{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IKPSQSTHFXO3HE2S5DLBJMX2ES","short_pith_number":"pith:IKPSQSTH","canonical_record":{"source":{"id":"1208.1640","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2012-08-08T11:04:55Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"b4be8746c0881c813ea60667dfe1212a1a54dfe0923fd2d9c64c0a56a5a19c4e","abstract_canon_sha256":"48cfb5180d839e855896e4fddd23f966b50b1dc026f245e4e72ff3bbc0154c38"},"schema_version":"1.0"},"canonical_sha256":"429f284a672dddb39352e8d614b2fa24a6dc2455808d88f2b37e906eb9dc63fb","source":{"kind":"arxiv","id":"1208.1640","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1640","created_at":"2026-05-18T02:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1640v1","created_at":"2026-05-18T02:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1640","created_at":"2026-05-18T02:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"IKPSQSTHFXO3","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IKPSQSTHFXO3HE2S","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IKPSQSTH","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IKPSQSTHFXO3HE2S5DLBJMX2ES","target":"record","payload":{"canonical_record":{"source":{"id":"1208.1640","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2012-08-08T11:04:55Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"b4be8746c0881c813ea60667dfe1212a1a54dfe0923fd2d9c64c0a56a5a19c4e","abstract_canon_sha256":"48cfb5180d839e855896e4fddd23f966b50b1dc026f245e4e72ff3bbc0154c38"},"schema_version":"1.0"},"canonical_sha256":"429f284a672dddb39352e8d614b2fa24a6dc2455808d88f2b37e906eb9dc63fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:01.415511Z","signature_b64":"ZWwtZ8tr09Bohl6E7/bf9rfn6zjcF4LR+q9GziLYbXyn5Ay9afEuPIfn9crsxujsHg644CXfJizo8TZ5j1fcAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"429f284a672dddb39352e8d614b2fa24a6dc2455808d88f2b37e906eb9dc63fb","last_reissued_at":"2026-05-18T02:21:01.414958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:01.414958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.1640","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":"2026-05-18T02:21:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MwBfO/MNOwqh3S5unaEA4BEUhHURXEydImnbxJoMMMKw5qSv5Q50KHcI6S3Rh94FnDdIIWgm8mWdKLuNmKKcDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:27:51.836220Z"},"content_sha256":"90e526f8d446432244dc4a4fadc9caedbc3f22eaf2ad3c1f7434d3c9726a950d","schema_version":"1.0","event_id":"sha256:90e526f8d446432244dc4a4fadc9caedbc3f22eaf2ad3c1f7434d3c9726a950d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IKPSQSTHFXO3HE2S5DLBJMX2ES","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graph Operations on Parity Games and Polynomial-Time Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.GT","authors_text":"Alexandru I. Tomescu, Christoph Dittmann, Stephan Kreutzer","submitted_at":"2012-08-08T11:04:55Z","abstract_excerpt":"Parity games are games that are played on directed graphs whose vertices are labeled by natural numbers, called priorities. The players push a token along the edges of the digraph. The winner is determined by the parity of the greatest priority occurring infinitely often in this infinite play.\n  A motivation for studying parity games comes from the area of formal verification of systems by model checking. Deciding the winner in a parity game is polynomial time equivalent to the model checking problem of the modal mu-calculus. Another strong motivation lies in the fact that the exact complexity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1640","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":"2026-05-18T02:21:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4CYo5n9KVI353FV/76JISnw3X2IxZ0KeQ/Uduz3nzAkJmHTfvJtHrlWiL+Wql3gc3wdZ6m0jUXmqU9v6Z7zlBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:27:51.836866Z"},"content_sha256":"b168e0f143cc0390386724a87e19f1762c21c791da051c57ad64b1b0f7dfab16","schema_version":"1.0","event_id":"sha256:b168e0f143cc0390386724a87e19f1762c21c791da051c57ad64b1b0f7dfab16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IKPSQSTHFXO3HE2S5DLBJMX2ES/bundle.json","state_url":"https://pith