{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:XZK6YVME4FWUCX47PYFLRYL45Z","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":"cc901fe3d31199220bfa7c5d75fa73ab520d60d39dbe22793621f4e6a6141795","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2021-04-15T07:12:19Z","title_canon_sha256":"b0d296bfe0bb2425b141c92c8be7fd4784df6d66a97177916d89f9616dce5b6e"},"schema_version":"1.0","source":{"id":"2104.07278","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.07278","created_at":"2026-07-05T09:34:07Z"},{"alias_kind":"arxiv_version","alias_value":"2104.07278v5","created_at":"2026-07-05T09:34:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.07278","created_at":"2026-07-05T09:34:07Z"},{"alias_kind":"pith_short_12","alias_value":"XZK6YVME4FWU","created_at":"2026-07-05T09:34:07Z"},{"alias_kind":"pith_short_16","alias_value":"XZK6YVME4FWUCX47","created_at":"2026-07-05T09:34:07Z"},{"alias_kind":"pith_short_8","alias_value":"XZK6YVME","created_at":"2026-07-05T09:34:07Z"}],"graph_snapshots":[{"event_id":"sha256:d8bc02846b084a519783f59ee874c079839b4b5096845473c42712fecd75b6d2","target":"graph","created_at":"2026-07-05T09:34:07Z","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/2104.07278/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected tota","authors_text":"Krishnendu Chatterjee, Laurent Doyen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2021-04-15T07:12:19Z","title":"Stochastic Processes with Expected Stopping Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.07278","kind":"arxiv","version":5},"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":"sha256:472427ad5ca70785cbad28220b954697e7811c43f28dfc320bf0af0055bf1d67","target":"record","created_at":"2026-07-05T09:34:07Z","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":"cc901fe3d31199220bfa7c5d75fa73ab520d60d39dbe22793621f4e6a6141795","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2021-04-15T07:12:19Z","title_canon_sha256":"b0d296bfe0bb2425b141c92c8be7fd4784df6d66a97177916d89f9616dce5b6e"},"schema_version":"1.0","source":{"id":"2104.07278","kind":"arxiv","version":5}},"canonical_sha256":"be55ec5584e16d415f9f7e0ab8e17cee6342e3f9ed2f827f265e72fa75dc7c93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be55ec5584e16d415f9f7e0ab8e17cee6342e3f9ed2f827f265e72fa75dc7c93","first_computed_at":"2026-07-05T09:34:07.837868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:34:07.837868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u/UFQBUX+o4TQB2weGI9p/HSvh4OQacZZYlHVEKaTfzhnBEXKkJbA3dhDZ85eA/U+tqMo3mbW5uFRrtFE+0qBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:34:07.838373Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.07278","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:472427ad5ca70785cbad28220b954697e7811c43f28dfc320bf0af0055bf1d67","sha256:d8bc02846b084a519783f59ee874c079839b4b5096845473c42712fecd75b6d2"],"state_sha256":"1e3e18e57d843fed8856ff856358e72ccdac2fe9a5f3b2d47edfba9ed7cf826f"}