRv6y8w7qa1CskzAAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T12:55:21.644108Z","bundle_sha256":"0ccc7d91232df58237a5f4d71f24387e5f0c1aee33f50935314b5bcb3c816df6"}}