{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:J33FMPRYCCKGMABKBAIWCCOMS3","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":"d28825b645036884cdbb09ace5cf535121cd0523a057aa80638ea54e7a8db4d2","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2026-05-18T03:01:06Z","title_canon_sha256":"c47207f0d151941ce6ac9f5f2bebcb4303ff5cd4acd9da9d17257b5eeeb16542"},"schema_version":"1.0","source":{"id":"2605.20243","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20243","created_at":"2026-05-21T00:04:22Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20243v1","created_at":"2026-05-21T00:04:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20243","created_at":"2026-05-21T00:04:22Z"},{"alias_kind":"pith_short_12","alias_value":"J33FMPRYCCKG","created_at":"2026-05-21T00:04:22Z"},{"alias_kind":"pith_short_16","alias_value":"J33FMPRYCCKGMABK","created_at":"2026-05-21T00:04:22Z"},{"alias_kind":"pith_short_8","alias_value":"J33FMPRY","created_at":"2026-05-21T00:04:22Z"}],"graph_snapshots":[{"event_id":"sha256:a2e35e87aeaef1e6bc14b8cac4a0bc999e1d19cb00cd50e5bf591e06087377b8","target":"graph","created_at":"2026-05-21T00:04:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.20243/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We describe and axiomatize finite solitaire puzzles and zero sum sequential games graph theoretically. Zermelo's theorem telling that there is a win for one of the players or a draw follows from the definitions. The god number is a geometric quantity that quantifies the number of moves necessary to solve the puzzle. In the solitaire case, the god number is the minimal distance from the initial state $v$ to the solution space $A$. If $v$ and $A$ are not specified, the god number is the graph diameter. God number computations are related to combinatorial sorting problems and is a NP-complete pro","authors_text":"C. Hou, M.H. Saleem, M.Z. Cassim, O. Knill, V. Seco Roopnaraine, Z. Adams","cross_cats":["cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2026-05-18T03:01:06Z","title":"God numbers for Graphs, Games and Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20243","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":"sha256:6dbcf761fdab92dbb2e6cce906d3835810683d8b122a480d47de0404085bd765","target":"record","created_at":"2026-05-21T00:04:22Z","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":"d28825b645036884cdbb09ace5cf535121cd0523a057aa80638ea54e7a8db4d2","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2026-05-18T03:01:06Z","title_canon_sha256":"c47207f0d151941ce6ac9f5f2bebcb4303ff5cd4acd9da9d17257b5eeeb16542"},"schema_version":"1.0","source":{"id":"2605.20243","kind":"arxiv","version":1}},"canonical_sha256":"4ef6563e38109466002a08116109cc96d3bf74c8bd68304156e975dbdf6b17e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ef6563e38109466002a08116109cc96d3bf74c8bd68304156e975dbdf6b17e2","first_computed_at":"2026-05-21T00:04:22.430933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T00:04:22.430933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p+nKOlu9iNr4W/9NjJI1hMm9+U0By2uBntRg5EQg3/WPxKXkuUwRRO3e54fPaWB5jeIlu3KcS5C9+wmjoxA5AQ==","signature_status":"signed_v1","signed_at":"2026-05-21T00:04:22.431675Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20243","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dbcf761fdab92dbb2e6cce906d3835810683d8b122a480d47de0404085bd765","sha256:a2e35e87aeaef1e6bc14b8cac4a0bc999e1d19cb00cd50e5bf591e06087377b8"],"state_sha256":"1e7cc2b21463f11123b09e1b421f6437ba766a57e284f2ca465244f17c2c23d5"}