{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:2JA75PXYN7DQLW4BHD5N4OFRR5","short_pith_number":"pith:2JA75PXY","canonical_record":{"source":{"id":"1104.1884","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-04-11T09:07:35Z","cross_cats_sorted":[],"title_canon_sha256":"8f19b54f39c617cc488eebdf4f9e8496ed5be4311fe2984545aad8c12d50d46a","abstract_canon_sha256":"1de6b7dc99151a0ed7467409e9ed32498efe48630b374c2ab590e041b0f38a93"},"schema_version":"1.0"},"canonical_sha256":"d241febef86fc705db8138fade38b18f6427e007322b250cd990f6f0e1ce0717","source":{"kind":"arxiv","id":"1104.1884","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1884","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1884v1","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1884","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"pith_short_12","alias_value":"2JA75PXYN7DQ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2JA75PXYN7DQLW4B","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2JA75PXY","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:2JA75PXYN7DQLW4BHD5N4OFRR5","target":"record","payload":{"canonical_record":{"source":{"id":"1104.1884","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-04-11T09:07:35Z","cross_cats_sorted":[],"title_canon_sha256":"8f19b54f39c617cc488eebdf4f9e8496ed5be4311fe2984545aad8c12d50d46a","abstract_canon_sha256":"1de6b7dc99151a0ed7467409e9ed32498efe48630b374c2ab590e041b0f38a93"},"schema_version":"1.0"},"canonical_sha256":"d241febef86fc705db8138fade38b18f6427e007322b250cd990f6f0e1ce0717","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:45.634160Z","signature_b64":"KBE0lOrZmKZRasKFZMJswhyffQXigyiJRdJgjeyuFxiZ9ZbOcP8aHy9kcJH6/1oMk8iUY4LH+Ka3EAWvwvqsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d241febef86fc705db8138fade38b18f6427e007322b250cd990f6f0e1ce0717","last_reissued_at":"2026-05-18T03:46:45.633446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:45.633446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.1884","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":"2026-05-18T03:46:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sOqumoBdK7yW6EoZYH8v8NHG4rb5QFUNJ2jfhBkZRrQcBbdL4rT/xyCKafngugfsFHNwsx1qX9+//UvLCqLZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T23:15:38.944266Z"},"content_sha256":"2ed7ee58b6a90cea2d7854f8bf3b26309b23c2f43c420665339e964ca98ef583","schema_version":"1.0","event_id":"sha256:2ed7ee58b6a90cea2d7854f8bf3b26309b23c2f43c420665339e964ca98ef583"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:2JA75PXYN7DQLW4BHD5N4OFRR5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moments of recurrence times for Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Frank Aurzada, Hanna Doering, Marcel Ortgiese, Michael Scheutzow","submitted_at":"2011-04-11T09:07:35Z","abstract_excerpt":"We consider moments of the return times (or first hitting times) in a discrete time discrete space Markov chain. It is classical that the finiteness of the first moment of a return time of one state implies the finiteness of the first moment of the first return time of any other state. We extend this statement to moments with respect to a function $f$, where $f$ satisfies a certain, best possible condition. This generalizes results of K. L. Chung (1954) who considered the functions $f(n)=n^p$ and wondered \"[...] what property of the power $n^p$ lies behind this theorem [...]\" (see Chung (1967)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1884","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":"2026-05-18T03:46:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RDBhvWWb3UCb78i2vFy0EClhq/xNLTso6bFvk+5YIo3N9UjyoChfCxXIcmepNHvMGH3cxzgrTRmEG22iGVrvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T23:15:38.945030Z"},"content_sha256":"8be206221a16495b550f25667823c9c5eaf81814c8d98f37a7703631410b0d60","schema_version":"1.0","event_id":"sha256:8be206221a16495b550f25667823c9c5eaf81814c8d98f37a7703631410b0d60"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2JA75PXYN7DQLW4BHD5N4OFRR5/bundle.json","state_url":"https://pith.science/pith