{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:APSDC7AJRSR563HHXCXKTBEMKK","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":"30627b2a0c072033229d015a6b237555db6ed4f5222cdf148af5e70eb6111b38","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-26T21:46:35Z","title_canon_sha256":"cae4325e5ee3baadbbd34c839c999e4abc812626247905320145d473175c966e"},"schema_version":"1.0","source":{"id":"1105.5413","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5413","created_at":"2026-05-18T04:21:11Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5413v1","created_at":"2026-05-18T04:21:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5413","created_at":"2026-05-18T04:21:11Z"},{"alias_kind":"pith_short_12","alias_value":"APSDC7AJRSR5","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"APSDC7AJRSR563HH","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"APSDC7AJ","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:5e6fb371efe597d18e6719775d70d5fac6133972fedf94a9dacb29d8e9b134b5","target":"graph","created_at":"2026-05-18T04:21:11Z","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":"This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a given position is a winning position, and to find a move to a winning position, if not; and (ii) to decide whether two given positions are congruent, in the sense of mis\\`ere quotient theory. The methods are based on the theory of short rational generating functions.","authors_text":"Alan Guo, Ezra Miller","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-26T21:46:35Z","title":"Algorithms for lattice games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5413","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:aea56cbb47f18ff5dbb1f1584ef0cb114a5b4fcd1ab3ea5d8514add519ce10ef","target":"record","created_at":"2026-05-18T04:21:11Z","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":"30627b2a0c072033229d015a6b237555db6ed4f5222cdf148af5e70eb6111b38","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-26T21:46:35Z","title_canon_sha256":"cae4325e5ee3baadbbd34c839c999e4abc812626247905320145d473175c966e"},"schema_version":"1.0","source":{"id":"1105.5413","kind":"arxiv","version":1}},"canonical_sha256":"03e4317c098ca3df6ce7b8aea9848c52ab24b4e5467f68aff2943f8be4dd3523","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03e4317c098ca3df6ce7b8aea9848c52ab24b4e5467f68aff2943f8be4dd3523","first_computed_at":"2026-05-18T04:21:11.865175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:11.865175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"do9IyEUtFu8+TCtCUDLhnPXnS6yWtKu7FVM5WUMXRVuPVZhXACeeQDgDidpYaeriNxuVcSONcMGrda8in+roBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:11.865654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.5413","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aea56cbb47f18ff5dbb1f1584ef0cb114a5b4fcd1ab3ea5d8514add519ce10ef","sha256:5e6fb371efe597d18e6719775d70d5fac6133972fedf94a9dacb29d8e9b134b5"],"state_sha256":"af4c2403a364df93226f32923cefaa85fc752652b6698501cb4b03739c77b87d"}