{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:TXYJS5FWZ7ANNALYJ6SWOPJWP6","short_pith_number":"pith:TXYJS5FW","canonical_record":{"source":{"id":"0712.1765","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2007-12-11T16:50:51Z","cross_cats_sorted":[],"title_canon_sha256":"af87812e1655bf612b7ffc0aaa8d4d48bdb8d89b47acbd4595e0e0a90cad3860","abstract_canon_sha256":"646d4e880a874f295591521dc5784813a8bb622379468d0807a8fe7b1f9ec95f"},"schema_version":"1.0"},"canonical_sha256":"9df09974b6cfc0d681784fa5673d367fbef88d1c15880c0a900fcf0d1fe4bfc3","source":{"kind":"arxiv","id":"0712.1765","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1765","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1765v6","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1765","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"TXYJS5FWZ7AN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"TXYJS5FWZ7ANNALY","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"TXYJS5FW","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:TXYJS5FWZ7ANNALYJ6SWOPJWP6","target":"record","payload":{"canonical_record":{"source":{"id":"0712.1765","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2007-12-11T16:50:51Z","cross_cats_sorted":[],"title_canon_sha256":"af87812e1655bf612b7ffc0aaa8d4d48bdb8d89b47acbd4595e0e0a90cad3860","abstract_canon_sha256":"646d4e880a874f295591521dc5784813a8bb622379468d0807a8fe7b1f9ec95f"},"schema_version":"1.0"},"canonical_sha256":"9df09974b6cfc0d681784fa5673d367fbef88d1c15880c0a900fcf0d1fe4bfc3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:42.573197Z","signature_b64":"3Mf86R/lwB/4kPVcO/DxNarul4bidaJEFSYDbaXXwcwBMa+8CEd8cGfE6k4tgGAx35nppSFuc8pXEgNDsNC3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9df09974b6cfc0d681784fa5673d367fbef88d1c15880c0a900fcf0d1fe4bfc3","last_reissued_at":"2026-05-18T01:37:42.572695Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:42.572695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.1765","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mpQ4Txyh5ig5KjuLRWi6J7qoKGP6C3dm45hpHj5jAAfsOR7wfTH7iT78oPMvyF7nnLYW6nkbve/PC/65GVLMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:53:35.541166Z"},"content_sha256":"2e7a01a186463d5226caad3ab5e1d6d30ea49144a350067454d5b4bbbcd68415","schema_version":"1.0","event_id":"sha256:2e7a01a186463d5226caad3ab5e1d6d30ea49144a350067454d5b4bbbcd68415"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:TXYJS5FWZ7ANNALYJ6SWOPJWP6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving Simple Stochastic Games with Few Random Vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"CWI), Florian Horn (LIAFA, Hugo Gimbert (LaBRI)","submitted_at":"2007-12-11T16:50:51Z","abstract_excerpt":"Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them rely on the existence of optimal permutation strategies, a class of positional strategies derived from permutations of the random vertices. The \"permutation-enumeration\" algorithm performs an exhaustive search among these strategies, while the \"permutation-improvement\" algorithm is based on successive improvements, \\`a la Hoffman-Karp. Our algorithms improve p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1765","kind":"arxiv","version":6},"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":"2026-05-18T01:37:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/bmLfUCBUaQcR0UUIscHutrCOP69ldwcpf/hvq4ENIOxCTbqL8K6bu3Wqon7bhA7lpQkl2bJvLoQl5fQ83toAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:53:35.541517Z"},"content_sha256":"7f176176b6f1d21cb4cef1599a5b7dc1e179d426d02c6ea73dce4f29506a7524","schema_version":"1.0","event_id":"sha256:7f176176b6f1d21cb4cef1599a5b7dc1e179d426d02c6ea73dce4f29506a7524"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TXYJS5FWZ7ANNALYJ6SWOPJWP6/bundle.json","state_url":"https://pith.science/pith/TXYJS5FWZ7ANNALYJ6SWOPJWP6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TXYJS5FWZ7ANNALYJ6SWOPJWP6/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":"2026-05-31T02:53:35Z","links":{"resolver":"https://pith.science/pith/TXYJS5FWZ7ANNALYJ6SWOPJWP6","bundle":"https://pith.science/pith/TXYJS5FWZ7ANNALYJ6SWOPJWP6/bundle.json","state":"https://pith.science/pith/TXYJS5FWZ7ANNALYJ6SWOPJWP6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TXYJS5FWZ7ANNALYJ6SWOPJWP6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:TXYJS5FWZ7ANNALYJ6SWOPJWP6","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":"646d4e880a874f295591521dc5784813a8bb622379468d0807a8fe7b1f9ec95f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2007-12-11T16:50:51Z","title_canon_sha256":"af87812e1655bf612b7ffc0aaa8d4d48bdb8d89b47acbd4595e0e0a90cad3860"},"schema_version":"1.0","source":{"id":"0712.1765","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1765","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1765v6","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1765","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"TXYJS5FWZ7AN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"TXYJS5FWZ7ANNALY","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"TXYJS5FW","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:7f176176b6f1d21cb4cef1599a5b7dc1e179d426d02c6ea73dce4f29506a7524","target":"graph","created_at":"2026-05-18T01:37:42Z","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":"Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them rely on the existence of optimal permutation strategies, a class of positional strategies derived from permutations of the random vertices. The \"permutation-enumeration\" algorithm performs an exhaustive search among these strategies, while the \"permutation-improvement\" algorithm is based on successive improvements, \\`a la Hoffman-Karp. Our algorithms improve p","authors_text":"CWI), Florian Horn (LIAFA, Hugo Gimbert (LaBRI)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2007-12-11T16:50:51Z","title":"Solving Simple Stochastic Games with Few Random Vertices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1765","kind":"arxiv","version":6},"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":"sha256:2e7a01a186463d5226caad3ab5e1d6d30ea49144a350067454d5b4bbbcd68415","target":"record","created_at":"2026-05-18T01:37:42Z","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":"646d4e880a874f295591521dc5784813a8bb622379468d0807a8fe7b1f9ec95f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2007-12-11T16:50:51Z","title_canon_sha256":"af87812e1655bf612b7ffc0aaa8d4d48bdb8d89b47acbd4595e0e0a90cad3860"},"schema_version":"1.0","source":{"id":"0712.1765","kind":"arxiv","version":6}},"canonical_sha256":"9df09974b6cfc0d681784fa5673d367fbef88d1c15880c0a900fcf0d1fe4bfc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9df09974b6cfc0d681784fa5673d367fbef88d1c15880c0a900fcf0d1fe4bfc3","first_computed_at":"2026-05-18T01:37:42.572695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:42.572695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Mf86R/lwB/4kPVcO/DxNarul4bidaJEFSYDbaXXwcwBMa+8CEd8cGfE6k4tgGAx35nppSFuc8pXEgNDsNC3Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:42.573197Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.1765","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e7a01a186463d5226caad3ab5e1d6d30ea49144a350067454d5b4bbbcd68415","sha256:7f176176b6f1d21cb4cef1599a5b7dc1e179d426d02c6ea73dce4f29506a7524"],"state_sha256":"55debbd326dd74f6f0f44f9d2fc0e4e29bf028b7db113dd248ad09420665dcee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tY2sW5eVWfXOmSKn37Lv5D7MB193ktEcJFeXmx4L1YsdUzC7KzLZfr7QcDTvn//emwQZONn7g52hOm3rXplYAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:53:35.543358Z","bundle_sha256":"0e4d39bbbcdb40828a7c73856c73fcb4d8f259886e8413a75117d5a788bf5463"}}