{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FXF4BAT6GD2PISZAI6SFS7JJYG","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":"68d20e5144d5da76e46398c7570df4a0ffca3de57bfff0658af784e2120d4e9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-02-25T10:39:00Z","title_canon_sha256":"964bcb941e12744f4c16e4677dfe14870d9b99c8792a72fc5f3d0bd60bb1885e"},"schema_version":"1.0","source":{"id":"1102.5206","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5206","created_at":"2026-05-18T03:01:56Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5206v1","created_at":"2026-05-18T03:01:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5206","created_at":"2026-05-18T03:01:56Z"},{"alias_kind":"pith_short_12","alias_value":"FXF4BAT6GD2P","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FXF4BAT6GD2PISZA","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FXF4BAT6","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:9a41849fe5c3b420d454075159247bd83bc02fd12022b5931ed3dec52a2e3df3","target":"graph","created_at":"2026-05-18T03:01:56Z","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":"In this paper, we conclude the calculation of the domination number of all $n\\times m$ grid graphs. Indeed, we prove Chang's conjecture saying that for every $16\\le n\\le m$, $\\gamma(G_{n,m})=\\lfloor\\frac{(n+2)(m+2)}{5}\\rfloor -4$.","authors_text":"Alexandre Pinlou, Daniel Gon\\c{c}alves, Michael Rao, St\\'ephan Thomass\\'e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-02-25T10:39:00Z","title":"The Domination Number of Grids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5206","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":"sha256:579c1f17ddeb1c660d23697e72b6e78a5b8a4182949e7c377481a3fc5229aad7","target":"record","created_at":"2026-05-18T03:01:56Z","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":"68d20e5144d5da76e46398c7570df4a0ffca3de57bfff0658af784e2120d4e9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-02-25T10:39:00Z","title_canon_sha256":"964bcb941e12744f4c16e4677dfe14870d9b99c8792a72fc5f3d0bd60bb1885e"},"schema_version":"1.0","source":{"id":"1102.5206","kind":"arxiv","version":1}},"canonical_sha256":"2dcbc0827e30f4f44b2047a4597d29c18fc5057e67ce2aeb7e6a191791988b59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2dcbc0827e30f4f44b2047a4597d29c18fc5057e67ce2aeb7e6a191791988b59","first_computed_at":"2026-05-18T03:01:56.702125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:56.702125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pYYuOfIpjz5TXonRhWX46x+wuJudf50KSt9KALl/ZTjF2/AJiRUKa/lWPqEgP2P7EwJCXTesbYKTMn4wZClhBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:56.702705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.5206","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:579c1f17ddeb1c660d23697e72b6e78a5b8a4182949e7c377481a3fc5229aad7","sha256:9a41849fe5c3b420d454075159247bd83bc02fd12022b5931ed3dec52a2e3df3"],"state_sha256":"16a9f9ca144c54e52b9f1008828a59a6430121299bb340e187af12b1024b8ed8"}