{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:Z3Z427KRJC2JH4C6SSGFIK5ASE","short_pith_number":"pith:Z3Z427KR","canonical_record":{"source":{"id":"2010.13566","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2020-10-26T13:17:47Z","cross_cats_sorted":[],"title_canon_sha256":"9a12fcbc8f3becb8ad1fc4d494abd539cee367c1142c7f2ba0cb8bce4877dd4a","abstract_canon_sha256":"65ef7393d9ff0404e8e8bad1802d2fd0603feabbcc469154a61620f5d5efafc0"},"schema_version":"1.0"},"canonical_sha256":"cef3cd7d5148b493f05e948c542ba09130ea5d2c0a0e42b884d6f604d4be3686","source":{"kind":"arxiv","id":"2010.13566","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.13566","created_at":"2026-07-05T02:05:09Z"},{"alias_kind":"arxiv_version","alias_value":"2010.13566v2","created_at":"2026-07-05T02:05:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.13566","created_at":"2026-07-05T02:05:09Z"},{"alias_kind":"pith_short_12","alias_value":"Z3Z427KRJC2J","created_at":"2026-07-05T02:05:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z3Z427KRJC2JH4C6","created_at":"2026-07-05T02:05:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z3Z427KR","created_at":"2026-07-05T02:05:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:Z3Z427KRJC2JH4C6SSGFIK5ASE","target":"record","payload":{"canonical_record":{"source":{"id":"2010.13566","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2020-10-26T13:17:47Z","cross_cats_sorted":[],"title_canon_sha256":"9a12fcbc8f3becb8ad1fc4d494abd539cee367c1142c7f2ba0cb8bce4877dd4a","abstract_canon_sha256":"65ef7393d9ff0404e8e8bad1802d2fd0603feabbcc469154a61620f5d5efafc0"},"schema_version":"1.0"},"canonical_sha256":"cef3cd7d5148b493f05e948c542ba09130ea5d2c0a0e42b884d6f604d4be3686","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:05:09.398823Z","signature_b64":"/FtxQ5k4d2/WOhsnuBOYHmdH86L+9ArSoMDsLq3WEZouUnSoVNwPre4vUxInOamTQIKJwu2nN2ZwioF1OxEPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cef3cd7d5148b493f05e948c542ba09130ea5d2c0a0e42b884d6f604d4be3686","last_reissued_at":"2026-07-05T02:05:09.398397Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:05:09.398397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.13566","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:05:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xv/Z+r1FI3Ble/s4qRUaUPuWHvZ2MacB2quHgf8aqqxuvi05+JaFnsmLvAqFJGV7KGY/KCmgKouNMLdwZbmVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:39:46.872427Z"},"content_sha256":"ce85bb2bfcd82136659422b38dd5579163b20418953dfc33d73b009773d19851","schema_version":"1.0","event_id":"sha256:ce85bb2bfcd82136659422b38dd5579163b20418953dfc33d73b009773d19851"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:Z3Z427KRJC2JH4C6SSGFIK5ASE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-objective Optimization of Long-run Average and Total Rewards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Joost-Pieter Katoen, Tim Quatmann","submitted_at":"2020-10-26T13:17:47Z","abstract_excerpt":"This paper presents an efficient procedure for multi-objective model checking of long-run average reward (aka: mean pay-off) and total reward objectives as well as their combination. We consider this for Markov automata, a compositional model that captures both traditional Markov decision processes (MDPs) as well as a continuous-time variant thereof. The crux of our procedure is a generalization of Forejt et al.'s approach for total rewards on MDPs to arbitrary combinations of long-run and total reward objectives on Markov automata. Experiments with a prototypical implementation on top of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.13566","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/2010.13566/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:05:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9WLvFHLPWF4yKlkzeqGOcorehMn7d5/0qWoBq6gWx6YSC3iRpFRB4VqypberQbwSwi7ixWIby+ktp31ieYbDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:39:46.872935Z"},"content_sha256":"dc2d30dc867b61d76ac814db86e71fdc01906e25d9941d0a7f3fcd9212dd1e07","schema_version":"1.0","event_id":"sha256:dc2d30dc867b61d76ac814db86e71fdc01906e25d9941d0a7f3fcd9212dd1e07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3Z427KRJC2JH4C6SSGFIK5ASE/bundle.json","state_url":"https://pith.science/pith/Z3Z427KRJC2JH4C6SSGFIK5ASE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3Z427KRJC2JH4C6SSGFIK5ASE/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":"2026-08-04T15:39:46Z","links":{"resolver":"https://pith.science/pith/Z3Z427KRJC2JH4C6SSGFIK5ASE","bundle":"https://pith.science/pith/Z3Z427KRJC2JH4C6SSGFIK5ASE/bundle.json","state":"https://pith.science/pith/Z3Z427KRJC2JH4C6SSGFIK5ASE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3Z427KRJC2JH4C6SSGFIK5ASE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:Z3Z427KRJC2JH4C6SSGFIK5ASE","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":"65ef7393d9ff0404e8e8bad1802d2fd0603feabbcc469154a61620f5d5efafc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2020-10-26T13:17:47Z","title_canon_sha256":"9a12fcbc8f3becb8ad1fc4d494abd539cee367c1142c7f2ba0cb8bce4877dd4a"},"schema_version":"1.0","source":{"id":"2010.13566","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.13566","created_at":"2026-07-05T02:05:09Z"},{"alias_kind":"arxiv_version","alias_value":"2010.13566v2","created_at":"2026-07-05T02:05:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.13566","created_at":"2026-07-05T02:05:09Z"},{"alias_kind":"pith_short_12","alias_value":"Z3Z427KRJC2J","created_at":"2026-07-05T02:05:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z3Z427KRJC2JH4C6","created_at":"2026-07-05T02:05:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z3Z427KR","created_at":"2026-07-05T02:05:09Z"}],"graph_snapshots":[{"event_id":"sha256:dc2d30dc867b61d76ac814db86e71fdc01906e25d9941d0a7f3fcd9212dd1e07","target":"graph","created_at":"2026-07-05T02:05:09Z","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/2010.13566/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper presents an efficient procedure for multi-objective model checking of long-run average reward (aka: mean pay-off) and total reward objectives as well as their combination. We consider this for Markov automata, a compositional model that captures both traditional Markov decision processes (MDPs) as well as a continuous-time variant thereof. The crux of our procedure is a generalization of Forejt et al.'s approach for total rewards on MDPs to arbitrary combinations of long-run and total reward objectives on Markov automata. Experiments with a prototypical implementation on top of the ","authors_text":"Joost-Pieter Katoen, Tim Quatmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2020-10-26T13:17:47Z","title":"Multi-objective Optimization of Long-run Average and Total Rewards"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.13566","kind":"arxiv","version":2},"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:ce85bb2bfcd82136659422b38dd5579163b20418953dfc33d73b009773d19851","target":"record","created_at":"2026-07-05T02:05:09Z","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":"65ef7393d9ff0404e8e8bad1802d2fd0603feabbcc469154a61620f5d5efafc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2020-10-26T13:17:47Z","title_canon_sha256":"9a12fcbc8f3becb8ad1fc4d494abd539cee367c1142c7f2ba0cb8bce4877dd4a"},"schema_version":"1.0","source":{"id":"2010.13566","kind":"arxiv","version":2}},"canonical_sha256":"cef3cd7d5148b493f05e948c542ba09130ea5d2c0a0e42b884d6f604d4be3686","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cef3cd7d5148b493f05e948c542ba09130ea5d2c0a0e42b884d6f604d4be3686","first_computed_at":"2026-07-05T02:05:09.398397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:05:09.398397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/FtxQ5k4d2/WOhsnuBOYHmdH86L+9ArSoMDsLq3WEZouUnSoVNwPre4vUxInOamTQIKJwu2nN2ZwioF1OxEPCg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:05:09.398823Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.13566","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce85bb2bfcd82136659422b38dd5579163b20418953dfc33d73b009773d19851","sha256:dc2d30dc867b61d76ac814db86e71fdc01906e25d9941d0a7f3fcd9212dd1e07"],"state_sha256":"b4588ae3c76996e6f8c3c37f9ef857d838b0e25a7cfe4eb9409080b76befa89d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zkdsRlCRkRzltdEISj9eRyd5KSbn3C8WwBuLZ2mghosWhRIjvfVKUTeJZS4J0DHZ6LE40iSbq/XfIjD2cKnDBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T15:39:46.879199Z","bundle_sha256":"ec0dcc0113026386f94d22cbea8bc8d8885a00e92bfadaea5ed1d534b4c6b153"}}