{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BDIHCBHDFADRSOJDWZ5WVSNC5N","short_pith_number":"pith:BDIHCBHD","canonical_record":{"source":{"id":"1410.0833","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-03T12:24:33Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"d4146de0b04a2f093ddbfd072b934479d44b4e0430f19eb6828c6add744de9f5","abstract_canon_sha256":"4e19c77dc43faac9fa9212f6d4017161c89e10c6b1540c8e3ba3eab6cc1a5467"},"schema_version":"1.0"},"canonical_sha256":"08d07104e32807193923b67b6ac9a2eb442c45865245eee1f582bc0a6824ad64","source":{"kind":"arxiv","id":"1410.0833","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0833","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0833v4","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0833","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"pith_short_12","alias_value":"BDIHCBHDFADR","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BDIHCBHDFADRSOJD","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BDIHCBHD","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BDIHCBHDFADRSOJDWZ5WVSNC5N","target":"record","payload":{"canonical_record":{"source":{"id":"1410.0833","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-03T12:24:33Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"d4146de0b04a2f093ddbfd072b934479d44b4e0430f19eb6828c6add744de9f5","abstract_canon_sha256":"4e19c77dc43faac9fa9212f6d4017161c89e10c6b1540c8e3ba3eab6cc1a5467"},"schema_version":"1.0"},"canonical_sha256":"08d07104e32807193923b67b6ac9a2eb442c45865245eee1f582bc0a6824ad64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:23.996129Z","signature_b64":"A7JF8+fXetbEnnTsxQQnT1A4NhJ/lY7PUaocOBIoqGORpGTg4mFNS7oLXZl0SkGeMbz7cdWCuwVfq+U5H/dUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08d07104e32807193923b67b6ac9a2eb442c45865245eee1f582bc0a6824ad64","last_reissued_at":"2026-05-17T23:51:23.995543Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:23.995543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.0833","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"00YtIMhTkM8vE3DNgpq4yn5oWpW6iHu6RKZryMZnFb64Pd9RXjxuF58cnP5uKeTgLvGiM/5hNlEx7Kx3jLBpAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:19:18.108373Z"},"content_sha256":"8eea83463df14d5187a90dc42d57e6f4a3745e18d71780f6faf4123c6eb263dc","schema_version":"1.0","event_id":"sha256:8eea83463df14d5187a90dc42d57e6f4a3745e18d71780f6faf4123c6eb263dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BDIHCBHDFADRSOJDWZ5WVSNC5N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved Algorithms for Parity and Streett objectives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.DS","authors_text":"Krishnendu Chatterjee, Monika Henzinger, Veronika Loitzenbauer","submitted_at":"2014-10-03T12:24:33Z","abstract_excerpt":"The computation of the winning set for parity objectives and for Streett objectives in graphs as well as in game graphs are central problems in computer-aided verification, with application to the verification of closed systems with strong fairness conditions, the verification of open systems, checking interface compatibility, well-formedness of specifications, and the synthesis of reactive systems. We show how to compute the winning set on $n$ vertices for (1) parity-3 (aka one-pair Streett) objectives in game graphs in time $O(n^{5/2})$ and for (2) k-pair Streett objectives in graphs in time"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0833","kind":"arxiv","version":4},"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":"2026-05-17T23:51:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dnp5AbcswAK7W7L3/klgtjEE3hTLBWnMqMWpLBp3vWVWJ6/cIHePcOndm8ngauBBRfxFNpgJLFfEY/Dx5foMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:19:18.108991Z"},"content_sha256":"231291dfe101c1b3b3e6dc763324ea9591e9ae1ffdee373e34372494ca1d3e1f","schema_version":"1.0","event_id":"sha256:231291dfe101c1b3b3e6dc763324ea9591e9ae1ffdee373e34372494ca1d3e1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDIHCBHDFADRSOJDWZ5WVSNC5N/bundle.json","state_url":"https://pith.science/pith/BDIHCBHDFADRSOJDWZ5WVSNC5N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDIHCBHDFADRSOJDWZ5WVSNC5N/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":"2026-05-25T18:19:18Z","links":{"resolver":"https://pith.science/pith/BDIHCBHDFADRSOJDWZ5WVSNC5N","bundle":"https://pith.science/pith/BDIHCBHDFADRSOJDWZ5WVSNC5N/bundle.json","state":"https://pith.science/pith/BDIHCBHDFADRSOJDWZ5WVSNC5N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDIHCBHDFADRSOJDWZ5WVSNC5N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BDIHCBHDFADRSOJDWZ5WVSNC5N","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":"4e19c77dc43faac9fa9212f6d4017161c89e10c6b1540c8e3ba3eab6cc1a5467","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-03T12:24:33Z","title_canon_sha256":"d4146de0b04a2f093ddbfd072b934479d44b4e0430f19eb6828c6add744de9f5"},"schema_version":"1.0","source":{"id":"1410.0833","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0833","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0833v4","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0833","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"pith_short_12","alias_value":"BDIHCBHDFADR","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BDIHCBHDFADRSOJD","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BDIHCBHD","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:231291dfe101c1b3b3e6dc763324ea9591e9ae1ffdee373e34372494ca1d3e1f","target":"graph","created_at":"2026-05-17T23:51:23Z","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":"The computation of the winning set for parity objectives and for Streett objectives in graphs as well as in game graphs are central problems in computer-aided verification, with application to the verification of closed systems with strong fairness conditions, the verification of open systems, checking interface compatibility, well-formedness of specifications, and the synthesis of reactive systems. We show how to compute the winning set on $n$ vertices for (1) parity-3 (aka one-pair Streett) objectives in game graphs in time $O(n^{5/2})$ and for (2) k-pair Streett objectives in graphs in time","authors_text":"Krishnendu Chatterjee, Monika Henzinger, Veronika Loitzenbauer","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-03T12:24:33Z","title":"Improved Algorithms for Parity and Streett objectives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0833","kind":"arxiv","version":4},"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":"sha256:8eea83463df14d5187a90dc42d57e6f4a3745e18d71780f6faf4123c6eb263dc","target":"record","created_at":"2026-05-17T23:51:23Z","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":"4e19c77dc43faac9fa9212f6d4017161c89e10c6b1540c8e3ba3eab6cc1a5467","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-03T12:24:33Z","title_canon_sha256":"d4146de0b04a2f093ddbfd072b934479d44b4e0430f19eb6828c6add744de9f5"},"schema_version":"1.0","source":{"id":"1410.0833","kind":"arxiv","version":4}},"canonical_sha256":"08d07104e32807193923b67b6ac9a2eb442c45865245eee1f582bc0a6824ad64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08d07104e32807193923b67b6ac9a2eb442c45865245eee1f582bc0a6824ad64","first_computed_at":"2026-05-17T23:51:23.995543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:23.995543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A7JF8+fXetbEnnTsxQQnT1A4NhJ/lY7PUaocOBIoqGORpGTg4mFNS7oLXZl0SkGeMbz7cdWCuwVfq+U5H/dUBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:23.996129Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0833","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8eea83463df14d5187a90dc42d57e6f4a3745e18d71780f6faf4123c6eb263dc","sha256:231291dfe101c1b3b3e6dc763324ea9591e9ae1ffdee373e34372494ca1d3e1f"],"state_sha256":"90c2575dd3fd70c203647a971ae6164c979bbd8ce0c3487829c48d607d6b9292"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QAFAfIpR0D+bSn7AN/YHMQoWxeQcx9JL/zbuxMf0pWAZ5uees7NhsNhUhUq3F5UPM3me4TFdeZYS1oSHLP5UDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:19:18.112466Z","bundle_sha256":"cfe18f800308955c2d0e9c9d6db93e9b23a0826d7fee0661a9273e04801aae81"}}