{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:N53JD6CGTBHBLWLZEAQO2OJDU3","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":"8a5179ae11adeddcc97103d18d32b92c7ba41205799a88039326b193e4a26fd1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-22T04:30:58Z","title_canon_sha256":"b9cd9fe0fc810965e25dedecc8e4c6a266d19b4ac15553a1678a7f01fdf0dde0"},"schema_version":"1.0","source":{"id":"2502.16073","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.16073","created_at":"2026-07-05T10:18:20Z"},{"alias_kind":"arxiv_version","alias_value":"2502.16073v1","created_at":"2026-07-05T10:18:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.16073","created_at":"2026-07-05T10:18:20Z"},{"alias_kind":"pith_short_12","alias_value":"N53JD6CGTBHB","created_at":"2026-07-05T10:18:20Z"},{"alias_kind":"pith_short_16","alias_value":"N53JD6CGTBHBLWLZ","created_at":"2026-07-05T10:18:20Z"},{"alias_kind":"pith_short_8","alias_value":"N53JD6CG","created_at":"2026-07-05T10:18:20Z"}],"graph_snapshots":[{"event_id":"sha256:31c53c846b382c2b54d02a45e4490d7a618b9a028e9a5e0d381da0dca1ff8ea9","target":"graph","created_at":"2026-07-05T10:18:20Z","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/2502.16073/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a graph $G$ and a list assignment $L$ for $G$, the indicated $L$-colouring game on $G$ is played by two players: Ann and Ben. In each round, Ann chooses an uncoloured vertex $v$, and Ben colours $v$ with a colour from $L(v)$ that is not used by its coloured neighbours. If all vertices are coloured, then Ann wins the game. Otherwise after a finite number of rounds, there remains an uncoloured vertex $v$ such that all colours in $L(v)$ have been used by its coloured neighbours, Ben wins. We say $G$ is indicated $L$-colourable if Ann has a winning strategy for the indicated $L$-colouring ga","authors_text":"Huan Zhou, Jialu Zhu, Xuding Zhu, Yangyan Gu, Yiting Jiang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-22T04:30:58Z","title":"Indicated list colouring game on graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.16073","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":"sha256:1abab599db370fe136e83eddc9fd4043fdd5abe1c02e949facab7e8478ec9c52","target":"record","created_at":"2026-07-05T10:18:20Z","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":"8a5179ae11adeddcc97103d18d32b92c7ba41205799a88039326b193e4a26fd1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-22T04:30:58Z","title_canon_sha256":"b9cd9fe0fc810965e25dedecc8e4c6a266d19b4ac15553a1678a7f01fdf0dde0"},"schema_version":"1.0","source":{"id":"2502.16073","kind":"arxiv","version":1}},"canonical_sha256":"6f7691f846984e15d9792020ed3923a6c390d6118a9858559a4d6952bcb6c1c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f7691f846984e15d9792020ed3923a6c390d6118a9858559a4d6952bcb6c1c9","first_computed_at":"2026-07-05T10:18:20.640726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:18:20.640726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9auAOlu4nqHvDmRfXzfotRcj4uFxBITVTk6IgUUWzgGWBw0f76NT1GHHNtgESahqe+OjI/lyDWHQyP8n1pPjAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:18:20.641243Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.16073","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1abab599db370fe136e83eddc9fd4043fdd5abe1c02e949facab7e8478ec9c52","sha256:31c53c846b382c2b54d02a45e4490d7a618b9a028e9a5e0d381da0dca1ff8ea9"],"state_sha256":"eb48f262ddc4af00bc902deb7a083d22701d34659e7d85f0def6b51a4dd6d121"}