{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:DW2ZZH3SPNV4Z3G6VFXHFEC2KU","short_pith_number":"pith:DW2ZZH3S","canonical_record":{"source":{"id":"math-ph/0509017","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-09-11T00:11:02Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.OA","quant-ph"],"title_canon_sha256":"324e23d8d281217bfb7d4c3c16e20693fabc6d6f7279a6ce429c4246ffb31ac8","abstract_canon_sha256":"5a3fb8be8a2430f80e5d0f33048cea9a96c3812156fdc0081c0c0243fc7c91e5"},"schema_version":"1.0"},"canonical_sha256":"1db59c9f727b6bccecdea96e72905a553f0562b503e37f25ee60566cb9411723","source":{"kind":"arxiv","id":"math-ph/0509017","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0509017","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0509017v2","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0509017","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"DW2ZZH3SPNV4","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"DW2ZZH3SPNV4Z3G6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"DW2ZZH3S","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:DW2ZZH3SPNV4Z3G6VFXHFEC2KU","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0509017","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-09-11T00:11:02Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.OA","quant-ph"],"title_canon_sha256":"324e23d8d281217bfb7d4c3c16e20693fabc6d6f7279a6ce429c4246ffb31ac8","abstract_canon_sha256":"5a3fb8be8a2430f80e5d0f33048cea9a96c3812156fdc0081c0c0243fc7c91e5"},"schema_version":"1.0"},"canonical_sha256":"1db59c9f727b6bccecdea96e72905a553f0562b503e37f25ee60566cb9411723","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:43.353670Z","signature_b64":"WXFDwfvSyE1Q0I9TQAqnLGVK3Ge8G7rdsy7bnllSOD6m/gRGufR5IIv9hH8FZgTwfJCljEXIKCXT3PscNriuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1db59c9f727b6bccecdea96e72905a553f0562b503e37f25ee60566cb9411723","last_reissued_at":"2026-05-18T04:08:43.353220Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:43.353220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0509017","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:08:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o1bZKmy8QYkSfTQsG7i7uoCRLLJANwC+8byRXdcbNEe5Gr4l/So0R9/XqNyAQc4rm6dA/n8xNdAB7251KP83CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:55:17.061406Z"},"content_sha256":"6996fc189500cf869887adc05e3b9a6704ce38b2a3d2d6b53b045485b19de3d0","schema_version":"1.0","event_id":"sha256:6996fc189500cf869887adc05e3b9a6704ce38b2a3d2d6b53b045485b19de3d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:DW2ZZH3SPNV4Z3G6VFXHFEC2KU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum spin systems at positive temperature","license":"","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","math.OA","quant-ph"],"primary_cat":"math-ph","authors_text":"Lincoln Chayes, Marek Biskup, Shannon Starr","submitted_at":"2005-09-11T00:11:02Z","abstract_excerpt":"We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature $\\beta$ and the magnitude of the quantum spins $\\CalS$ satisfy $\\beta\\ll\\sqrt\\CalS$. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an exten"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0509017","kind":"arxiv","version":2},"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":"2026-05-18T04:08:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Gs1/2L52FrIk1k0iNySeGbIwutqvHJCA5ArKonF6wbGz5NAELaI9ECsHli7k781cEazyMEsZBc0FLSKiedYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:55:17.061763Z"},"content_sha256":"2fe583f706cae46647035d7d33e08f091b95056790f5441ad364e1cc8786fa07","schema_version":"1.0","event_id":"sha256:2fe583f706cae46647035d7d33e08f091b95056790f5441ad364e1cc8786fa07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DW2ZZH3SPNV4Z3G6VFXHFEC2KU/bundle.json","state_url":"https://pith.science/pith/DW2ZZH3SPNV4Z3G6VFXHFEC2KU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DW2ZZH3SPNV4Z3G6VFXHFEC2KU/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":"2026-06-24T21:55:17Z","links":{"resolver":"https://pith.science/pith/DW2ZZH3SPNV4Z3G6VFXHFEC2KU","bundle":"https://pith.science/pith/DW2ZZH3SPNV4Z3G6VFXHFEC2KU/bundle.json","state":"https://pith.science/pith/DW2ZZH3SPNV4Z3G6VFXHFEC2KU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DW2ZZH3SPNV4Z3G6VFXHFEC2KU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:DW2ZZH3SPNV4Z3G6VFXHFEC2KU","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":"5a3fb8be8a2430f80e5d0f33048cea9a96c3812156fdc0081c0c0243fc7c91e5","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.OA","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2005-09-11T00:11:02Z","title_canon_sha256":"324e23d8d281217bfb7d4c3c16e20693fabc6d6f7279a6ce429c4246ffb31ac8"},"schema_version":"1.0","source":{"id":"math-ph/0509017","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0509017","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0509017v2","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0509017","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"DW2ZZH3SPNV4","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"DW2ZZH3SPNV4Z3G6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"DW2ZZH3S","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:2fe583f706cae46647035d7d33e08f091b95056790f5441ad364e1cc8786fa07","target":"graph","created_at":"2026-05-18T04:08:43Z","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":"We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature $\\beta$ and the magnitude of the quantum spins $\\CalS$ satisfy $\\beta\\ll\\sqrt\\CalS$. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an exten","authors_text":"Lincoln Chayes, Marek Biskup, Shannon Starr","cross_cats":["cond-mat.stat-mech","math.MP","math.OA","quant-ph"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2005-09-11T00:11:02Z","title":"Quantum spin systems at positive temperature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0509017","kind":"arxiv","version":2},"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":"sha256:6996fc189500cf869887adc05e3b9a6704ce38b2a3d2d6b53b045485b19de3d0","target":"record","created_at":"2026-05-18T04:08:43Z","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":"5a3fb8be8a2430f80e5d0f33048cea9a96c3812156fdc0081c0c0243fc7c91e5","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.OA","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2005-09-11T00:11:02Z","title_canon_sha256":"324e23d8d281217bfb7d4c3c16e20693fabc6d6f7279a6ce429c4246ffb31ac8"},"schema_version":"1.0","source":{"id":"math-ph/0509017","kind":"arxiv","version":2}},"canonical_sha256":"1db59c9f727b6bccecdea96e72905a553f0562b503e37f25ee60566cb9411723","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1db59c9f727b6bccecdea96e72905a553f0562b503e37f25ee60566cb9411723","first_computed_at":"2026-05-18T04:08:43.353220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:43.353220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WXFDwfvSyE1Q0I9TQAqnLGVK3Ge8G7rdsy7bnllSOD6m/gRGufR5IIv9hH8FZgTwfJCljEXIKCXT3PscNriuAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:43.353670Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0509017","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6996fc189500cf869887adc05e3b9a6704ce38b2a3d2d6b53b045485b19de3d0","sha256:2fe583f706cae46647035d7d33e08f091b95056790f5441ad364e1cc8786fa07"],"state_sha256":"0f7290b489608427d68a40d4f9cb9942f15b36be9943cfac8b3c462ab5ee54ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G0Psvmo+6N2Wo0eUsiYRlJR2PAB4xxo1e0FFEvkeM+sndmoG+Jf5S5dF04ICBJ1MmH2TMN3aiwiEMCfoU6bqCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:55:17.063763Z","bundle_sha256":"037eb23ca50b0dd2116ccb2f62a9d0b7252f598eb9ab2267590cf7eab578a252"}}