{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VPO2PO5DAZYS4ZNV4NXJR2L34Z","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":"a654b9fb5327651b26feea26ca49fc4906e51cb64dec6c7782134c668046bfe3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-25T09:05:20Z","title_canon_sha256":"bda045ad7f8ddb04dc2a90a21088b22db7eb4678e6f19f8e1d54e73232abfdd1"},"schema_version":"1.0","source":{"id":"1908.09284","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.09284","created_at":"2026-07-04T23:59:38Z"},{"alias_kind":"arxiv_version","alias_value":"1908.09284v1","created_at":"2026-07-04T23:59:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.09284","created_at":"2026-07-04T23:59:38Z"},{"alias_kind":"pith_short_12","alias_value":"VPO2PO5DAZYS","created_at":"2026-07-04T23:59:38Z"},{"alias_kind":"pith_short_16","alias_value":"VPO2PO5DAZYS4ZNV","created_at":"2026-07-04T23:59:38Z"},{"alias_kind":"pith_short_8","alias_value":"VPO2PO5D","created_at":"2026-07-04T23:59:38Z"}],"graph_snapshots":[{"event_id":"sha256:234228eeba7e5b66d51b08488ca619e79cd6945045ebbf294e567cb37ce983f3","target":"graph","created_at":"2026-07-04T23:59:38Z","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/1908.09284/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study certain properties of the function space of autocorrelation functions of Unit Continuous Time Markov Chains (CTMCs). It is shown that under particular conditions, the $L^p$ norm of the autocorrelation function of arbitrary finite state space CTMCs is infinite. Several interesting inferences are made for point processes associated with CTMCs/ Discrete Time Markov Chains (DTMCs).","authors_text":"Douglas G. Down, G. Rama Murthy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-25T09:05:20Z","title":"Autocorrelation Function Characterization of Continuous Time Markov Chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09284","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":"sha256:9cc60a57b196d67d756ccf0fe15df07d228672cc3ffa668ac4cdf46f4355b6cf","target":"record","created_at":"2026-07-04T23:59:38Z","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":"a654b9fb5327651b26feea26ca49fc4906e51cb64dec6c7782134c668046bfe3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-25T09:05:20Z","title_canon_sha256":"bda045ad7f8ddb04dc2a90a21088b22db7eb4678e6f19f8e1d54e73232abfdd1"},"schema_version":"1.0","source":{"id":"1908.09284","kind":"arxiv","version":1}},"canonical_sha256":"abdda7bba306712e65b5e36e98e97be658baf072eb67ff129e409c654457046d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abdda7bba306712e65b5e36e98e97be658baf072eb67ff129e409c654457046d","first_computed_at":"2026-07-04T23:59:38.857194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:38.857194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"utdoMpxk4KA4wlKHoqg6MPtnku2zmLZUUrqCozPwNXDPnuQv7h8brPpVl4t7EskgGYv0khBBVL7EPOzzxGHeDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:38.857622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.09284","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cc60a57b196d67d756ccf0fe15df07d228672cc3ffa668ac4cdf46f4355b6cf","sha256:234228eeba7e5b66d51b08488ca619e79cd6945045ebbf294e567cb37ce983f3"],"state_sha256":"bd386178c1daefa24451cf7e86d15d0ca58f13d028d1e01d57c74f8c72600fdf"}