{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:3R73PNY7LPG4QD7SCMCHYXENEZ","short_pith_number":"pith:3R73PNY7","canonical_record":{"source":{"id":"2104.07466","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2021-04-15T13:53:28Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"99f533fc089a3748de41076edd65141fa39654421b928b5f3293681201c9cbe9","abstract_canon_sha256":"17c9ff0eb9ab02023b938d4afdedf486f104952708414ca1ecfedb5f50f8b4fd"},"schema_version":"1.0"},"canonical_sha256":"dc7fb7b71f5bcdc80ff213047c5c8d26790bb7e07ae8b22cb59fbe38f98f3cb9","source":{"kind":"arxiv","id":"2104.07466","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.07466","created_at":"2026-07-05T02:32:28Z"},{"alias_kind":"arxiv_version","alias_value":"2104.07466v1","created_at":"2026-07-05T02:32:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.07466","created_at":"2026-07-05T02:32:28Z"},{"alias_kind":"pith_short_12","alias_value":"3R73PNY7LPG4","created_at":"2026-07-05T02:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"3R73PNY7LPG4QD7S","created_at":"2026-07-05T02:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"3R73PNY7","created_at":"2026-07-05T02:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:3R73PNY7LPG4QD7SCMCHYXENEZ","target":"record","payload":{"canonical_record":{"source":{"id":"2104.07466","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2021-04-15T13:53:28Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"99f533fc089a3748de41076edd65141fa39654421b928b5f3293681201c9cbe9","abstract_canon_sha256":"17c9ff0eb9ab02023b938d4afdedf486f104952708414ca1ecfedb5f50f8b4fd"},"schema_version":"1.0"},"canonical_sha256":"dc7fb7b71f5bcdc80ff213047c5c8d26790bb7e07ae8b22cb59fbe38f98f3cb9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:32:28.227470Z","signature_b64":"8fKqZ3JKC87QTSWbciPorC8YhaEoSY+QS0YIp6ynjk0iryhCRD0DJK3Y+ML52NU3nbdJI0M44SuO4Zs6hhk/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc7fb7b71f5bcdc80ff213047c5c8d26790bb7e07ae8b22cb59fbe38f98f3cb9","last_reissued_at":"2026-07-05T02:32:28.226996Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:32:28.226996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.07466","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":"2026-07-05T02:32:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Kx3FopARRS65ItF9b1M1kAmprFX15IZ+9wqUFlPabeDhUywFS8HigMfqYO7/PsbAB96QLzdN8gkkqOstVXdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T13:25:50.511214Z"},"content_sha256":"44a517794a919e00251bae1c1fe830a0a4cd68d7f4f2441b60cd9c4a3bb47a8a","schema_version":"1.0","event_id":"sha256:44a517794a919e00251bae1c1fe830a0a4cd68d7f4f2441b60cd9c4a3bb47a8a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:3R73PNY7LPG4QD7SCMCHYXENEZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symbolic Time and Space Tradeoffs for Probabilistic Verification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.LO","authors_text":"Alexander Svozil, Krishnendu Chatterjee, Monika Henzinger, Wolfgang Dvo\\v{r}\\'ak","submitted_at":"2021-04-15T13:53:28Z","abstract_excerpt":"We present a faster symbolic algorithm for the following central problem in probabilistic verification: Compute the maximal end-component (MEC) decomposition of Markov decision processes (MDPs). This problem generalizes the SCC decomposition problem of graphs and closed recurrent sets of Markov chains. The model of symbolic algorithms is widely used in formal verification and model-checking, where access to the input model is restricted to only symbolic operations (e.g., basic set operations and computation of one-step neighborhood). For an input MDP with $n$ vertices and $m$ edges, the classi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.07466","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.07466/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":"2026-07-05T02:32:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qtbz4soNDJ1kx5o32FVBmSB+ahBggfWkMDXvh+dSsIFcN+9lB3DYozzgwnMghQZDQ6doA9LSgRCOfkFo+1Y4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T13:25:50.511839Z"},"content_sha256":"1142b7e3b9c63acd4a1bbd6500125e01715f9d45392544615e31916a23287555","schema_version":"1.0","event_id":"sha256:1142b7e3b9c63acd4a1bbd6500125e01715f9d45392544615e31916a23287555"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3R73PNY7LPG4QD7SCMCHYXENEZ/bundle.json","state_url":"https://pith.