{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BMRFPDR2XTLCZIVAYSDPLVJGIV","short_pith_number":"pith:BMRFPDR2","canonical_record":{"source":{"id":"1308.4117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-19T19:56:56Z","cross_cats_sorted":["math-ph","math.MP","math.ST","stat.TH"],"title_canon_sha256":"5e4a4a17ac80882e9359c32abe0d9161c4f29371425c5076da14ed4319010ebd","abstract_canon_sha256":"fbcbac595a9776151578101ac997f66a0f9371e18140c02c36c39443447075db"},"schema_version":"1.0"},"canonical_sha256":"0b22578e3abcd62ca2a0c486f5d526454b191ba0d40ab7dfd79f528a554d2dc7","source":{"kind":"arxiv","id":"1308.4117","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4117","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4117v1","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4117","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"pith_short_12","alias_value":"BMRFPDR2XTLC","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BMRFPDR2XTLCZIVA","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BMRFPDR2","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BMRFPDR2XTLCZIVAYSDPLVJGIV","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-19T19:56:56Z","cross_cats_sorted":["math-ph","math.MP","math.ST","stat.TH"],"title_canon_sha256":"5e4a4a17ac80882e9359c32abe0d9161c4f29371425c5076da14ed4319010ebd","abstract_canon_sha256":"fbcbac595a9776151578101ac997f66a0f9371e18140c02c36c39443447075db"},"schema_version":"1.0"},"canonical_sha256":"0b22578e3abcd62ca2a0c486f5d526454b191ba0d40ab7dfd79f528a554d2dc7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:05.539942Z","signature_b64":"8s55St5EYBsCNC/zR7Ge652nkygwKMHSUn4CunJBx4vMN6tr0LhcgWF9GRd4Hq1zz7OD2WKW0Ep49/KTQ2x0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b22578e3abcd62ca2a0c486f5d526454b191ba0d40ab7dfd79f528a554d2dc7","last_reissued_at":"2026-05-18T02:28:05.539503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:05.539503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4117","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aVXoNEWRHCLOxAvMqxQImFPQVDn+/XRp2qRGGlD1pR2Iz2S0ROANiP0d7G0rNsKuVOLoG31jkyPGy/VvmsJCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:44:32.646518Z"},"content_sha256":"38794c6b7cb2f3f1536f761944a9b36d4df6c4fb89bdaf630273c5fe278e6b8b","schema_version":"1.0","event_id":"sha256:38794c6b7cb2f3f1536f761944a9b36d4df6c4fb89bdaf630273c5fe278e6b8b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BMRFPDR2XTLCZIVAYSDPLVJGIV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Comparison Theorems for Gibbs Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Patrick Rebeschini, Ramon van Handel","submitted_at":"2013-08-19T19:56:56Z","abstract_excerpt":"The Dobrushin comparison theorem is a powerful tool to bound the difference between the marginals of high-dimensional probability distributions in terms of their local specifications. Originally introduced to prove uniqueness and decay of correlations of Gibbs measures, it has been widely used in statistical mechanics as well as in the analysis of algorithms on random fields and interacting Markov chains. However, the classical comparison theorem requires validity of the Dobrushin uniqueness criterion, essentially restricting its applicability in most models to a small subset of the natural pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4117","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b55MgJ8SjephKno29BXaN1fGOh02pTFBA0Ufk02H0gQFJxLNCKb75nwqkMWA4RBcWUKEpZKDP3+YlVS3CK45DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:44:32.647185Z"},"content_sha256":"03bb15874e7203777d068a7eb96c6e41a25f2d9ed3576c64cd8bd295a8b7f860","schema_version":"1.0","event_id":"sha256:03bb15874e7203777d068a7eb96c6e41a25f2d9ed3576c64cd8bd295a8b7f860"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BMRFPDR2XTLCZIVAYSDPLVJGIV/bundle.json","state_url":"https://pith.science/pith/BMRFPDR2XTLCZIVAYSDPLVJGIV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BMRFPDR2XTLCZIVAYSDPLVJGIV/