.science/pith/IKPSQSTHFXO3HE2S5DLBJMX2ES/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IKPSQSTHFXO3HE2S5DLBJMX2ES/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":"2026-05-31T14:27:51Z","links":{"resolver":"https://pith.science/pith/IKPSQSTHFXO3HE2S5DLBJMX2ES","bundle":"https://pith.science/pith/IKPSQSTHFXO3HE2S5DLBJMX2ES/bundle.json","state":"https://pith.science/pith/IKPSQSTHFXO3HE2S5DLBJMX2ES/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IKPSQSTHFXO3HE2S5DLBJMX2ES/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IKPSQSTHFXO3HE2S5DLBJMX2ES","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":"48cfb5180d839e855896e4fddd23f966b50b1dc026f245e4e72ff3bbc0154c38","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2012-08-08T11:04:55Z","title_canon_sha256":"b4be8746c0881c813ea60667dfe1212a1a54dfe0923fd2d9c64c0a56a5a19c4e"},"schema_version":"1.0","source":{"id":"1208.1640","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1640","created_at":"2026-05-18T02:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1640v1","created_at":"2026-05-18T02:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1640","created_at":"2026-05-18T02:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"IKPSQSTHFXO3","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IKPSQSTHFXO3HE2S","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IKPSQSTH","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:b168e0f143cc0390386724a87e19f1762c21c791da051c57ad64b1b0f7dfab16","target":"graph","created_at":"2026-05-18T02:21:01Z","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":"Parity games are games that are played on directed graphs whose vertices are labeled by natural numbers, called priorities. The players push a token along the edges of the digraph. The winner is determined by the parity of the greatest priority occurring infinitely often in this infinite play.\n  A motivation for studying parity games comes from the area of formal verification of systems by model checking. Deciding the winner in a parity game is polynomial time equivalent to the model checking problem of the modal mu-calculus. Another strong motivation lies in the fact that the exact complexity","authors_text":"Alexandru I. Tomescu, Christoph Dittmann, Stephan Kreutzer","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2012-08-08T11:04:55Z","title":"Graph Operations on Parity Games and Polynomial-Time Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1640","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":"sha256:90e526f8d446432244dc4a4fadc9caedbc3f22eaf2ad3c1f7434d3c9726a950d","target":"record","created_at":"2026-05-18T02:21:01Z","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":"48cfb5180d839e855896e4fddd23f966b50b1dc026f245e4e72ff3bbc0154c38","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2012-08-08T11:04:55Z","title_canon_sha256":"b4be8746c0881c813ea60667dfe1212a1a54dfe0923fd2d9c64c0a56a5a19c4e"},"schema_version":"1.0","source":{"id":"1208.1640","kind":"arxiv","version":1}},"canonical_sha256":"429f284a672dddb39352e8d614b2fa24a6dc2455808d88f2b37e906eb9dc63fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"429f284a672dddb39352e8d614b2fa24a6dc2455808d88f2b37e906eb9dc63fb","first_computed_at":"2026-05-18T02:21:01.414958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:01.414958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZWwtZ8tr09Bohl6E7/bf9rfn6zjcF4LR+q9GziLYbXyn5Ay9afEuPIfn9crsxujsHg644CXfJizo8TZ5j1fcAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:01.415511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1640","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90e526f8d446432244dc4a4fadc9caedbc3f22eaf2ad3c1f7434d3c9726a950d","sha256:b168e0f143cc0390386724a87e19f1762c21c791da051c57ad64b1b0f7dfab16"],"state_sha256":"d5c7d327617eef5e76ef3a3738b50ca8559f0f8a9b55c3ecd8fdde17cd82de7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iAOoHBJXQeHagdGGkk2nI0QcJsq+3NjfEmVUrxkESYEfaj91MoPCduGjNpo1QNJNucqimYCkqMU3pQLEDXWuDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:27:51.840164Z","bundle_sha256":"576b8ef28da2434e04b44630b2de20c8c3537b97a1c001742fb3dab6d16c78c1"}}