science/pith/3R73PNY7LPG4QD7SCMCHYXENEZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3R73PNY7LPG4QD7SCMCHYXENEZ/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":"2026-08-06T13:25:50Z","links":{"resolver":"https://pith.science/pith/3R73PNY7LPG4QD7SCMCHYXENEZ","bundle":"https://pith.science/pith/3R73PNY7LPG4QD7SCMCHYXENEZ/bundle.json","state":"https://pith.science/pith/3R73PNY7LPG4QD7SCMCHYXENEZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3R73PNY7LPG4QD7SCMCHYXENEZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:3R73PNY7LPG4QD7SCMCHYXENEZ","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":"17c9ff0eb9ab02023b938d4afdedf486f104952708414ca1ecfedb5f50f8b4fd","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2021-04-15T13:53:28Z","title_canon_sha256":"99f533fc089a3748de41076edd65141fa39654421b928b5f3293681201c9cbe9"},"schema_version":"1.0","source":{"id":"2104.07466","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.07466","created_at":"2026-07-05T02:32:28Z"},{"alias_kind":"arxiv_version","alias_value":"2104.07466v1","created_at":"2026-07-05T02:32:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.07466","created_at":"2026-07-05T02:32:28Z"},{"alias_kind":"pith_short_12","alias_value":"3R73PNY7LPG4","created_at":"2026-07-05T02:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"3R73PNY7LPG4QD7S","created_at":"2026-07-05T02:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"3R73PNY7","created_at":"2026-07-05T02:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:1142b7e3b9c63acd4a1bbd6500125e01715f9d45392544615e31916a23287555","target":"graph","created_at":"2026-07-05T02:32:28Z","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/2104.07466/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a faster symbolic algorithm for the following central problem in probabilistic verification: Compute the maximal end-component (MEC) decomposition of Markov decision processes (MDPs). This problem generalizes the SCC decomposition problem of graphs and closed recurrent sets of Markov chains. The model of symbolic algorithms is widely used in formal verification and model-checking, where access to the input model is restricted to only symbolic operations (e.g., basic set operations and computation of one-step neighborhood). For an input MDP with $n$ vertices and $m$ edges, the classi","authors_text":"Alexander Svozil, Krishnendu Chatterjee, Monika Henzinger, Wolfgang Dvo\\v{r}\\'ak","cross_cats":["cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2021-04-15T13:53:28Z","title":"Symbolic Time and Space Tradeoffs for Probabilistic Verification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.07466","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":"sha256:44a517794a919e00251bae1c1fe830a0a4cd68d7f4f2441b60cd9c4a3bb47a8a","target":"record","created_at":"2026-07-05T02:32:28Z","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":"17c9ff0eb9ab02023b938d4afdedf486f104952708414ca1ecfedb5f50f8b4fd","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2021-04-15T13:53:28Z","title_canon_sha256":"99f533fc089a3748de41076edd65141fa39654421b928b5f3293681201c9cbe9"},"schema_version":"1.0","source":{"id":"2104.07466","kind":"arxiv","version":1}},"canonical_sha256":"dc7fb7b71f5bcdc80ff213047c5c8d26790bb7e07ae8b22cb59fbe38f98f3cb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc7fb7b71f5bcdc80ff213047c5c8d26790bb7e07ae8b22cb59fbe38f98f3cb9","first_computed_at":"2026-07-05T02:32:28.226996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:32:28.226996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8fKqZ3JKC87QTSWbciPorC8YhaEoSY+QS0YIp6ynjk0iryhCRD0DJK3Y+ML52NU3nbdJI0M44SuO4Zs6hhk/Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T02:32:28.227470Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.07466","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44a517794a919e00251bae1c1fe830a0a4cd68d7f4f2441b60cd9c4a3bb47a8a","sha256:1142b7e3b9c63acd4a1bbd6500125e01715f9d45392544615e31916a23287555"],"state_sha256":"8b397d87f6f0d6583fc28b7c1da9ebe98322d84c735bb8d80d94179cf38a90af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V9iUnSXy5DhBflnGzQ9R6BwEt0NR88+HAqRp3Iu4GLE2L6d4eGfrc6vQatbTwB/7qp2dxEEXcOLaH5d98H4BAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T13:25:50.518060Z","bundle_sha256":"73603842e77c0f4c0d8b873eda70fa8c13284d803d5b38defce17f6617a97824"}}