{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KP3RU7BGDNJ5HLM3E3QQQ2JPR4","short_pith_number":"pith:KP3RU7BG","canonical_record":{"source":{"id":"1704.08536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-04-27T12:42:54Z","cross_cats_sorted":[],"title_canon_sha256":"e0d082f992ba2bb1c603ffa946d13eb3234af09065bfa71770fd2749484edd5e","abstract_canon_sha256":"d8de04ff4e56f14c8490fe4112410ae780235fb57a1ae9fafcac51d56191eb6f"},"schema_version":"1.0"},"canonical_sha256":"53f71a7c261b53d3ad9b26e108692f8f0129a6f395a25db89f67fb5ae78c12e7","source":{"kind":"arxiv","id":"1704.08536","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08536","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08536v1","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08536","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"pith_short_12","alias_value":"KP3RU7BGDNJ5","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KP3RU7BGDNJ5HLM3","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KP3RU7BG","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KP3RU7BGDNJ5HLM3E3QQQ2JPR4","target":"record","payload":{"canonical_record":{"source":{"id":"1704.08536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-04-27T12:42:54Z","cross_cats_sorted":[],"title_canon_sha256":"e0d082f992ba2bb1c603ffa946d13eb3234af09065bfa71770fd2749484edd5e","abstract_canon_sha256":"d8de04ff4e56f14c8490fe4112410ae780235fb57a1ae9fafcac51d56191eb6f"},"schema_version":"1.0"},"canonical_sha256":"53f71a7c261b53d3ad9b26e108692f8f0129a6f395a25db89f67fb5ae78c12e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:27.437550Z","signature_b64":"CzISXEuGTteqb3J/cDovIvL0FToAM6rySTL1LgGzAOVzfMMk4hQr1CqViiTzIle1J03DWlcFFeUilKioNjAyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53f71a7c261b53d3ad9b26e108692f8f0129a6f395a25db89f67fb5ae78c12e7","last_reissued_at":"2026-05-18T00:45:27.436899Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:27.436899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.08536","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":"2026-05-18T00:45:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YbUjzkYJICrtBe+bALmU2RdoEB4LFw6a1UavjfMqzYOjCsFzn79OwV6GHo2cyLmoVgstrRcu0+UpD1Yycex5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:02:42.812571Z"},"content_sha256":"a1bfa8f6d47d741e8850aa8a7a12d5a9a3f8d9845b77a081aa81db932daa3034","schema_version":"1.0","event_id":"sha256:a1bfa8f6d47d741e8850aa8a7a12d5a9a3f8d9845b77a081aa81db932daa3034"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KP3RU7BGDNJ5HLM3E3QQQ2JPR4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Parameterized Complexity of Positional Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Abdallah Saffidine, Antonin Lambilliotte, \\'Edouard Bonnet, Serge Gaspers, Stefan R\\\"ummele","submitted_at":"2017-04-27T12:42:54Z","abstract_excerpt":"We study the parameterized complexity of several positional games. Our main result is that Short Generalized Hex is W[1]-complete parameterized by the number of moves. This solves an open problem from Downey and Fellows' influential list of open problems from 1999. Previously, the problem was thought of as a natural candidate for AW[*]-completeness. Our main tool is a new fragment of first-order logic where universally quantified variables only occur in inequalities. We show that model-checking on arbitrary relational structures for a formula in this fragment is W[1]-complete when parameterize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08536","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":"2026-05-18T00:45:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XFuu5oNK69XHA50KjdWmERBDWGCWjTsHrOP08FK6erW0F8JuejaN955ZaSSkSFebSLyVAETdkxNqi7tNB5u2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:02:42.812911Z"},"content_sha256":"9966dbd03350439206f6a38ad3404a71b74edb737107dcdea162ec37f49946c2","schema_version":"1.0","event_id":"sha256:9966dbd03350439206f6a38ad3404a71b74edb737107dcdea162ec37f49946c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KP3RU7BGDNJ5HLM3E3QQQ2JPR4/bundle.json","state_url":"https://pith.science/pith