{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:57I4BPAYUZNH6AU2EUC4MZ2DCH","short_pith_number":"pith:57I4BPAY","canonical_record":{"source":{"id":"0708.2152","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2007-08-16T08:14:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c8a0892eb0650f93a918f03e1b5c9ca30fb3be4b39e67c8f31ef397e96f5cd8c","abstract_canon_sha256":"6ab8f600b820071263a100a6ad6b432f07a11ec59c3614c5d6d9ca7c8bfcaba3"},"schema_version":"1.0"},"canonical_sha256":"efd1c0bc18a65a7f029a2505c6674311d04890916138f8c9cb5150910fb810ad","source":{"kind":"arxiv","id":"0708.2152","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.2152","created_at":"2026-05-18T01:37:45Z"},{"alias_kind":"arxiv_version","alias_value":"0708.2152v4","created_at":"2026-05-18T01:37:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.2152","created_at":"2026-05-18T01:37:45Z"},{"alias_kind":"pith_short_12","alias_value":"57I4BPAYUZNH","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"57I4BPAYUZNH6AU2","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"57I4BPAY","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:57I4BPAYUZNH6AU2EUC4MZ2DCH","target":"record","payload":{"canonical_record":{"source":{"id":"0708.2152","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2007-08-16T08:14:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c8a0892eb0650f93a918f03e1b5c9ca30fb3be4b39e67c8f31ef397e96f5cd8c","abstract_canon_sha256":"6ab8f600b820071263a100a6ad6b432f07a11ec59c3614c5d6d9ca7c8bfcaba3"},"schema_version":"1.0"},"canonical_sha256":"efd1c0bc18a65a7f029a2505c6674311d04890916138f8c9cb5150910fb810ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:45.229764Z","signature_b64":"iPFBRxkZwcQ/KTsAo6TQ4SsPGeAkcOJJqN6mSDjsybJS2YVazJse8mVRh27p1b6oL4dj6nF/h5CsEm4Zt9XzBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efd1c0bc18a65a7f029a2505c6674311d04890916138f8c9cb5150910fb810ad","last_reissued_at":"2026-05-18T01:37:45.229382Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:45.229382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0708.2152","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zSVK2H7Nu3kWxVmdCttG0xzzlVGM8KiqpyKuaonrDUeYFHpErMAEEaBhlxFU7g/Z+5GuWRJ98hOUNltg/uVLBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:08:42.466692Z"},"content_sha256":"4d55335e17d93dbe488d8795e804c37fbea21ae256d15ec3d337cf758a9e79bb","schema_version":"1.0","event_id":"sha256:4d55335e17d93dbe488d8795e804c37fbea21ae256d15ec3d337cf758a9e79bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:57I4BPAYUZNH6AU2EUC4MZ2DCH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coupling, concentration inequalities and stochastic dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Frank Redig, Jean Ren\\'e Chazottes, Pierre Collet","submitted_at":"2007-08-16T08:14:32Z","abstract_excerpt":"In the context of interacting particle systems, we study the influence of the action of the semigroup on the concentration property of Lipschitz functions. As an application, this gives a new approach to estimate the relaxation speed to equilibrium of interacting particle systems. We illustrate our approach in a variety of examples for which we obtain several new results with short and non-technical proofs. These examples include the symmetric and asymmetric exclusion process and high-temperature spin-flip dynamics (\"Glauber dynamics\"). We also give a new proof of the Poincar\\'e inequality, ba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.2152","kind":"arxiv","version":4},"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":"2026-05-18T01:37:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hi9BnY42XVdbtuKHeZZGsrTfbJH8FJYYG3h+JwHrgJ7+lnu4yaLqoOPUQwECYi6M4dLa3sP9ZEA9ifeea389AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:08:42.467373Z"},"content_sha256":"63dddbddcc264a9f6854ca8d4fd53eee733244431ea9a2fc31b4edb52119d952","schema_version":"1.0","event_id":"sha256:63dddbddcc264a9f6854ca8d4fd53eee733244431ea9a2fc31b4edb52119d952"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/57I4BPAYUZNH6AU2EUC4MZ2DCH/bundle.json","state_url":"https://pith.science/pith/57I4BPAYUZNH6AU2EUC4MZ2DCH