/2JA75PXYN7DQLW4BHD5N4OFRR5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2JA75PXYN7DQLW4BHD5N4OFRR5/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":"2026-06-05T23:15:38Z","links":{"resolver":"https://pith.science/pith/2JA75PXYN7DQLW4BHD5N4OFRR5","bundle":"https://pith.science/pith/2JA75PXYN7DQLW4BHD5N4OFRR5/bundle.json","state":"https://pith.science/pith/2JA75PXYN7DQLW4BHD5N4OFRR5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2JA75PXYN7DQLW4BHD5N4OFRR5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2JA75PXYN7DQLW4BHD5N4OFRR5","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":"1de6b7dc99151a0ed7467409e9ed32498efe48630b374c2ab590e041b0f38a93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-04-11T09:07:35Z","title_canon_sha256":"8f19b54f39c617cc488eebdf4f9e8496ed5be4311fe2984545aad8c12d50d46a"},"schema_version":"1.0","source":{"id":"1104.1884","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1884","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1884v1","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1884","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"pith_short_12","alias_value":"2JA75PXYN7DQ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2JA75PXYN7DQLW4B","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2JA75PXY","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:8be206221a16495b550f25667823c9c5eaf81814c8d98f37a7703631410b0d60","target":"graph","created_at":"2026-05-18T03:46:45Z","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":"We consider moments of the return times (or first hitting times) in a discrete time discrete space Markov chain. It is classical that the finiteness of the first moment of a return time of one state implies the finiteness of the first moment of the first return time of any other state. We extend this statement to moments with respect to a function $f$, where $f$ satisfies a certain, best possible condition. This generalizes results of K. L. Chung (1954) who considered the functions $f(n)=n^p$ and wondered \"[...] what property of the power $n^p$ lies behind this theorem [...]\" (see Chung (1967)","authors_text":"Frank Aurzada, Hanna Doering, Marcel Ortgiese, Michael Scheutzow","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-04-11T09:07:35Z","title":"Moments of recurrence times for Markov chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1884","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":"sha256:2ed7ee58b6a90cea2d7854f8bf3b26309b23c2f43c420665339e964ca98ef583","target":"record","created_at":"2026-05-18T03:46:45Z","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":"1de6b7dc99151a0ed7467409e9ed32498efe48630b374c2ab590e041b0f38a93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-04-11T09:07:35Z","title_canon_sha256":"8f19b54f39c617cc488eebdf4f9e8496ed5be4311fe2984545aad8c12d50d46a"},"schema_version":"1.0","source":{"id":"1104.1884","kind":"arxiv","version":1}},"canonical_sha256":"d241febef86fc705db8138fade38b18f6427e007322b250cd990f6f0e1ce0717","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d241febef86fc705db8138fade38b18f6427e007322b250cd990f6f0e1ce0717","first_computed_at":"2026-05-18T03:46:45.633446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:45.633446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KBE0lOrZmKZRasKFZMJswhyffQXigyiJRdJgjeyuFxiZ9ZbOcP8aHy9kcJH6/1oMk8iUY4LH+Ka3EAWvwvqsCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:45.634160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1884","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ed7ee58b6a90cea2d7854f8bf3b26309b23c2f43c420665339e964ca98ef583","sha256:8be206221a16495b550f25667823c9c5eaf81814c8d98f37a7703631410b0d60"],"state_sha256":"9e90e4bb9c58fe3519c0a2558c1b711edd6a9a28f2b90a846fc0e02edc3869ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uw+fAgxXjVHdIDs4+O0skXo2Gsq3SStYkLbxEoqyi9shKtCXluI9EeZHg9uXA05s61MYH1xkZqE8Ztvt3yNzCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T23:15:38.949435Z","bundle_sha256":"0fa31e13378fb378e5f4dd256e7d4e66d6b35bd75aeabbedebd8dd2bc23bcb64"}}