{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TLJPPOYGFFDPYU32WVXVEL44LH","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":"7fb5c51ae898969f15f5750af1f66badd052bb51cebbd225d3ee00b29c1f1809","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-06-01T19:51:28Z","title_canon_sha256":"42a0940db9e88675353b92af66d146f048896a560113437268d06bf3802face2"},"schema_version":"1.0","source":{"id":"1506.00625","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00625","created_at":"2026-05-18T00:09:20Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00625v2","created_at":"2026-05-18T00:09:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00625","created_at":"2026-05-18T00:09:20Z"},{"alias_kind":"pith_short_12","alias_value":"TLJPPOYGFFDP","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TLJPPOYGFFDPYU32","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TLJPPOYG","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:51ebd5da7e7623f01600b3465d104d41725381458f62dc4261fa53580af9fc64","target":"graph","created_at":"2026-05-18T00:09:20Z","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":"The truncated two-point function of the nearest-neighbor ferromagnetic Ising model on $\\mathbb Z^d$ ($d\\ge3$) in its pure phases is proven to decays exponentially fast throughout the ordered regime ($T<T_c$). Together with known results, this implies that the exponential clustering property holds throughout the model's phase diagram except for the critical point: $(T,h) = (T_c,0)$.","authors_text":"Hugo Duminil-Copin, Michael Aizenman","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-06-01T19:51:28Z","title":"The truncated correlations of the Ising model in any dimension decay exponentially fast at all but the critical temperature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00625","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":"sha256:700462d8bf89f6b498806167c3d8722fca12898da58b0c30a31342eefc3625d0","target":"record","created_at":"2026-05-18T00:09:20Z","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":"7fb5c51ae898969f15f5750af1f66badd052bb51cebbd225d3ee00b29c1f1809","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-06-01T19:51:28Z","title_canon_sha256":"42a0940db9e88675353b92af66d146f048896a560113437268d06bf3802face2"},"schema_version":"1.0","source":{"id":"1506.00625","kind":"arxiv","version":2}},"canonical_sha256":"9ad2f7bb062946fc537ab56f522f9c59f547170fa13117d9c62b02c1ca59fd6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ad2f7bb062946fc537ab56f522f9c59f547170fa13117d9c62b02c1ca59fd6b","first_computed_at":"2026-05-18T00:09:20.641920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:20.641920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b7puRrpRI4KYrfWXUo5gz21f9diucu8wJ825enpkjjWkZV/Nf4uKOKvhLpZo1ntvgMfBaomNShglqJ8vJ3wVBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:20.642550Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.00625","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:700462d8bf89f6b498806167c3d8722fca12898da58b0c30a31342eefc3625d0","sha256:51ebd5da7e7623f01600b3465d104d41725381458f62dc4261fa53580af9fc64"],"state_sha256":"9fab167f6f33cadee80c310da44fe7976c3cb4ceaf28261f15619fb13f1eee11"}