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/57I4BPAYUZNH6AU2EUC4MZ2DCH/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":"2026-06-07T20:08:42Z","links":{"resolver":"https://pith.science/pith/57I4BPAYUZNH6AU2EUC4MZ2DCH","bundle":"https://pith.science/pith/57I4BPAYUZNH6AU2EUC4MZ2DCH/bundle.json","state":"https://pith.science/pith/57I4BPAYUZNH6AU2EUC4MZ2DCH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/57I4BPAYUZNH6AU2EUC4MZ2DCH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:57I4BPAYUZNH6AU2EUC4MZ2DCH","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":"6ab8f600b820071263a100a6ad6b432f07a11ec59c3614c5d6d9ca7c8bfcaba3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2007-08-16T08:14:32Z","title_canon_sha256":"c8a0892eb0650f93a918f03e1b5c9ca30fb3be4b39e67c8f31ef397e96f5cd8c"},"schema_version":"1.0","source":{"id":"0708.2152","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.2152","created_at":"2026-05-18T01:37:45Z"},{"alias_kind":"arxiv_version","alias_value":"0708.2152v4","created_at":"2026-05-18T01:37:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.2152","created_at":"2026-05-18T01:37:45Z"},{"alias_kind":"pith_short_12","alias_value":"57I4BPAYUZNH","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"57I4BPAYUZNH6AU2","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"57I4BPAY","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:63dddbddcc264a9f6854ca8d4fd53eee733244431ea9a2fc31b4edb52119d952","target":"graph","created_at":"2026-05-18T01:37:45Z","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":"In the context of interacting particle systems, we study the influence of the action of the semigroup on the concentration property of Lipschitz functions. As an application, this gives a new approach to estimate the relaxation speed to equilibrium of interacting particle systems. We illustrate our approach in a variety of examples for which we obtain several new results with short and non-technical proofs. These examples include the symmetric and asymmetric exclusion process and high-temperature spin-flip dynamics (\"Glauber dynamics\"). We also give a new proof of the Poincar\\'e inequality, ba","authors_text":"Frank Redig, Jean Ren\\'e Chazottes, Pierre Collet","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2007-08-16T08:14:32Z","title":"Coupling, concentration inequalities and stochastic dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.2152","kind":"arxiv","version":4},"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":"sha256:4d55335e17d93dbe488d8795e804c37fbea21ae256d15ec3d337cf758a9e79bb","target":"record","created_at":"2026-05-18T01:37:45Z","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":"6ab8f600b820071263a100a6ad6b432f07a11ec59c3614c5d6d9ca7c8bfcaba3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2007-08-16T08:14:32Z","title_canon_sha256":"c8a0892eb0650f93a918f03e1b5c9ca30fb3be4b39e67c8f31ef397e96f5cd8c"},"schema_version":"1.0","source":{"id":"0708.2152","kind":"arxiv","version":4}},"canonical_sha256":"efd1c0bc18a65a7f029a2505c6674311d04890916138f8c9cb5150910fb810ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efd1c0bc18a65a7f029a2505c6674311d04890916138f8c9cb5150910fb810ad","first_computed_at":"2026-05-18T01:37:45.229382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:45.229382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iPFBRxkZwcQ/KTsAo6TQ4SsPGeAkcOJJqN6mSDjsybJS2YVazJse8mVRh27p1b6oL4dj6nF/h5CsEm4Zt9XzBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:45.229764Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.2152","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d55335e17d93dbe488d8795e804c37fbea21ae256d15ec3d337cf758a9e79bb","sha256:63dddbddcc264a9f6854ca8d4fd53eee733244431ea9a2fc31b4edb52119d952"],"state_sha256":"8cc3b5ddc3104f3e99c9c48cd9cc79bda1265aabb248e02de630a2285795c38a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nzt2PgpWI2NZMfI/YNRZGq/gLGT8EV7+9iJM954qn5R3KKjL2jC4iPvl0o3bSoPC7tygxf9q1yIrmMxtzYuoCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T20:08:42.471397Z","bundle_sha256":"476db6333a4aa6268c75168cf4f3ac6959f20b0eafdaf5c6c6cea5df46210d66"}}