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Proving a conjecture of Jahanbekam, Kim, O, and West, we show that the $m$-by-$n$ grid has no $3$-dynamic $4$-coloring when $mn\\equiv2\\mod 4$. This completes the determination of the $r$-dynamic chromatic number of the $m$-by-$n$ grid for all $r,m,n$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.3504","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-13T19:51:17Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"d85f1a39d9f709d25c8200ebbb11e0d21e33524e853361a8f904870499fc06c4","abstract_canon_sha256":"cbfb97294ec1a4ac10f701e5788fcc4ede3a09949fc6767ff036b5365f6e95b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:08.728852Z","signature_b64":"qPMB2M5EpSdLwjvwHpy1NNmvwnUa17qSd/XP/Bsp66BjpIvb/QDWNczxBkIjgIdYot8NdtADc/dtdB45n126AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96fbebe4cc4e426c212bb5dbb95992486d411826e2e782945182447a76f6536d","last_reissued_at":"2026-05-18T00:40:08.728385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:08.728385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On r-dynamic Coloring of Grids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Douglas B. 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