{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BXYKIGVT3KMBXXSZFRUF3Z6KZ2","short_pith_number":"pith:BXYKIGVT","canonical_record":{"source":{"id":"1410.7225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-10-27T13:31:45Z","cross_cats_sorted":[],"title_canon_sha256":"4c0fe5434122b2ecd3234efd53a8aeb413b78eb7c645ec9a9d62ccd80204b6be","abstract_canon_sha256":"973a392c09a74b3e8a3cf09d4bad47e84c6fdb20381225896367171635046881"},"schema_version":"1.0"},"canonical_sha256":"0df0a41ab3da981bde592c685de7caceb63e63ded25655cec983d508220c8b10","source":{"kind":"arxiv","id":"1410.7225","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7225","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7225v1","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7225","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"BXYKIGVT3KMB","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BXYKIGVT3KMBXXSZ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BXYKIGVT","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BXYKIGVT3KMBXXSZFRUF3Z6KZ2","target":"record","payload":{"canonical_record":{"source":{"id":"1410.7225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-10-27T13:31:45Z","cross_cats_sorted":[],"title_canon_sha256":"4c0fe5434122b2ecd3234efd53a8aeb413b78eb7c645ec9a9d62ccd80204b6be","abstract_canon_sha256":"973a392c09a74b3e8a3cf09d4bad47e84c6fdb20381225896367171635046881"},"schema_version":"1.0"},"canonical_sha256":"0df0a41ab3da981bde592c685de7caceb63e63ded25655cec983d508220c8b10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:17.781338Z","signature_b64":"E7eO0w3jdJgEJjPdftYkZMVTasdPsFgYxPTJzg2spKXd4ZCwscfIeUe7tmzQ06qjqso7kM5OWrar1/p7f63nCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0df0a41ab3da981bde592c685de7caceb63e63ded25655cec983d508220c8b10","last_reissued_at":"2026-05-18T02:39:17.780842Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:17.780842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.7225","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":"2026-05-18T02:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b1gAayXLnNlazOWNafcd58wxMGkPeY0WnnmKIFyUC7aDXIZQR/Wy4h8t3HgaFssGL8jFv+maxjYVWEBxDFDRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T16:21:29.151398Z"},"content_sha256":"e80aa6f734a5294b1dd372bbdff163fee48afc151aaacb9775c60996ed0a02f7","schema_version":"1.0","event_id":"sha256:e80aa6f734a5294b1dd372bbdff163fee48afc151aaacb9775c60996ed0a02f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BXYKIGVT3KMBXXSZFRUF3Z6KZ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analyzing Expected Outcomes and Almost-Sure Termination of Probabilistic Programs is Hard","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Benjamin Lucien Kaminski, Joost-Pieter Katoen","submitted_at":"2014-10-27T13:31:45Z","abstract_excerpt":"This paper considers the computational hardness of computing expected outcomes and deciding almost-sure termination of probabilistic programs. We show that deciding almost-sure termination and deciding whether the expected outcome of a program equals a given rational value is $\\Pi^0_2$-complete. Computing lower and upper bounds on the expected outcome is shown to be recursively enumerable and $\\Sigma^0_2$-complete, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7225","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":"2026-05-18T02:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"umDn3YC9IAFt+aFELK4Tq8G2pkQ8g/1uToXbrMdUFnWzGHWsJMYEN3HEC6GmCRkO3MGnE0TfhkT6PuH8CIxuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T16:21:29.152093Z"},"content_sha256":"3c4934cbf33c299b11b19de4f882c78030e3e4e0c30ef34daf2b40f0721dfc97","schema_version":"1.0","event_id":"sha256:3c4934cbf33c299b11b19de4f882c78030e3e4e0c30ef34daf2b40f0721dfc97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BXYKIGVT3KMBXXSZFRUF3Z6KZ2/bundle.json","state_url":"https://pith.science/pith/BXYKIGVT3KMBXXSZFRUF3Z6KZ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BXYKIGVT3KMBXXSZFRUF3Z6KZ2/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":"2026-05-23T16:21:29Z","links":{"resolver":"https://pith.science/pith/BXYKIGVT3KMBXXSZFRUF3Z6KZ2","bundle":"https://pith.science/pith/BXYKIGVT3KMBXXSZFRUF3Z6KZ2/bundle.json","state":"https://pith.science/pith/BXYKIGVT3KMBXXSZFRUF3Z6KZ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BXYKIGVT3KMBXXSZFRUF3Z6KZ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BXYKIGVT3KMBXXSZFRUF3Z6KZ2","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":"973a392c09a74b3e8a3cf09d4bad47e84c6fdb20381225896367171635046881","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-10-27T13:31:45Z","title_canon_sha256":"4c0fe5434122b2ecd3234efd53a8aeb413b78eb7c645ec9a9d62ccd80204b6be"},"schema_version":"1.0","source":{"id":"1410.7225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7225","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7225v1","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7225","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"BXYKIGVT3KMB","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BXYKIGVT3KMBXXSZ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BXYKIGVT","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:3c4934cbf33c299b11b19de4f882c78030e3e4e0c30ef34daf2b40f0721dfc97","target":"graph","created_at":"2026-05-18T02:39:17Z","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":"This paper considers the computational hardness of computing expected outcomes and deciding almost-sure termination of probabilistic programs. We show that deciding almost-sure termination and deciding whether the expected outcome of a program equals a given rational value is $\\Pi^0_2$-complete. Computing lower and upper bounds on the expected outcome is shown to be recursively enumerable and $\\Sigma^0_2$-complete, respectively.","authors_text":"Benjamin Lucien Kaminski, Joost-Pieter Katoen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-10-27T13:31:45Z","title":"Analyzing Expected Outcomes and Almost-Sure Termination of Probabilistic Programs is Hard"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7225","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:e80aa6f734a5294b1dd372bbdff163fee48afc151aaacb9775c60996ed0a02f7","target":"record","created_at":"2026-05-18T02:39:17Z","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":"973a392c09a74b3e8a3cf09d4bad47e84c6fdb20381225896367171635046881","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-10-27T13:31:45Z","title_canon_sha256":"4c0fe5434122b2ecd3234efd53a8aeb413b78eb7c645ec9a9d62ccd80204b6be"},"schema_version":"1.0","source":{"id":"1410.7225","kind":"arxiv","version":1}},"canonical_sha256":"0df0a41ab3da981bde592c685de7caceb63e63ded25655cec983d508220c8b10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0df0a41ab3da981bde592c685de7caceb63e63ded25655cec983d508220c8b10","first_computed_at":"2026-05-18T02:39:17.780842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:17.780842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E7eO0w3jdJgEJjPdftYkZMVTasdPsFgYxPTJzg2spKXd4ZCwscfIeUe7tmzQ06qjqso7kM5OWrar1/p7f63nCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:17.781338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e80aa6f734a5294b1dd372bbdff163fee48afc151aaacb9775c60996ed0a02f7","sha256:3c4934cbf33c299b11b19de4f882c78030e3e4e0c30ef34daf2b40f0721dfc97"],"state_sha256":"d0cd581d74ec35fe88996eb721a9f7528d3dbd86f1f0bbefea0e7dc668f3cdd4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ZAvsMK2KCxCICIE5kfB5olAv1K7I3f7DCtiOpG6AtW3sW6v68ANIGgzQ62WqdVs0YUNDVlxvoIU3w8vi2rbAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T16:21:29.155513Z","bundle_sha256":"9e1299c656b949838bb5a241952c31db5580bfea3ea17924a2abc4f77c15dc40"}}