/KP3RU7BGDNJ5HLM3E3QQQ2JPR4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KP3RU7BGDNJ5HLM3E3QQQ2JPR4/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":"2026-06-05T15:02:42Z","links":{"resolver":"https://pith.science/pith/KP3RU7BGDNJ5HLM3E3QQQ2JPR4","bundle":"https://pith.science/pith/KP3RU7BGDNJ5HLM3E3QQQ2JPR4/bundle.json","state":"https://pith.science/pith/KP3RU7BGDNJ5HLM3E3QQQ2JPR4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KP3RU7BGDNJ5HLM3E3QQQ2JPR4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KP3RU7BGDNJ5HLM3E3QQQ2JPR4","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":"d8de04ff4e56f14c8490fe4112410ae780235fb57a1ae9fafcac51d56191eb6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-04-27T12:42:54Z","title_canon_sha256":"e0d082f992ba2bb1c603ffa946d13eb3234af09065bfa71770fd2749484edd5e"},"schema_version":"1.0","source":{"id":"1704.08536","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08536","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08536v1","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08536","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"pith_short_12","alias_value":"KP3RU7BGDNJ5","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KP3RU7BGDNJ5HLM3","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KP3RU7BG","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:9966dbd03350439206f6a38ad3404a71b74edb737107dcdea162ec37f49946c2","target":"graph","created_at":"2026-05-18T00:45:27Z","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":"We study the parameterized complexity of several positional games. Our main result is that Short Generalized Hex is W[1]-complete parameterized by the number of moves. This solves an open problem from Downey and Fellows' influential list of open problems from 1999. Previously, the problem was thought of as a natural candidate for AW[*]-completeness. Our main tool is a new fragment of first-order logic where universally quantified variables only occur in inequalities. We show that model-checking on arbitrary relational structures for a formula in this fragment is W[1]-complete when parameterize","authors_text":"Abdallah Saffidine, Antonin Lambilliotte, \\'Edouard Bonnet, Serge Gaspers, Stefan R\\\"ummele","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-04-27T12:42:54Z","title":"The Parameterized Complexity of Positional Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08536","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:a1bfa8f6d47d741e8850aa8a7a12d5a9a3f8d9845b77a081aa81db932daa3034","target":"record","created_at":"2026-05-18T00:45:27Z","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":"d8de04ff4e56f14c8490fe4112410ae780235fb57a1ae9fafcac51d56191eb6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-04-27T12:42:54Z","title_canon_sha256":"e0d082f992ba2bb1c603ffa946d13eb3234af09065bfa71770fd2749484edd5e"},"schema_version":"1.0","source":{"id":"1704.08536","kind":"arxiv","version":1}},"canonical_sha256":"53f71a7c261b53d3ad9b26e108692f8f0129a6f395a25db89f67fb5ae78c12e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53f71a7c261b53d3ad9b26e108692f8f0129a6f395a25db89f67fb5ae78c12e7","first_computed_at":"2026-05-18T00:45:27.436899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:27.436899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CzISXEuGTteqb3J/cDovIvL0FToAM6rySTL1LgGzAOVzfMMk4hQr1CqViiTzIle1J03DWlcFFeUilKioNjAyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:27.437550Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.08536","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1bfa8f6d47d741e8850aa8a7a12d5a9a3f8d9845b77a081aa81db932daa3034","sha256:9966dbd03350439206f6a38ad3404a71b74edb737107dcdea162ec37f49946c2"],"state_sha256":"b2ead3cef94fcaf9a8ceeb2c01d8dbf98005aa4d9402b930ba071b87c2562951"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SdNtX++Qq8us2CuAEHxRpxPNPUMDy8crlQjMY8zqZ8FzthBmNyG6FQkKwIay2gmjzIIaQfa+hL10373qQa2LDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T15:02:42.815105Z","bundle_sha256":"c0dc805fcaf981fd4819590bcc397dd81c7bd49e56fdea6e41953d2149306127"}}