{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:JPT4XY3DVODGEYFPYAUWGMYBEW","short_pith_number":"pith:JPT4XY3D","canonical_record":{"source":{"id":"2308.00516","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-08-01T12:56:33Z","cross_cats_sorted":[],"title_canon_sha256":"66cd01f18c6ad5ffbdfd7e79333827b123b42d9ea0fe91e7b14b65cb9da91cf0","abstract_canon_sha256":"444a9dd1f1256e51ec335cb6d7baaa6d52620c028b80b9e7ab1299e521cb3849"},"schema_version":"1.0"},"canonical_sha256":"4be7cbe363ab866260afc02963330125b7fb89df2e432edb8a3334b2e724c39b","source":{"kind":"arxiv","id":"2308.00516","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.00516","created_at":"2026-07-05T10:21:55Z"},{"alias_kind":"arxiv_version","alias_value":"2308.00516v2","created_at":"2026-07-05T10:21:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.00516","created_at":"2026-07-05T10:21:55Z"},{"alias_kind":"pith_short_12","alias_value":"JPT4XY3DVODG","created_at":"2026-07-05T10:21:55Z"},{"alias_kind":"pith_short_16","alias_value":"JPT4XY3DVODGEYFP","created_at":"2026-07-05T10:21:55Z"},{"alias_kind":"pith_short_8","alias_value":"JPT4XY3D","created_at":"2026-07-05T10:21:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:JPT4XY3DVODGEYFPYAUWGMYBEW","target":"record","payload":{"canonical_record":{"source":{"id":"2308.00516","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-08-01T12:56:33Z","cross_cats_sorted":[],"title_canon_sha256":"66cd01f18c6ad5ffbdfd7e79333827b123b42d9ea0fe91e7b14b65cb9da91cf0","abstract_canon_sha256":"444a9dd1f1256e51ec335cb6d7baaa6d52620c028b80b9e7ab1299e521cb3849"},"schema_version":"1.0"},"canonical_sha256":"4be7cbe363ab866260afc02963330125b7fb89df2e432edb8a3334b2e724c39b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:21:55.454119Z","signature_b64":"ACS97fDp/LCKYsZSfUURq8RMr1ifLtqxkdFSITgel59WsXq4AXPLU2blLQjtoWeCm1bMxGZ8/3Y3AX1OKREDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4be7cbe363ab866260afc02963330125b7fb89df2e432edb8a3334b2e724c39b","last_reissued_at":"2026-07-05T10:21:55.453581Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:21:55.453581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2308.00516","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:21:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UexuJ3aX3CGd8FbGy0JTBh8d0SMF4YUyOOvI8hkl61vQldbZBP0laqSdWJIIKymd/yr2Y/6BMiU/tB2DOjdUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T20:37:48.372973Z"},"content_sha256":"7872518b99e380eb2ea8301adab0f926ad0252c25e94c422cf743d084575bb72","schema_version":"1.0","event_id":"sha256:7872518b99e380eb2ea8301adab0f926ad0252c25e94c422cf743d084575bb72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:JPT4XY3DVODGEYFPYAUWGMYBEW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contractive coupling rates and curvature lower bounds for Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Francesco Pedrotti","submitted_at":"2023-08-01T12:56:33Z","abstract_excerpt":"Contractive coupling rates have been recently introduced by Conforti as a tool to establish convex Sobolev inequalities (including modified log-Sobolev and Poincar\\'{e} inequality) for some classes of Markov chains. In this work, we show how contractive coupling rates can also be used to prove stronger inequalities, in the form of curvature lower bounds for Markov chains and geodesic convexity of entropic functionals. We illustrate this in several examples discussed by Conforti, where in particular, after appropriately choosing a parameter function, we establish positive curvature in the entro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.00516","kind":"arxiv","version":2},"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/2308.00516/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":"2026-07-05T10:21:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/TIpjwudexEATaCNfotu2ZW0la7pYmAEcFcXRcvRLN/90qhtQOtDSZ/isFAT1QKpdxJanLjlA4Y+kzGC2/a8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T20:37:48.373506Z"},"content_sha256":"8ed282f45cc30be280a9348c3bf29db38149c3f748b4c030933957c3c7d68f61","schema_version":"1.0","event_id":"sha256:8ed282f45cc30be280a9348c3bf29db38149c3f748b4c030933957c3c7d68f61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JPT4XY3DVODGEYFPYAUWGMYBEW/bundle.json","state_url":"https://pith.