{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V3SD3VZCLZUQ5RQEU7AGV2SZ73","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":"b9cf12172e9df47dfad6fd9e8c1b34356ab09aa29d353a8dacf9dd063cd5b841","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-31T23:19:55Z","title_canon_sha256":"aace9adb5e2c986528ada54af9a500169dc7cb335225d32713a1a69ad72e9a1d"},"schema_version":"1.0","source":{"id":"1706.00121","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00121","created_at":"2026-05-18T00:36:13Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00121v2","created_at":"2026-05-18T00:36:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00121","created_at":"2026-05-18T00:36:13Z"},{"alias_kind":"pith_short_12","alias_value":"V3SD3VZCLZUQ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V3SD3VZCLZUQ5RQE","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V3SD3VZC","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:33eb57b4018b8d6eed97e85d432237ac2b9e7f283f4a1fb4afa0d608a32b27b9","target":"graph","created_at":"2026-05-18T00:36:13Z","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 study the concentration of a degree-$d$ polynomial of the $N$ spins of a general Ising model, in the regime where single-site Glauber dynamics is contracting. For $d=1$, Gaussian concentration was shown by Marton (1996) and Samson (2000) as a special case of concentration for convex Lipschitz functions, and extended to a variety of related settings by e.g., Chazottes et al. (2007) and Kontorovich and Ramanan (2008). For $d=2$, exponential concentration was shown by Marton (2003) on lattices. We treat a general fixed degree $d$ with $O(1)$ coefficients, and show that the polynomial has varia","authors_text":"Eyal Lubetzky, Reza Gheissari, Yuval Peres","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-31T23:19:55Z","title":"Concentration inequalities for polynomials of contracting Ising models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00121","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:dacb8e95e77764c0d52741994e488ca0635de86487a67cfd0ad3b388643a1e42","target":"record","created_at":"2026-05-18T00:36:13Z","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":"b9cf12172e9df47dfad6fd9e8c1b34356ab09aa29d353a8dacf9dd063cd5b841","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-31T23:19:55Z","title_canon_sha256":"aace9adb5e2c986528ada54af9a500169dc7cb335225d32713a1a69ad72e9a1d"},"schema_version":"1.0","source":{"id":"1706.00121","kind":"arxiv","version":2}},"canonical_sha256":"aee43dd7225e690ec604a7c06aea59fee22c6e2fbf6b12322e4cf8e702da0286","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aee43dd7225e690ec604a7c06aea59fee22c6e2fbf6b12322e4cf8e702da0286","first_computed_at":"2026-05-18T00:36:13.987935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:13.987935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y80qe0a7kfaxa+Lg32zJ27Wz7C46kYcRX893L4A7m8+rbN6F3PK9glzJTufYiZUvFsjStcQKa48+NSeAztprBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:13.988818Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00121","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dacb8e95e77764c0d52741994e488ca0635de86487a67cfd0ad3b388643a1e42","sha256:33eb57b4018b8d6eed97e85d432237ac2b9e7f283f4a1fb4afa0d608a32b27b9"],"state_sha256":"fc3eb7b40c69193129ac6101b8944f550cb6d8cf9462297367ad41b293f7c625"}