{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:WBUGCDJYDTUBJHHGVFNXGA6Y7Y","short_pith_number":"pith:WBUGCDJY","canonical_record":{"source":{"id":"1009.2347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-13T10:49:04Z","cross_cats_sorted":[],"title_canon_sha256":"04e4153fa2c374351876d8c5079170be3e086eeff574bc2d0a13e80c32486d54","abstract_canon_sha256":"52cfdc788deb8822cc60150752f86efb5bfa18f6f7c777c92fd0aeaee45cbacf"},"schema_version":"1.0"},"canonical_sha256":"b068610d381ce8149ce6a95b7303d8fe0bee04a3e948eb3b951fe3e096e49d35","source":{"kind":"arxiv","id":"1009.2347","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2347","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2347v1","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2347","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"pith_short_12","alias_value":"WBUGCDJYDTUB","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"WBUGCDJYDTUBJHHG","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"WBUGCDJY","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:WBUGCDJYDTUBJHHGVFNXGA6Y7Y","target":"record","payload":{"canonical_record":{"source":{"id":"1009.2347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-13T10:49:04Z","cross_cats_sorted":[],"title_canon_sha256":"04e4153fa2c374351876d8c5079170be3e086eeff574bc2d0a13e80c32486d54","abstract_canon_sha256":"52cfdc788deb8822cc60150752f86efb5bfa18f6f7c777c92fd0aeaee45cbacf"},"schema_version":"1.0"},"canonical_sha256":"b068610d381ce8149ce6a95b7303d8fe0bee04a3e948eb3b951fe3e096e49d35","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:04.385006Z","signature_b64":"LGG6WrMaxRUjdd+b8A/D46nvhRypWFZ2tLlQadivhCRtoP/SB6X6WvDd08n3hASbkN9NXelFF1HnZ+J4fUORDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b068610d381ce8149ce6a95b7303d8fe0bee04a3e948eb3b951fe3e096e49d35","last_reissued_at":"2026-05-18T04:41:04.384367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:04.384367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.2347","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":"2026-05-18T04:41:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q+NR5UmqkBgOA3CfWtxbvAGXzUylHb/6cn597//IUHSg77DCSOP2h8T1iUSU8qRAAxeg3k1F0UzFwYiUS7NaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T07:16:59.725218Z"},"content_sha256":"08504b21ee0ecdc91627ce318190cab7c55bac1d39aa1af35f12f3eb7f9eb192","schema_version":"1.0","event_id":"sha256:08504b21ee0ecdc91627ce318190cab7c55bac1d39aa1af35f12f3eb7f9eb192"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:WBUGCDJYDTUBJHHGVFNXGA6Y7Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stationary distributions for jump processes with inert drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Krzysztof Burdzy, Rene Schilling, Tadeusz Kulczycki","submitted_at":"2010-09-13T10:49:04Z","abstract_excerpt":"We analyze jump processes $Z$ with ``inert drift'' determined by a ``memory'' process $S$. The state space of $(Z,S)$ is the Cartesian product of the unit circle and the real line. We prove that the stationary distribution of $(Z,S)$ is the product of the uniform probability measure and a Gaussian distribution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2347","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":"2026-05-18T04:41:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2J5zYlDgt5QVOTQNum9FZMdmW/aZ/in5uUe0wduAgJ+GsGlEGZt0TrYqF/KuFxWBeFTdBcYVrYXT1L/0scA4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T07:16:59.725590Z"},"content_sha256":"ced12d7927a47af9135a7f272e849563b5521996f8e3a6227dacd98b3d067065","schema_version":"1.0","event_id":"sha256:ced12d7927a47af9135a7f272e849563b5521996f8e3a6227dacd98b3d067065"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WBUGCDJYDTUBJHHGVFNXGA6Y7Y/bundle.json","state_url":"https://pith.science/pith/WBUGCDJYDTUBJHHGVFNXGA6Y7Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WBUGCDJYDTUBJHHGVFNXGA6Y7Y/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":"2026-05-20T07:16:59Z","links":{"resolver":"https://pith.science/pith/WBUGCDJYDTUBJHHGVFNXGA6Y7Y","bundle":"https://pith.science/pith/WBUGCDJYDTUBJHHGVFNXGA6Y7Y/bundle.json","state":"https://pith.science/pith/WBUGCDJYDTUBJHHGVFNXGA6Y7Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WBUGCDJYDTUBJHHGVFNXGA6Y7Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WBUGCDJYDTUBJHHGVFNXGA6Y7Y","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":"52cfdc788deb8822cc60150752f86efb5bfa18f6f7c777c92fd0aeaee45cbacf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-13T10:49:04Z","title_canon_sha256":"04e4153fa2c374351876d8c5079170be3e086eeff574bc2d0a13e80c32486d54"},"schema_version":"1.0","source":{"id":"1009.2347","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2347","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2347v1","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2347","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"pith_short_12","alias_value":"WBUGCDJYDTUB","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"WBUGCDJYDTUBJHHG","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"WBUGCDJY","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:ced12d7927a47af9135a7f272e849563b5521996f8e3a6227dacd98b3d067065","target":"graph","created_at":"2026-05-18T04:41:04Z","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 analyze jump processes $Z$ with ``inert drift'' determined by a ``memory'' process $S$. The state space of $(Z,S)$ is the Cartesian product of the unit circle and the real line. We prove that the stationary distribution of $(Z,S)$ is the product of the uniform probability measure and a Gaussian distribution.","authors_text":"Krzysztof Burdzy, Rene Schilling, Tadeusz Kulczycki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-13T10:49:04Z","title":"Stationary distributions for jump processes with inert drift"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2347","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":"sha256:08504b21ee0ecdc91627ce318190cab7c55bac1d39aa1af35f12f3eb7f9eb192","target":"record","created_at":"2026-05-18T04:41:04Z","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":"52cfdc788deb8822cc60150752f86efb5bfa18f6f7c777c92fd0aeaee45cbacf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-13T10:49:04Z","title_canon_sha256":"04e4153fa2c374351876d8c5079170be3e086eeff574bc2d0a13e80c32486d54"},"schema_version":"1.0","source":{"id":"1009.2347","kind":"arxiv","version":1}},"canonical_sha256":"b068610d381ce8149ce6a95b7303d8fe0bee04a3e948eb3b951fe3e096e49d35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b068610d381ce8149ce6a95b7303d8fe0bee04a3e948eb3b951fe3e096e49d35","first_computed_at":"2026-05-18T04:41:04.384367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:04.384367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LGG6WrMaxRUjdd+b8A/D46nvhRypWFZ2tLlQadivhCRtoP/SB6X6WvDd08n3hASbkN9NXelFF1HnZ+J4fUORDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:04.385006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2347","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08504b21ee0ecdc91627ce318190cab7c55bac1d39aa1af35f12f3eb7f9eb192","sha256:ced12d7927a47af9135a7f272e849563b5521996f8e3a6227dacd98b3d067065"],"state_sha256":"ca660e2e208bb7ad755b1f5c9b386db89d76478bfb4347b411fe2b2e307380db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wNlMrBF9+pTfWHiWM2r2B46N6z2q8UpGj4odmAhwJWFLnVjsPLKV/KiG/evWr30vj8gQMs84YieA6+bQA9H4Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T07:16:59.727524Z","bundle_sha256":"442891915fbb15268e12067e81920886740f951a222aaa76b268b4ea64379b94"}}