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":"2026-05-28T20:44:32Z","links":{"resolver":"https://pith.science/pith/BMRFPDR2XTLCZIVAYSDPLVJGIV","bundle":"https://pith.science/pith/BMRFPDR2XTLCZIVAYSDPLVJGIV/bundle.json","state":"https://pith.science/pith/BMRFPDR2XTLCZIVAYSDPLVJGIV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BMRFPDR2XTLCZIVAYSDPLVJGIV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BMRFPDR2XTLCZIVAYSDPLVJGIV","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":"fbcbac595a9776151578101ac997f66a0f9371e18140c02c36c39443447075db","cross_cats_sorted":["math-ph","math.MP","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-19T19:56:56Z","title_canon_sha256":"5e4a4a17ac80882e9359c32abe0d9161c4f29371425c5076da14ed4319010ebd"},"schema_version":"1.0","source":{"id":"1308.4117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4117","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4117v1","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4117","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"pith_short_12","alias_value":"BMRFPDR2XTLC","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BMRFPDR2XTLCZIVA","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BMRFPDR2","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:03bb15874e7203777d068a7eb96c6e41a25f2d9ed3576c64cd8bd295a8b7f860","target":"graph","created_at":"2026-05-18T02:28:05Z","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 Dobrushin comparison theorem is a powerful tool to bound the difference between the marginals of high-dimensional probability distributions in terms of their local specifications. Originally introduced to prove uniqueness and decay of correlations of Gibbs measures, it has been widely used in statistical mechanics as well as in the analysis of algorithms on random fields and interacting Markov chains. However, the classical comparison theorem requires validity of the Dobrushin uniqueness criterion, essentially restricting its applicability in most models to a small subset of the natural pa","authors_text":"Patrick Rebeschini, Ramon van Handel","cross_cats":["math-ph","math.MP","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-19T19:56:56Z","title":"Comparison Theorems for Gibbs Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4117","kind":"arxiv","version":1},"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":"sha256:38794c6b7cb2f3f1536f761944a9b36d4df6c4fb89bdaf630273c5fe278e6b8b","target":"record","created_at":"2026-05-18T02:28:05Z","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":"fbcbac595a9776151578101ac997f66a0f9371e18140c02c36c39443447075db","cross_cats_sorted":["math-ph","math.MP","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-19T19:56:56Z","title_canon_sha256":"5e4a4a17ac80882e9359c32abe0d9161c4f29371425c5076da14ed4319010ebd"},"schema_version":"1.0","source":{"id":"1308.4117","kind":"arxiv","version":1}},"canonical_sha256":"0b22578e3abcd62ca2a0c486f5d526454b191ba0d40ab7dfd79f528a554d2dc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b22578e3abcd62ca2a0c486f5d526454b191ba0d40ab7dfd79f528a554d2dc7","first_computed_at":"2026-05-18T02:28:05.539503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:05.539503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8s55St5EYBsCNC/zR7Ge652nkygwKMHSUn4CunJBx4vMN6tr0LhcgWF9GRd4Hq1zz7OD2WKW0Ep49/KTQ2x0Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:05.539942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38794c6b7cb2f3f1536f761944a9b36d4df6c4fb89bdaf630273c5fe278e6b8b","sha256:03bb15874e7203777d068a7eb96c6e41a25f2d9ed3576c64cd8bd295a8b7f860"],"state_sha256":"85df4046dcfa767033906ff5c12c792389966445228b3aa9e0fcea7665d11650"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U2puKgDtAvnv7jLmz03Z58eFHRhJzWRcpcD01R1EqqVKB0wLelqDERol2QonKopo3mciAHTJ339MdXScjZN3Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:44:32.650914Z","bundle_sha256":"cf7d9a5a471281b0d04a4f3640040be09e9667805c5744c12cd33848da884f13"}}