{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:DPTZVWJPBCUZUE26QN5Z3LQJHM","short_pith_number":"pith:DPTZVWJP","canonical_record":{"source":{"id":"1002.4478","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-02-24T06:17:54Z","cross_cats_sorted":[],"title_canon_sha256":"0438e1ed8b2eda91a3afbc8e050d91bac6c46f05b1b45158f361f1aea30b1f7b","abstract_canon_sha256":"61c4cb7454ec3336a24c4ad079c6f8eb9084a6f5c8e6d98d8775d2ad46d9a4d2"},"schema_version":"1.0"},"canonical_sha256":"1be79ad92f08a99a135e837b9dae093b0466aa0342d16a35f0395b43ba680ed3","source":{"kind":"arxiv","id":"1002.4478","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4478","created_at":"2026-05-18T03:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4478v1","created_at":"2026-05-18T03:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4478","created_at":"2026-05-18T03:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"DPTZVWJPBCUZ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DPTZVWJPBCUZUE26","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DPTZVWJP","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:DPTZVWJPBCUZUE26QN5Z3LQJHM","target":"record","payload":{"canonical_record":{"source":{"id":"1002.4478","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-02-24T06:17:54Z","cross_cats_sorted":[],"title_canon_sha256":"0438e1ed8b2eda91a3afbc8e050d91bac6c46f05b1b45158f361f1aea30b1f7b","abstract_canon_sha256":"61c4cb7454ec3336a24c4ad079c6f8eb9084a6f5c8e6d98d8775d2ad46d9a4d2"},"schema_version":"1.0"},"canonical_sha256":"1be79ad92f08a99a135e837b9dae093b0466aa0342d16a35f0395b43ba680ed3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:00.730283Z","signature_b64":"1bVZYC4lVXmlDLQffap0CFNeEshmewi/fXEp37DA1UuXTMy1FqPh0I8pN/e9p6Vq1eHnWUTgVFbgtJWRRua8CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1be79ad92f08a99a135e837b9dae093b0466aa0342d16a35f0395b43ba680ed3","last_reissued_at":"2026-05-18T03:13:00.729426Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:00.729426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.4478","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":"2026-05-18T03:13:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z6HRhemRg+Z0erlZqW1Zl8CsF2RqQeKzLNfEbky6KjuBQXEcXlC5To3GXxf18NexzsVigqvFzJGT+iWgz/bkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:22:04.671706Z"},"content_sha256":"6f2d0dbdd6913d7ea77e701a17ce5a4ef6e95b10c9dfc34818869f27decefb4b","schema_version":"1.0","event_id":"sha256:6f2d0dbdd6913d7ea77e701a17ce5a4ef6e95b10c9dfc34818869f27decefb4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:DPTZVWJPBCUZUE26QN5Z3LQJHM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phi-entropy inequalities and Fokker-Planck equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fran\\c{c}ois Bolley (CEREMADE), Ivan Gentil (CEREMADE)","submitted_at":"2010-02-24T06:17:54Z","abstract_excerpt":"We present new $\\Phi$-entropy inequalities for diffusion semigroups under the curvature-dimension criterion. They include the isoperimetric function of the Gaussian measure. Applications to the long time behaviour of solutions to Fokker-Planck equations are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4478","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":"2026-05-18T03:13:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kvh+Y3rK5A+CcxeL9P/COQXk3qfePOpC773dwjPV53jWYuvWZMZrsbMO30WysvlP4Rml57Y9ZltQQ0tUQLBDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:22:04.672044Z"},"content_sha256":"fd2c6159441e5132852ded08e5e94456c827388e7466518d1e02c855030208ba","schema_version":"1.0","event_id":"sha256:fd2c6159441e5132852ded08e5e94456c827388e7466518d1e02c855030208ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DPTZVWJPBCUZUE26QN5Z3LQJHM/bundle.json","state_url":"https://pith.science/pith/DPTZVWJPBCUZUE26QN5Z3LQJHM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DPTZVWJPBCUZUE26QN5Z3LQJHM/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":"2026-06-03T02:22:04Z","links":{"resolver":"https://pith.science/pith/DPTZVWJPBCUZUE26QN5Z3LQJHM","bundle":"https://pith.science/pith/DPTZVWJPBCUZUE26QN5Z3LQJHM/bundle.json","state":"https://pith.science/pith/DPTZVWJPBCUZUE26QN5Z3LQJHM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DPTZVWJPBCUZUE26QN5Z3LQJHM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DPTZVWJPBCUZUE26QN5Z3LQJHM","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":"61c4cb7454ec3336a24c4ad079c6f8eb9084a6f5c8e6d98d8775d2ad46d9a4d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-02-24T06:17:54Z","title_canon_sha256":"0438e1ed8b2eda91a3afbc8e050d91bac6c46f05b1b45158f361f1aea30b1f7b"},"schema_version":"1.0","source":{"id":"1002.4478","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4478","created_at":"2026-05-18T03:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4478v1","created_at":"2026-05-18T03:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4478","created_at":"2026-05-18T03:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"DPTZVWJPBCUZ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DPTZVWJPBCUZUE26","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DPTZVWJP","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:fd2c6159441e5132852ded08e5e94456c827388e7466518d1e02c855030208ba","target":"graph","created_at":"2026-05-18T03:13:00Z","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 present new $\\Phi$-entropy inequalities for diffusion semigroups under the curvature-dimension criterion. They include the isoperimetric function of the Gaussian measure. Applications to the long time behaviour of solutions to Fokker-Planck equations are given.","authors_text":"Fran\\c{c}ois Bolley (CEREMADE), Ivan Gentil (CEREMADE)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-02-24T06:17:54Z","title":"Phi-entropy inequalities and Fokker-Planck equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4478","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":"sha256:6f2d0dbdd6913d7ea77e701a17ce5a4ef6e95b10c9dfc34818869f27decefb4b","target":"record","created_at":"2026-05-18T03:13:00Z","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":"61c4cb7454ec3336a24c4ad079c6f8eb9084a6f5c8e6d98d8775d2ad46d9a4d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-02-24T06:17:54Z","title_canon_sha256":"0438e1ed8b2eda91a3afbc8e050d91bac6c46f05b1b45158f361f1aea30b1f7b"},"schema_version":"1.0","source":{"id":"1002.4478","kind":"arxiv","version":1}},"canonical_sha256":"1be79ad92f08a99a135e837b9dae093b0466aa0342d16a35f0395b43ba680ed3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1be79ad92f08a99a135e837b9dae093b0466aa0342d16a35f0395b43ba680ed3","first_computed_at":"2026-05-18T03:13:00.729426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:00.729426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1bVZYC4lVXmlDLQffap0CFNeEshmewi/fXEp37DA1UuXTMy1FqPh0I8pN/e9p6Vq1eHnWUTgVFbgtJWRRua8CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:00.730283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.4478","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f2d0dbdd6913d7ea77e701a17ce5a4ef6e95b10c9dfc34818869f27decefb4b","sha256:fd2c6159441e5132852ded08e5e94456c827388e7466518d1e02c855030208ba"],"state_sha256":"4be5fcae18afe3d4423bf3703afbcbcb9c30b4036a263063d571479ee9786551"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iCQStFc9/3P7yevzNBYznKzksEf4GWqSWhT6zsGi7B1UWxsH3UkHJA/1sK8YhdbF2RsNBNew4LzUIc7PuZ7aAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:22:04.673922Z","bundle_sha256":"3f949a51e45b82b78bbb10a587ecc97bf6b2c713046aad5394f7e9ea01b8fcab"}}