{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:P2ORHOOYZAYHWGZV452H7U2RIG","short_pith_number":"pith:P2ORHOOY","canonical_record":{"source":{"id":"1407.2149","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-07-08T16:06:49Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"fc36d840c98508b412879a9908fda29e07bd110312fee0beecfcfadda3957650","abstract_canon_sha256":"32643e96e8de4dd3520a6a90ef293fb57f70053c20f1dadbeea4c94fa9c36905"},"schema_version":"1.0"},"canonical_sha256":"7e9d13b9d8c8307b1b35e7747fd3514188b98b69815aaba269348504432233ec","source":{"kind":"arxiv","id":"1407.2149","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2149","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2149v3","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2149","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"pith_short_12","alias_value":"P2ORHOOYZAYH","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"P2ORHOOYZAYHWGZV","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"P2ORHOOY","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:P2ORHOOYZAYHWGZV452H7U2RIG","target":"record","payload":{"canonical_record":{"source":{"id":"1407.2149","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-07-08T16:06:49Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"fc36d840c98508b412879a9908fda29e07bd110312fee0beecfcfadda3957650","abstract_canon_sha256":"32643e96e8de4dd3520a6a90ef293fb57f70053c20f1dadbeea4c94fa9c36905"},"schema_version":"1.0"},"canonical_sha256":"7e9d13b9d8c8307b1b35e7747fd3514188b98b69815aaba269348504432233ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:24.349506Z","signature_b64":"ElHuBXLdR//KsDgtGEUF1pyzvrQLvYydahrzIsBVr2ty85CkpVnjI3TmcNEV43ySu56jFqHFQuXUEJc1F5zEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e9d13b9d8c8307b1b35e7747fd3514188b98b69815aaba269348504432233ec","last_reissued_at":"2026-05-18T02:05:24.348960Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:24.348960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.2149","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:05:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"npoG/DuqpkgMQM02brkXT0KhQPUIbiqUWHFwqNEa6ZZE0YRBAnij/XmJTeXqn+1w5e3BIWclcyE3qBZ79cYEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:24:03.736921Z"},"content_sha256":"8287442ce6aa55bb7e0906b8d3b01ffe9f9316b3c2760351864b9a263b5f7aad","schema_version":"1.0","event_id":"sha256:8287442ce6aa55bb7e0906b8d3b01ffe9f9316b3c2760351864b9a263b5f7aad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:P2ORHOOYZAYHWGZV452H7U2RIG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strategy Derivation for Small Progress Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.LO","authors_text":"Maciej Gazda, Tim A.C. Willemse","submitted_at":"2014-07-08T16:06:49Z","abstract_excerpt":"Small Progress Measures is one of the most efficient parity game solving algorithms. The original algorithm provides the full solution (winning regions and strategies) in $O(dm \\cdot (n/\\lceil d / 2 \\rceil)^{\\lceil d/2 \\rceil})$ time, and requires a re-run of the algorithm on one of the winning regions. We provide a novel operational interpretation of progress measures, and modify the algorithm so that it derives the winning strategies for both players in one pass. This reduces the upper bound on strategy derivation for SPM to $O(dm \\cdot (n/\\lfloor d / 2 \\rfloor)^{\\lfloor d/2 \\rfloor})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2149","kind":"arxiv","version":3},"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":"2026-05-18T02:05:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KwFT5mcxMM0HoMuBzEgIwLe8pAbHGSHLcTSJxVOxwY1FMKeDGvYw+f+/uAd2BlV3FFkGUusfrJnwe39KD84DAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:24:03.737569Z"},"content_sha256":"217484ac776cdb2efeeb34c634d4fdceb363a61f7873f55a8d630f91795b130d","schema_version":"1.0","event_id":"sha256:217484ac776cdb2efeeb34c634d4fdceb363a61f7873f55a8d630f91795b130d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P2ORHOOYZAYHWGZV452H7U2RIG/bundle.json","state_url":"https://pith.science/pith/