{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:T2A67WAN7JSTVE6INAOAAL46VW","short_pith_number":"pith:T2A67WAN","canonical_record":{"source":{"id":"1303.1257","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-06T06:41:12Z","cross_cats_sorted":[],"title_canon_sha256":"40239a9f01d6780912ccb294e43e94cd876a83d603d8c51b3a8ce461115aacaf","abstract_canon_sha256":"57d39a1b7a9f6eb754e7b804105b65a08db1c8b11d473630cd1acc1c0ef8f742"},"schema_version":"1.0"},"canonical_sha256":"9e81efd80dfa653a93c8681c002f9eadb7e9684d13159c3b05d928f177624f4b","source":{"kind":"arxiv","id":"1303.1257","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1257","created_at":"2026-05-18T03:31:44Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1257v1","created_at":"2026-05-18T03:31:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1257","created_at":"2026-05-18T03:31:44Z"},{"alias_kind":"pith_short_12","alias_value":"T2A67WAN7JST","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T2A67WAN7JSTVE6I","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T2A67WAN","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:T2A67WAN7JSTVE6INAOAAL46VW","target":"record","payload":{"canonical_record":{"source":{"id":"1303.1257","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-06T06:41:12Z","cross_cats_sorted":[],"title_canon_sha256":"40239a9f01d6780912ccb294e43e94cd876a83d603d8c51b3a8ce461115aacaf","abstract_canon_sha256":"57d39a1b7a9f6eb754e7b804105b65a08db1c8b11d473630cd1acc1c0ef8f742"},"schema_version":"1.0"},"canonical_sha256":"9e81efd80dfa653a93c8681c002f9eadb7e9684d13159c3b05d928f177624f4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:44.056738Z","signature_b64":"MA8il8Am5WJJVgU+qyCKPoDddOaGuYE7TT0bq9vL97k3Q5oPdl7p1NBwg/R3gPOt2aaPl5ys7iqLePTaZRbsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e81efd80dfa653a93c8681c002f9eadb7e9684d13159c3b05d928f177624f4b","last_reissued_at":"2026-05-18T03:31:44.055988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:44.055988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.1257","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":"2026-05-18T03:31:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"01w8fuWByqdRjfjdZL4mS76IMXHMufZ3cMTomkBotjcBrLHwmrfa4f3fhLPayRrJ4VBwzrX4KzRzJ4co5j5pAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T20:12:09.328763Z"},"content_sha256":"6a9366bdefb8e1e8ca273258a45aabc60b18a960e75bc3a85af4c9d51839c3a8","schema_version":"1.0","event_id":"sha256:6a9366bdefb8e1e8ca273258a45aabc60b18a960e75bc3a85af4c9d51839c3a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:T2A67WAN7JSTVE6INAOAAL46VW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poincare inequality and exponential integrability of the hitting times of a Markov process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexei M. Kulik","submitted_at":"2013-03-06T06:41:12Z","abstract_excerpt":"Extending the approach of the paper [Mathieu, P. (1997) Hitting times and spectral gap inequalities, Ann. Inst. Henri Poincare 33, 4, 437 -- 465], we prove that the Poincare inequality for a (possibly non-symmetric) Markov process yields the exponential integrability of the hitting times of this process. For symmetric elliptic diffusions, this provides a criterion for the Poincare inequality in the terms of hitting times."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1257","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":"2026-05-18T03:31:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+8GLd4D/4ESo9zhTFkCsEghkKjWoFBGV0W86LD9OnTrqrw+HQC2+o/1BRXHskNmMBEv5+hLchLuPH02+Yv8uBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T20:12:09.329102Z"},"content_sha256":"81bca8f399ea453bb644a973a91ec9e0a56b77b2926c57422e3d7398e304d02b","schema_version":"1.0","event_id":"sha256:81bca8f399ea453bb644a973a91ec9e0a56b77b2926c57422e3d7398e304d02b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T2A67WAN7JSTVE6INAOAAL46VW/bundle.json","state_url":"https://pith.science