science/pith/JPT4XY3DVODGEYFPYAUWGMYBEW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JPT4XY3DVODGEYFPYAUWGMYBEW/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":"2026-08-19T20:37:48Z","links":{"resolver":"https://pith.science/pith/JPT4XY3DVODGEYFPYAUWGMYBEW","bundle":"https://pith.science/pith/JPT4XY3DVODGEYFPYAUWGMYBEW/bundle.json","state":"https://pith.science/pith/JPT4XY3DVODGEYFPYAUWGMYBEW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JPT4XY3DVODGEYFPYAUWGMYBEW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:JPT4XY3DVODGEYFPYAUWGMYBEW","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":"444a9dd1f1256e51ec335cb6d7baaa6d52620c028b80b9e7ab1299e521cb3849","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-08-01T12:56:33Z","title_canon_sha256":"66cd01f18c6ad5ffbdfd7e79333827b123b42d9ea0fe91e7b14b65cb9da91cf0"},"schema_version":"1.0","source":{"id":"2308.00516","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.00516","created_at":"2026-07-05T10:21:55Z"},{"alias_kind":"arxiv_version","alias_value":"2308.00516v2","created_at":"2026-07-05T10:21:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.00516","created_at":"2026-07-05T10:21:55Z"},{"alias_kind":"pith_short_12","alias_value":"JPT4XY3DVODG","created_at":"2026-07-05T10:21:55Z"},{"alias_kind":"pith_short_16","alias_value":"JPT4XY3DVODGEYFP","created_at":"2026-07-05T10:21:55Z"},{"alias_kind":"pith_short_8","alias_value":"JPT4XY3D","created_at":"2026-07-05T10:21:55Z"}],"graph_snapshots":[{"event_id":"sha256:8ed282f45cc30be280a9348c3bf29db38149c3f748b4c030933957c3c7d68f61","target":"graph","created_at":"2026-07-05T10:21:55Z","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/2308.00516/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Contractive coupling rates have been recently introduced by Conforti as a tool to establish convex Sobolev inequalities (including modified log-Sobolev and Poincar\\'{e} inequality) for some classes of Markov chains. In this work, we show how contractive coupling rates can also be used to prove stronger inequalities, in the form of curvature lower bounds for Markov chains and geodesic convexity of entropic functionals. We illustrate this in several examples discussed by Conforti, where in particular, after appropriately choosing a parameter function, we establish positive curvature in the entro","authors_text":"Francesco Pedrotti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-08-01T12:56:33Z","title":"Contractive coupling rates and curvature lower bounds for Markov chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.00516","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":"sha256:7872518b99e380eb2ea8301adab0f926ad0252c25e94c422cf743d084575bb72","target":"record","created_at":"2026-07-05T10:21:55Z","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":"444a9dd1f1256e51ec335cb6d7baaa6d52620c028b80b9e7ab1299e521cb3849","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-08-01T12:56:33Z","title_canon_sha256":"66cd01f18c6ad5ffbdfd7e79333827b123b42d9ea0fe91e7b14b65cb9da91cf0"},"schema_version":"1.0","source":{"id":"2308.00516","kind":"arxiv","version":2}},"canonical_sha256":"4be7cbe363ab866260afc02963330125b7fb89df2e432edb8a3334b2e724c39b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4be7cbe363ab866260afc02963330125b7fb89df2e432edb8a3334b2e724c39b","first_computed_at":"2026-07-05T10:21:55.453581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:21:55.453581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ACS97fDp/LCKYsZSfUURq8RMr1ifLtqxkdFSITgel59WsXq4AXPLU2blLQjtoWeCm1bMxGZ8/3Y3AX1OKREDCg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:21:55.454119Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.00516","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7872518b99e380eb2ea8301adab0f926ad0252c25e94c422cf743d084575bb72","sha256:8ed282f45cc30be280a9348c3bf29db38149c3f748b4c030933957c3c7d68f61"],"state_sha256":"b0a48b7fbbed29423b4be25e5f38952b93f6cbd93b50bbd70e9b810eeefba3b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UYv/afJF3F2OsKnwfJSdOJFKPe7AbNB3xFv35kDbNsg4aoeDSl/FWIIlZqHlWGuOcyNOsOWryUQtLRdKy437Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T20:37:48.378905Z","bundle_sha256":"4d04b34923897438be51717cb15cd01e62155bdc16954edb32eb36903ae0e904"}}