{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GTJWDEXLJQKXMLI6PG76S4Q52Y","short_pith_number":"pith:GTJWDEXL","canonical_record":{"source":{"id":"2607.06813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-07T21:20:41Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"8a3812bb6796b037c601a0c78d93b89d31e20c23817069406938a48c992a7126","abstract_canon_sha256":"17bf42c13d323412860516f92ab218ad3aa8dae095ebf43be81f4cc548995f5e"},"schema_version":"1.0"},"canonical_sha256":"34d36192eb4c15762d1e79bfe9721dd6332ef6d871d6b971a8d9ef544fd3a142","source":{"kind":"arxiv","id":"2607.06813","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06813","created_at":"2026-07-09T00:19:29Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06813v1","created_at":"2026-07-09T00:19:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06813","created_at":"2026-07-09T00:19:29Z"},{"alias_kind":"pith_short_12","alias_value":"GTJWDEXLJQKX","created_at":"2026-07-09T00:19:29Z"},{"alias_kind":"pith_short_16","alias_value":"GTJWDEXLJQKXMLI6","created_at":"2026-07-09T00:19:29Z"},{"alias_kind":"pith_short_8","alias_value":"GTJWDEXL","created_at":"2026-07-09T00:19:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GTJWDEXLJQKXMLI6PG76S4Q52Y","target":"record","payload":{"canonical_record":{"source":{"id":"2607.06813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-07T21:20:41Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"8a3812bb6796b037c601a0c78d93b89d31e20c23817069406938a48c992a7126","abstract_canon_sha256":"17bf42c13d323412860516f92ab218ad3aa8dae095ebf43be81f4cc548995f5e"},"schema_version":"1.0"},"canonical_sha256":"34d36192eb4c15762d1e79bfe9721dd6332ef6d871d6b971a8d9ef544fd3a142","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T00:19:29.139576Z","signature_b64":"/fbCd+CtbdNbZU1WjHxjMK592qyD3m9nURLxlYUzfcmB26qIHt/e6qv+84TMw/BTjh2ryC9rLHTjgh3uJLREDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34d36192eb4c15762d1e79bfe9721dd6332ef6d871d6b971a8d9ef544fd3a142","last_reissued_at":"2026-07-09T00:19:29.138725Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T00:19:29.138725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.06813","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":"2026-07-09T00:19:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QPTnUG/CSnFjdlscH6gpBoVWM/eSf5ZRHYsoNF1893fbmoxOp/LpsSdx7RMC/X1caMoCvqX44T2x7XRBUI99Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T13:01:44.225192Z"},"content_sha256":"f7ca1207181da29247690a87ea35895930f32eebb2faf03c750a1b1e60ef0033","schema_version":"1.0","event_id":"sha256:f7ca1207181da29247690a87ea35895930f32eebb2faf03c750a1b1e60ef0033"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GTJWDEXLJQKXMLI6PG76S4Q52Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mixing of Glauber Dynamics on High Overlap Gibbs Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Afonso S. Bandeira, Ahmed El Alaoui, Almut R\\\"odder","submitted_at":"2026-07-07T21:20:41Z","abstract_excerpt":"We show fast mixing of Glauber dynamics for certain quadratic Gibbs measures with large external fields. The main ingredient is an overlap condition that allows us to control correlation matrices uniformly over all pinnings, by controlling norms of small submatrices of the interaction matrix. Using stochastic localization, we then obtain a lower bound on the spectral gap and, consequently, polynomial-time mixing of Glauber dynamics. As a direct application, we consider the Sherrington-Kirkpatrick model, whose interaction matrix is a scaled GOE matrix. For this model, we show that for any fixed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06813","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06813/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-09T00:19:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B/WAHvp1SwC9ofwDSsLJ0RswdV47t7tIZ9mt4FE23YxixxS/gY/1UJ8ZDAmstXmN5ABjR0O4daJD6lzWukuwDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T13:01:44.226200Z"},"content_sha256":"4a01e88c0e75c46a83b8d79aa04d1c4f36e84356cce5efa3feff1a052eedc5a8","schema_version":"1.0","event_id":"sha256:4a01e88c0e75c46a83b8d79aa04d1c4f36e84356cce5efa3feff1a052eedc5a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GTJWDEXLJQKXMLI6PG76S4Q52Y/bundle.json","state_url":"https://pith