{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2000:42EPPZKNSVATSAZVWOXRE4X7CC","short_pith_number":"pith:42EPPZKN","schema_version":"1.0","canonical_sha256":"e688f7e54d9541390335b3af1272ff1097856f776e33da8969ed97d060ff1f4a","source":{"kind":"arxiv","id":"cond-mat/0010372","version":1},"attestation_state":"computed","paper":{"title":"1D Potts, Yang-Lee Edges and Chaos","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"B.P.Dolan, D. Johnston","submitted_at":"2000-10-24T15:40:32Z","abstract_excerpt":"It is known that the (exact) renormalization transformations for the one-dimensional Ising model in field can be cast in the form of a logistic map f(x) = 4 x (1 - x) with x a function of the Ising couplings. Remarkably, the line bounding the region of chaotic behaviour in x is precisely that defining the Yang-Lee edge singularity in the Ising model.\n  In this paper we show that the one dimensional q-state Potts model for q greater than or equal to 1 also displays such behaviour. A suitable combination of Potts couplings can again be used to define an x satisfying f(x) = 4 x (1 -x). The Yang-L"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"cond-mat/0010372","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2000-10-24T15:40:32Z","cross_cats_sorted":[],"title_canon_sha256":"c9dd938f42ee23933f82c73375821f52626f0f2519b9a4100cd31ee779cd8372","abstract_canon_sha256":"28e6a0c3fef30c4bf86666113f6be90337a26b2a4386b946dc35911101c6f50f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:07.977458Z","signature_b64":"8t32HnwjhZKqNiTUJXjGfs3QHs6h/Egx6Vr8jb07zSwksgZIX5HbUElk3Y/LMjfr5W2lCRXtyUYteEjbA2VfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e688f7e54d9541390335b3af1272ff1097856f776e33da8969ed97d060ff1f4a","last_reissued_at":"2026-05-18T01:40:07.976825Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:07.976825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"1D Potts, Yang-Lee Edges and Chaos","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"B.P.Dolan, D. Johnston","submitted_at":"2000-10-24T15:40:32Z","abstract_excerpt":"It is known that the (exact) renormalization transformations for the one-dimensional Ising model in field can be cast in the form of a logistic map f(x) = 4 x (1 - x) with x a function of the Ising couplings. Remarkably, the line bounding the region of chaotic behaviour in x is precisely that defining the Yang-Lee edge singularity in the Ising model.\n  In this paper we show that the one dimensional q-state Potts model for q greater than or equal to 1 also displays such behaviour. A suitable combination of Potts couplings can again be used to define an x satisfying f(x) = 4 x (1 -x). The Yang-L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0010372","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0010372","created_at":"2026-05-18T01:40:07.976924+00:00"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0010372v1","created_at":"2026-05-18T01:40:07.976924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0010372","created_at":"2026-05-18T01:40:07.976924+00:00"},{"alias_kind":"pith_short_12","alias_value":"42EPPZKNSVAT","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_16","alias_value":"42EPPZKNSVATSAZV","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_8","alias_value":"42EPPZKN","created_at":"2026-05-18T12:25:49.631198+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/42EPPZKNSVATSAZVWOXRE4X7CC","json":"https://pith.science/pith/42EPPZKNSVATSAZVWOXRE4X7CC.json","graph_json":"https://pith.science/api/pith-number/42EPPZKNSVATSAZVWOXRE4X7CC/graph.json","events_json":"https://pith.science/api/pith-number/42EPPZKNSVATSAZVWOXRE4X7CC/events.json","paper":"https://pith.science/paper/42EPPZKN"},"agent_actions":{"view_html":"https://pith.science/pith/42EPPZKNSVATSAZVWOXRE4X7CC","download_json":"https://pith.science/pith/42EPPZKNSVATSAZVWOXRE4X7CC.json","view_paper":"https://pith.science/paper/42EPPZKN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cond-mat/0010372&json=true","fetch_graph":"https://pith.science/api/pith-number/42EPPZKNSVATSAZVWOXRE4X7CC/graph.json","fetch_events":"https://pith.science/api/pith-number/42EPPZKNSVATSAZVWOXRE4X7CC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/42EPPZKNSVATSAZVWOXRE4X7CC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/42EPPZKNSVATSAZVWOXRE4X7CC/action/storage_attestation","attest_author":"https://pith.science/pith/42EPPZKNSVATSAZVWOXRE4X7CC/action/author_attestation","sign_citation":"https://pith.science/pith/42EPPZKNSVATSAZVWOXRE4X7CC/action/citation_signature","submit_replication":"https://pith.science/pith/42EPPZKNSVATSAZVWOXRE4X7CC/action/replication_record"}},"created_at":"2026-05-18T01:40:07.976924+00:00","updated_at":"2026-05-18T01:40:07.976924+00:00"}