{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2W77COE7UOHI2HYXE4D44VHRY4","short_pith_number":"pith:2W77COE7","canonical_record":{"source":{"id":"1506.01431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-03T23:17:45Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"06e1c18a15e111f96c226a94d7013b25c95c29c84aa0b4390d4f916e160321f0","abstract_canon_sha256":"6ebcdb1ec951e50b34647e5891ded20bf38ca78869892d6ff107787e4a3d8f34"},"schema_version":"1.0"},"canonical_sha256":"d5bff1389fa38e8d1f172707ce54f1c7219fededf1701c44d4f34554ccb2906f","source":{"kind":"arxiv","id":"1506.01431","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01431","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01431v1","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01431","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"pith_short_12","alias_value":"2W77COE7UOHI","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2W77COE7UOHI2HYX","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2W77COE7","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2W77COE7UOHI2HYXE4D44VHRY4","target":"record","payload":{"canonical_record":{"source":{"id":"1506.01431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-03T23:17:45Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"06e1c18a15e111f96c226a94d7013b25c95c29c84aa0b4390d4f916e160321f0","abstract_canon_sha256":"6ebcdb1ec951e50b34647e5891ded20bf38ca78869892d6ff107787e4a3d8f34"},"schema_version":"1.0"},"canonical_sha256":"d5bff1389fa38e8d1f172707ce54f1c7219fededf1701c44d4f34554ccb2906f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:41.423291Z","signature_b64":"EEC0R5riY5WlahWeLoWEbFj0SwYk3WFVfS09hxHYql4gErRoPBZ5DWouOEeNu0+fnPOEC4kwX+a1EPhoeIbMBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5bff1389fa38e8d1f172707ce54f1c7219fededf1701c44d4f34554ccb2906f","last_reissued_at":"2026-05-18T01:57:41.422587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:41.422587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.01431","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":"2026-05-18T01:57:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YWb7kZmGl+v8Ak62eOF6aH1osJ5bRZ7HZrLCf6fvT7FqeManHN3NX5a9GEUmB9RgeBThUOt2WqKbKlPjQWMvCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:56:05.302311Z"},"content_sha256":"681898907f9a1445dfe0abea565fe9cb0ee0e24bb7f0e91d90e8c2bb86419954","schema_version":"1.0","event_id":"sha256:681898907f9a1445dfe0abea565fe9cb0ee0e24bb7f0e91d90e8c2bb86419954"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2W77COE7UOHI2HYXE4D44VHRY4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Cellular Automaton for Blocking Queen Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CO","authors_text":"Matthew Cook, Turlough Neary, Urban Larsson","submitted_at":"2015-06-03T23:17:45Z","abstract_excerpt":"We show that the winning positions of a certain type of two-player game form interesting patterns which often defy analysis, yet can be computed by a cellular automaton. The game, known as {\\em Blocking Wythoff Nim}, consists of moving a queen as in chess, but always towards (0,0), and it may not be moved to any of $k-1$ temporarily \"blocked\" positions specified on the previous turn by the other player. The game ends when a player wins by blocking all possible moves of the other player. The value of $k$ is a parameter that defines the game, and the pattern of winning positions can be very sens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01431","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":"2026-05-18T01:57:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fzj9IoxkLMVGHA/T9sfiWlvVimf4dtwxsVvLvOYpRyG7b8+TfgxGK6vLdpNAcQedVfj9PXfMbneTMq8wvBh0CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:56:05.302680Z"},"content_sha256":"2d11a9322d134ea47d6b13e4b2db07d96fe16e93874b7a76433a793f27faa9d1","schema_version":"1.0","event_id":"sha256:2d11a9322d134ea47d6b13e4b2db07d96fe16e93874b7a76433a793f27faa9d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2W77COE7UOHI2HYXE4D44VHRY4/bundle.json","state_url":"https://pith.science/pith/2W77COE7UOHI2HYXE4D44VHRY4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2W77COE7UOHI2HYXE4D44VHRY4/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":"2026-06-24T07:56:05Z","links":{"resolver":"https://pith.science/pith/2W77COE7UOHI2HYXE4D44VHRY4","bundle":"https://pith.science/pith/2W77COE7UOHI2HYXE4D44VHRY4/bundle.json","state":"https://pith.science/pith/2W77COE7UOHI2HYXE4D44VHRY4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2W77COE7UOHI2HYXE4D44VHRY4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2W77COE7UOHI2HYXE4D44VHRY4","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":"6ebcdb1ec951e50b34647e5891ded20bf38ca78869892d6ff107787e4a3d8f34","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-03T23:17:45Z","title_canon_sha256":"06e1c18a15e111f96c226a94d7013b25c95c29c84aa0b4390d4f916e160321f0"},"schema_version":"1.0","source":{"id":"1506.01431","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01431","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01431v1","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01431","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"pith_short_12","alias_value":"2W77COE7UOHI","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2W77COE7UOHI2HYX","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2W77COE7","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:2d11a9322d134ea47d6b13e4b2db07d96fe16e93874b7a76433a793f27faa9d1","target":"graph","created_at":"2026-05-18T01:57:41Z","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 show that the winning positions of a certain type of two-player game form interesting patterns which often defy analysis, yet can be computed by a cellular automaton. The game, known as {\\em Blocking Wythoff Nim}, consists of moving a queen as in chess, but always towards (0,0), and it may not be moved to any of $k-1$ temporarily \"blocked\" positions specified on the previous turn by the other player. The game ends when a player wins by blocking all possible moves of the other player. The value of $k$ is a parameter that defines the game, and the pattern of winning positions can be very sens","authors_text":"Matthew Cook, Turlough Neary, Urban Larsson","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-03T23:17:45Z","title":"A Cellular Automaton for Blocking Queen Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01431","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":"sha256:681898907f9a1445dfe0abea565fe9cb0ee0e24bb7f0e91d90e8c2bb86419954","target":"record","created_at":"2026-05-18T01:57:41Z","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":"6ebcdb1ec951e50b34647e5891ded20bf38ca78869892d6ff107787e4a3d8f34","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-03T23:17:45Z","title_canon_sha256":"06e1c18a15e111f96c226a94d7013b25c95c29c84aa0b4390d4f916e160321f0"},"schema_version":"1.0","source":{"id":"1506.01431","kind":"arxiv","version":1}},"canonical_sha256":"d5bff1389fa38e8d1f172707ce54f1c7219fededf1701c44d4f34554ccb2906f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5bff1389fa38e8d1f172707ce54f1c7219fededf1701c44d4f34554ccb2906f","first_computed_at":"2026-05-18T01:57:41.422587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:41.422587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EEC0R5riY5WlahWeLoWEbFj0SwYk3WFVfS09hxHYql4gErRoPBZ5DWouOEeNu0+fnPOEC4kwX+a1EPhoeIbMBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:41.423291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01431","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:681898907f9a1445dfe0abea565fe9cb0ee0e24bb7f0e91d90e8c2bb86419954","sha256:2d11a9322d134ea47d6b13e4b2db07d96fe16e93874b7a76433a793f27faa9d1"],"state_sha256":"c987cfe4bf04634f7176e2afed5cea863602c6d4f5531a4e50cba19b1b634574"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3AKpN3RXMszdYibHVP2iq927f8bKSqLKeKqhdtxgrHJE/prXgHCK88s527kxstsD7TOMZ0Qt7kZD7MTHFfiMBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T07:56:05.304946Z","bundle_sha256":"28eed454d69a177303e70954d40fc80101d5fa52616fe450042cf9a87b83896c"}}