{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:24ENRZFXNXXUXLN4RALBTDQ4JA","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":"b4fa48051999d179448c3c668027095433818522b02b58c4168fd21498d36960","cross_cats_sorted":["math.MP","math.PR"],"license":"","primary_cat":"math-ph","submitted_at":"2002-11-25T12:46:24Z","title_canon_sha256":"68da3045983e6e21532e0b3ffa0a8a4f4f4f8e8ca51c823f1c4156c654ba960e"},"schema_version":"1.0","source":{"id":"math-ph/0211062","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0211062","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0211062v2","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0211062","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"pith_short_12","alias_value":"24ENRZFXNXXU","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"24ENRZFXNXXUXLN4","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"24ENRZFX","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:93047f753b64d4db9994caa70514d857316ee862806c470e06c37c3a1e02e3ee","target":"graph","created_at":"2026-05-18T04:08:53Z","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":"Following Fr\\\"ohlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+\\alpha}$, $0\\leq \\alpha\\leq 1/2$. We introduce a geometric description of the spin configurations in terms of triangles which play the role of contours and for which we establish Peierls bounds. This in particular yields a direct proof of the well known result by Dyson about phase transitions at low temperatures.","authors_text":"E. Presutti, I. Merola, M. Cassandro, P.A. Ferrari","cross_cats":["math.MP","math.PR"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2002-11-25T12:46:24Z","title":"Geometry of contours and Peierls estimates in d=1 Ising models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0211062","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:f1999da4ab38b0a7b435ee179d47853822b2b4e827eeccebce40fc52bba055f3","target":"record","created_at":"2026-05-18T04:08:53Z","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":"b4fa48051999d179448c3c668027095433818522b02b58c4168fd21498d36960","cross_cats_sorted":["math.MP","math.PR"],"license":"","primary_cat":"math-ph","submitted_at":"2002-11-25T12:46:24Z","title_canon_sha256":"68da3045983e6e21532e0b3ffa0a8a4f4f4f8e8ca51c823f1c4156c654ba960e"},"schema_version":"1.0","source":{"id":"math-ph/0211062","kind":"arxiv","version":2}},"canonical_sha256":"d708d8e4b76def4badbc8816198e1c4809a0b583e979a8ae1912c2d86d7d839c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d708d8e4b76def4badbc8816198e1c4809a0b583e979a8ae1912c2d86d7d839c","first_computed_at":"2026-05-18T04:08:53.871739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:53.871739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9uvVXOoYDq8YHpRBdmS6bcEF5a7G+BwGbMvsNx52q/iB7PGMefW2+gRUanamu8Nmnwa3mAW823XJ1WiRZIfCCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:53.872186Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0211062","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1999da4ab38b0a7b435ee179d47853822b2b4e827eeccebce40fc52bba055f3","sha256:93047f753b64d4db9994caa70514d857316ee862806c470e06c37c3a1e02e3ee"],"state_sha256":"5f95124d4779f7b2d8b150e420048a33c928da9dcebe03ff5be59a53b4547414"}