.science/pith/GTJWDEXLJQKXMLI6PG76S4Q52Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GTJWDEXLJQKXMLI6PG76S4Q52Y/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":"2026-08-10T13:01:44Z","links":{"resolver":"https://pith.science/pith/GTJWDEXLJQKXMLI6PG76S4Q52Y","bundle":"https://pith.science/pith/GTJWDEXLJQKXMLI6PG76S4Q52Y/bundle.json","state":"https://pith.science/pith/GTJWDEXLJQKXMLI6PG76S4Q52Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GTJWDEXLJQKXMLI6PG76S4Q52Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GTJWDEXLJQKXMLI6PG76S4Q52Y","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":"17bf42c13d323412860516f92ab218ad3aa8dae095ebf43be81f4cc548995f5e","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-07T21:20:41Z","title_canon_sha256":"8a3812bb6796b037c601a0c78d93b89d31e20c23817069406938a48c992a7126"},"schema_version":"1.0","source":{"id":"2607.06813","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06813","created_at":"2026-07-09T00:19:29Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06813v1","created_at":"2026-07-09T00:19:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06813","created_at":"2026-07-09T00:19:29Z"},{"alias_kind":"pith_short_12","alias_value":"GTJWDEXLJQKX","created_at":"2026-07-09T00:19:29Z"},{"alias_kind":"pith_short_16","alias_value":"GTJWDEXLJQKXMLI6","created_at":"2026-07-09T00:19:29Z"},{"alias_kind":"pith_short_8","alias_value":"GTJWDEXL","created_at":"2026-07-09T00:19:29Z"}],"graph_snapshots":[{"event_id":"sha256:4a01e88c0e75c46a83b8d79aa04d1c4f36e84356cce5efa3feff1a052eedc5a8","target":"graph","created_at":"2026-07-09T00:19:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.06813/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show fast mixing of Glauber dynamics for certain quadratic Gibbs measures with large external fields. The main ingredient is an overlap condition that allows us to control correlation matrices uniformly over all pinnings, by controlling norms of small submatrices of the interaction matrix. Using stochastic localization, we then obtain a lower bound on the spectral gap and, consequently, polynomial-time mixing of Glauber dynamics. As a direct application, we consider the Sherrington-Kirkpatrick model, whose interaction matrix is a scaled GOE matrix. For this model, we show that for any fixed","authors_text":"Afonso S. Bandeira, Ahmed El Alaoui, Almut R\\\"odder","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-07T21:20:41Z","title":"Mixing of Glauber Dynamics on High Overlap Gibbs Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06813","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:f7ca1207181da29247690a87ea35895930f32eebb2faf03c750a1b1e60ef0033","target":"record","created_at":"2026-07-09T00:19:29Z","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":"17bf42c13d323412860516f92ab218ad3aa8dae095ebf43be81f4cc548995f5e","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-07T21:20:41Z","title_canon_sha256":"8a3812bb6796b037c601a0c78d93b89d31e20c23817069406938a48c992a7126"},"schema_version":"1.0","source":{"id":"2607.06813","kind":"arxiv","version":1}},"canonical_sha256":"34d36192eb4c15762d1e79bfe9721dd6332ef6d871d6b971a8d9ef544fd3a142","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34d36192eb4c15762d1e79bfe9721dd6332ef6d871d6b971a8d9ef544fd3a142","first_computed_at":"2026-07-09T00:19:29.138725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T00:19:29.138725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/fbCd+CtbdNbZU1WjHxjMK592qyD3m9nURLxlYUzfcmB26qIHt/e6qv+84TMw/BTjh2ryC9rLHTjgh3uJLREDw==","signature_status":"signed_v1","signed_at":"2026-07-09T00:19:29.139576Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.06813","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7ca1207181da29247690a87ea35895930f32eebb2faf03c750a1b1e60ef0033","sha256:4a01e88c0e75c46a83b8d79aa04d1c4f36e84356cce5efa3feff1a052eedc5a8"],"state_sha256":"0c17f4e76cf1a245eec464a4db2598b0eaf522a33c67f4598df14e14a29afc22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BGVXwfLY9pv/le9Ep8yjO/M2SPYHmqhAugJIiQt7wwkfyyF66Xe53enTBRuStHsDlwhU4JZ6TH6XVwL4BzGFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T13:01:44.232447Z","bundle_sha256":"7754bd71e283391241f2a2695586a077559cdb0fb4547ff8c01020915438d5dc"}}