{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MJE53F3YOBF5722US3DPTFKHHL","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":"74b6b736d3a382204c5920cbfe90c77aeec5eca57a2ec18e5974dec398872819","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2026-06-22T18:17:19Z","title_canon_sha256":"f0049feb8d0df84e9f1c789552eda7095295a5bfdfe7344c7ea80c67f66957b1"},"schema_version":"1.0","source":{"id":"2606.23837","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23837","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23837v1","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23837","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"MJE53F3YOBF5","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"pith_short_16","alias_value":"MJE53F3YOBF5722U","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"pith_short_8","alias_value":"MJE53F3Y","created_at":"2026-06-24T00:14:28Z"}],"graph_snapshots":[{"event_id":"sha256:a68b1e0c9104c55069ae2f06bee2b2059b6627af960946fc8b2021444c89517f","target":"graph","created_at":"2026-06-24T00:14:28Z","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/2606.23837/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Flood-It is a single-player game played on a precolored graph $G$, where the objective is to make $G$ monochromatic using as few flooding moves as possible. In each move, a color $c$ is selected and all vertices reachable from a fixed pivot vertex via a monochromatic path are recolored with $c$. In the free variant, the pivot may be chosen anew in every move. Deciding whether a graph can be made monochromatic in at most $k$ moves is NP-complete for both variants, fixed and free. This hardness persists even under strong structural restrictions such as split graphs and trees. The Free Flood-It v","authors_text":"Christian Rosenke, Mark Scheibner, Martin Darm\\\"untzel","cross_cats":["cs.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2026-06-22T18:17:19Z","title":"Flood-It with Jewelry -- Characterizing the Game Complexity for Cograph Generalizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23837","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:a9cc4394561316880c1ecf5a451238332ac7dd4781ce6654defbc8d01039e6a0","target":"record","created_at":"2026-06-24T00:14:28Z","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":"74b6b736d3a382204c5920cbfe90c77aeec5eca57a2ec18e5974dec398872819","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2026-06-22T18:17:19Z","title_canon_sha256":"f0049feb8d0df84e9f1c789552eda7095295a5bfdfe7344c7ea80c67f66957b1"},"schema_version":"1.0","source":{"id":"2606.23837","kind":"arxiv","version":1}},"canonical_sha256":"6249dd9778704bdfeb5496c6f995473ac34b76515f68e99c055595f655aca132","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6249dd9778704bdfeb5496c6f995473ac34b76515f68e99c055595f655aca132","first_computed_at":"2026-06-24T00:14:28.240671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T00:14:28.240671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ww6mkZsKgT9rkV9K2XJY7HZJoQgCpPtlLGsJvo2fWBDxvWbRSxzhzzSdhOxZqsqY2bxS28pTAq1wZLSWr/g2DQ==","signature_status":"signed_v1","signed_at":"2026-06-24T00:14:28.241037Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23837","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9cc4394561316880c1ecf5a451238332ac7dd4781ce6654defbc8d01039e6a0","sha256:a68b1e0c9104c55069ae2f06bee2b2059b6627af960946fc8b2021444c89517f"],"state_sha256":"672a43dfd6fc70e2ee630c39a96b88b56983c338634cccd9c3f053320bf638ab"}