/pith/T2A67WAN7JSTVE6INAOAAL46VW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T2A67WAN7JSTVE6INAOAAL46VW/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":"2026-06-26T20:12:09Z","links":{"resolver":"https://pith.science/pith/T2A67WAN7JSTVE6INAOAAL46VW","bundle":"https://pith.science/pith/T2A67WAN7JSTVE6INAOAAL46VW/bundle.json","state":"https://pith.science/pith/T2A67WAN7JSTVE6INAOAAL46VW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T2A67WAN7JSTVE6INAOAAL46VW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:T2A67WAN7JSTVE6INAOAAL46VW","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":"57d39a1b7a9f6eb754e7b804105b65a08db1c8b11d473630cd1acc1c0ef8f742","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-06T06:41:12Z","title_canon_sha256":"40239a9f01d6780912ccb294e43e94cd876a83d603d8c51b3a8ce461115aacaf"},"schema_version":"1.0","source":{"id":"1303.1257","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1257","created_at":"2026-05-18T03:31:44Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1257v1","created_at":"2026-05-18T03:31:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1257","created_at":"2026-05-18T03:31:44Z"},{"alias_kind":"pith_short_12","alias_value":"T2A67WAN7JST","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T2A67WAN7JSTVE6I","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T2A67WAN","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:81bca8f399ea453bb644a973a91ec9e0a56b77b2926c57422e3d7398e304d02b","target":"graph","created_at":"2026-05-18T03:31:44Z","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":"Extending the approach of the paper [Mathieu, P. (1997) Hitting times and spectral gap inequalities, Ann. Inst. Henri Poincare 33, 4, 437 -- 465], we prove that the Poincare inequality for a (possibly non-symmetric) Markov process yields the exponential integrability of the hitting times of this process. For symmetric elliptic diffusions, this provides a criterion for the Poincare inequality in the terms of hitting times.","authors_text":"Alexei M. Kulik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-06T06:41:12Z","title":"Poincare inequality and exponential integrability of the hitting times of a Markov process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1257","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":"sha256:6a9366bdefb8e1e8ca273258a45aabc60b18a960e75bc3a85af4c9d51839c3a8","target":"record","created_at":"2026-05-18T03:31:44Z","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":"57d39a1b7a9f6eb754e7b804105b65a08db1c8b11d473630cd1acc1c0ef8f742","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-06T06:41:12Z","title_canon_sha256":"40239a9f01d6780912ccb294e43e94cd876a83d603d8c51b3a8ce461115aacaf"},"schema_version":"1.0","source":{"id":"1303.1257","kind":"arxiv","version":1}},"canonical_sha256":"9e81efd80dfa653a93c8681c002f9eadb7e9684d13159c3b05d928f177624f4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e81efd80dfa653a93c8681c002f9eadb7e9684d13159c3b05d928f177624f4b","first_computed_at":"2026-05-18T03:31:44.055988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:44.055988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MA8il8Am5WJJVgU+qyCKPoDddOaGuYE7TT0bq9vL97k3Q5oPdl7p1NBwg/R3gPOt2aaPl5ys7iqLePTaZRbsAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:44.056738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1257","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a9366bdefb8e1e8ca273258a45aabc60b18a960e75bc3a85af4c9d51839c3a8","sha256:81bca8f399ea453bb644a973a91ec9e0a56b77b2926c57422e3d7398e304d02b"],"state_sha256":"9e4c3dc719fb480e265fb8d9b310c3c80718c68f7390b2a03c1a70cc54bd1d05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IaBV+X8XBekZieWxYqCphhCCGBLCxkPW95KxYzL6klsPzDx5QHJ2Peb55nMJhMR1KK7+LK21SWahJoUEoJ33AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T20:12:09.330924Z","bundle_sha256":"9254be31e43fb0f94b943e87a9cf7bf2a59e8128adb494476af33899cd115ed6"}}