P2ORHOOYZAYHWGZV452H7U2RIG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P2ORHOOYZAYHWGZV452H7U2RIG/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":"2026-06-06T19:24:03Z","links":{"resolver":"https://pith.science/pith/P2ORHOOYZAYHWGZV452H7U2RIG","bundle":"https://pith.science/pith/P2ORHOOYZAYHWGZV452H7U2RIG/bundle.json","state":"https://pith.science/pith/P2ORHOOYZAYHWGZV452H7U2RIG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P2ORHOOYZAYHWGZV452H7U2RIG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:P2ORHOOYZAYHWGZV452H7U2RIG","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":"32643e96e8de4dd3520a6a90ef293fb57f70053c20f1dadbeea4c94fa9c36905","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-07-08T16:06:49Z","title_canon_sha256":"fc36d840c98508b412879a9908fda29e07bd110312fee0beecfcfadda3957650"},"schema_version":"1.0","source":{"id":"1407.2149","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2149","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2149v3","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2149","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"pith_short_12","alias_value":"P2ORHOOYZAYH","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"P2ORHOOYZAYHWGZV","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"P2ORHOOY","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:217484ac776cdb2efeeb34c634d4fdceb363a61f7873f55a8d630f91795b130d","target":"graph","created_at":"2026-05-18T02:05:24Z","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":"Small Progress Measures is one of the most efficient parity game solving algorithms. The original algorithm provides the full solution (winning regions and strategies) in $O(dm \\cdot (n/\\lceil d / 2 \\rceil)^{\\lceil d/2 \\rceil})$ time, and requires a re-run of the algorithm on one of the winning regions. We provide a novel operational interpretation of progress measures, and modify the algorithm so that it derives the winning strategies for both players in one pass. This reduces the upper bound on strategy derivation for SPM to $O(dm \\cdot (n/\\lfloor d / 2 \\rfloor)^{\\lfloor d/2 \\rfloor})$.","authors_text":"Maciej Gazda, Tim A.C. Willemse","cross_cats":["cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-07-08T16:06:49Z","title":"Strategy Derivation for Small Progress Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2149","kind":"arxiv","version":3},"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":"sha256:8287442ce6aa55bb7e0906b8d3b01ffe9f9316b3c2760351864b9a263b5f7aad","target":"record","created_at":"2026-05-18T02:05:24Z","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":"32643e96e8de4dd3520a6a90ef293fb57f70053c20f1dadbeea4c94fa9c36905","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-07-08T16:06:49Z","title_canon_sha256":"fc36d840c98508b412879a9908fda29e07bd110312fee0beecfcfadda3957650"},"schema_version":"1.0","source":{"id":"1407.2149","kind":"arxiv","version":3}},"canonical_sha256":"7e9d13b9d8c8307b1b35e7747fd3514188b98b69815aaba269348504432233ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e9d13b9d8c8307b1b35e7747fd3514188b98b69815aaba269348504432233ec","first_computed_at":"2026-05-18T02:05:24.348960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:24.348960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ElHuBXLdR//KsDgtGEUF1pyzvrQLvYydahrzIsBVr2ty85CkpVnjI3TmcNEV43ySu56jFqHFQuXUEJc1F5zEBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:24.349506Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2149","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8287442ce6aa55bb7e0906b8d3b01ffe9f9316b3c2760351864b9a263b5f7aad","sha256:217484ac776cdb2efeeb34c634d4fdceb363a61f7873f55a8d630f91795b130d"],"state_sha256":"f6bbc275205b7cc3c834272775a200bb6167559b38ff6272519a3d568142a660"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"30kNzbFgtEM/ZnaLVGppM1ebKtOgog+D3mMoGYwp+hsWbUJXZX3akNJObRd6VCraCqbearJRb9dENoHxcY3wBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:24:03.740631Z","bundle_sha256":"a87f37295021a52e59039bf0c125418ccfb43ac5ec91bd83078dca64c1e4bb34"}}