{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:RPC2MOGPIDNXIXWQMEXJU6XZDO","short_pith_number":"pith:RPC2MOGP","schema_version":"1.0","canonical_sha256":"8bc5a638cf40db745ed0612e9a7af91baaa9c1e1bb756c880b39a4efb65b5a24","source":{"kind":"arxiv","id":"1601.01001","version":2},"attestation_state":"computed","paper":{"title":"Weakest Precondition Reasoning for Expected Run-Times of Probabilistic Programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.PL"],"primary_cat":"cs.LO","authors_text":"Benjamin Lucien Kaminski, Christoph Matheja, Federico Olmedo, Joost-Pieter Katoen","submitted_at":"2016-01-05T22:31:57Z","abstract_excerpt":"This paper presents a wp-style calculus for obtaining bounds on the expected run-time of probabilistic programs. Its application includes determining the (possibly infinite) expected termination time of a probabilistic program and proving positive almost-sure termination - does a program terminate with probability one in finite expected time? We provide several proof rules for bounding the run-time of loops, and prove the soundness of the approach with respect to a simple operational model. We show that our approach is a conservative extension of Nielson's approach for reasoning about the run-"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1601.01001","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-01-05T22:31:57Z","cross_cats_sorted":["cs.PL"],"title_canon_sha256":"bcfcca996de472d809627dee07dc6e1a29089d0a1c2e9b0cdc0171b18edf7aa0","abstract_canon_sha256":"f843ebfe8016e811e817a177c81b82f466b1e11f2c946bd1657bc6e02ac8702b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:57:22.393789Z","signature_b64":"W1d0NCUpvHrVJFtuA1HwcHf3M5AyhpReEvwFsNpLbu4nooD1Xj/K7w06yEiLsY7CAyUWwgjmQD9ljt6f6qswBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8bc5a638cf40db745ed0612e9a7af91baaa9c1e1bb756c880b39a4efb65b5a24","last_reissued_at":"2026-07-05T03:57:22.393363Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:57:22.393363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weakest Precondition Reasoning for Expected Run-Times of Probabilistic Programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.PL"],"primary_cat":"cs.LO","authors_text":"Benjamin Lucien Kaminski, Christoph Matheja, Federico Olmedo, Joost-Pieter Katoen","submitted_at":"2016-01-05T22:31:57Z","abstract_excerpt":"This paper presents a wp-style calculus for obtaining bounds on the expected run-time of probabilistic programs. Its application includes determining the (possibly infinite) expected termination time of a probabilistic program and proving positive almost-sure termination - does a program terminate with probability one in finite expected time? We provide several proof rules for bounding the run-time of loops, and prove the soundness of the approach with respect to a simple operational model. We show that our approach is a conservative extension of Nielson's approach for reasoning about the run-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01001","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1601.01001/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1601.01001","created_at":"2026-07-05T03:57:22.393432+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.01001v2","created_at":"2026-07-05T03:57:22.393432+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01001","created_at":"2026-07-05T03:57:22.393432+00:00"},{"alias_kind":"pith_short_12","alias_value":"RPC2MOGPIDNX","created_at":"2026-07-05T03:57:22.393432+00:00"},{"alias_kind":"pith_short_16","alias_value":"RPC2MOGPIDNXIXWQ","created_at":"2026-07-05T03:57:22.393432+00:00"},{"alias_kind":"pith_short_8","alias_value":"RPC2MOGP","created_at":"2026-07-05T03:57:22.393432+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RPC2MOGPIDNXIXWQMEXJU6XZDO","json":"https://pith.science/pith/RPC2MOGPIDNXIXWQMEXJU6XZDO.json","graph_json":"https://pith.science/api/pith-number/RPC2MOGPIDNXIXWQMEXJU6XZDO/graph.json","events_json":"https://pith.science/api/pith-number/RPC2MOGPIDNXIXWQMEXJU6XZDO/events.json","paper":"https://pith.science/paper/RPC2MOGP"},"agent_actions":{"view_html":"https://pith.science/pith/RPC2MOGPIDNXIXWQMEXJU6XZDO","download_json":"https://pith.science/pith/RPC2MOGPIDNXIXWQMEXJU6XZDO.json","view_paper":"https://pith.science/paper/RPC2MOGP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.01001&json=true","fetch_graph":"https://pith.science/api/pith-number/RPC2MOGPIDNXIXWQMEXJU6XZDO/graph.json","fetch_events":"https://pith.science/api/pith-number/RPC2MOGPIDNXIXWQMEXJU6XZDO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RPC2MOGPIDNXIXWQMEXJU6XZDO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RPC2MOGPIDNXIXWQMEXJU6XZDO/action/storage_attestation","attest_author":"https://pith.science/pith/RPC2MOGPIDNXIXWQMEXJU6XZDO/action/author_attestation","sign_citation":"https://pith.science/pith/RPC2MOGPIDNXIXWQMEXJU6XZDO/action/citation_signature","submit_replication":"https://pith.science/pith/RPC2MOGPIDNXIXWQMEXJU6XZDO/action/replication_record"}},"created_at":"2026-07-05T03:57:22.393432+00:00","updated_at":"2026-07-05T03:57:22.393432+00:00"}