{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:S356XZGMJZBGYIJLWXN3SWMSJB","short_pith_number":"pith:S356XZGM","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"},"canonical_sha256":"96fbebe4cc4e426c212bb5dbb95992486d411826e2e782945182447a76f6536d","source":{"kind":"arxiv","id":"1407.3504","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3504","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3504v1","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3504","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"S356XZGMJZBG","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"S356XZGMJZBGYIJL","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"S356XZGM","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:S356XZGMJZBGYIJLWXN3SWMSJB","target":"record","payload":{"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"},"canonical_sha256":"96fbebe4cc4e426c212bb5dbb95992486d411826e2e782945182447a76f6536d","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"},"source_kind":"arxiv","source_id":"1407.3504","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YcyNzLApiLabRfFRGCs8cGTg5Z5Lsy8v91IXlSf75ZponP15MIW0mEdVAIvBwHijfS+V+Wdsap3KXdBky97hDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:26:58.042721Z"},"content_sha256":"e57593abf9e7660861054b5536e59209920b1a461e7740526e9f6d8112efb8f8","schema_version":"1.0","event_id":"sha256:e57593abf9e7660861054b5536e59209920b1a461e7740526e9f6d8112efb8f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:S356XZGMJZBGYIJLWXN3SWMSJB","target":"graph","payload":{"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. West, Ross Kang, Tobias Muller","submitted_at":"2014-07-13T19:51:17Z","abstract_excerpt":"An \\textit{$r$-dynamic $k$-coloring} of a graph $G$ is a proper $k$-coloring of $G$ such that every vertex in $V(G)$ has neighbors in at least $\\min\\{d(v),r\\}$ different color classes. The \\textit{$r$-dynamic chromatic number} of a graph $G$, written $\\chi_r(G)$, is the least $k$ such that $G$ has such a coloring. 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 $r,m,n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3504","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iuqTtHPHQLYLeGzwsapalNYl1Bxaj3UG2SvV7VyEApCrxNQeElISRCxr9OUcY6CaKo4qINmm/0Q7SivkZGbXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:26:58.043079Z"},"content_sha256":"0d120f32d8da9d37f4672a31fa4456e1691185c78001c9bb9618c5e8eafc6f46","schema_version":"1.0","event_id":"sha256:0d120f32d8da9d37f4672a31fa4456e1691185c78001c9bb9618c5e8eafc6f46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S356XZGMJZBGYIJLWXN3SWMSJB/bundle.json","state_url":"https://pith.science/pith/S356XZGMJZBGYIJLWXN3SWMSJB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S356XZGMJZBGYIJLWXN3SWMSJB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T03:26:58Z","links":{"resolver":"https://pith.science/pith/S356XZGMJZBGYIJLWXN3SWMSJB","bundle":"https://pith.science/pith/S356XZGMJZBGYIJLWXN3SWMSJB/bundle.json","state":"https://pith.science/pith/S356XZGMJZBGYIJLWXN3SWMSJB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S356XZGMJZBGYIJLWXN3SWMSJB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:S356XZGMJZBGYIJLWXN3SWMSJB","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":"cbfb97294ec1a4ac10f701e5788fcc4ede3a09949fc6767ff036b5365f6e95b8","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-13T19:51:17Z","title_canon_sha256":"d85f1a39d9f709d25c8200ebbb11e0d21e33524e853361a8f904870499fc06c4"},"schema_version":"1.0","source":{"id":"1407.3504","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3504","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3504v1","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3504","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"S356XZGMJZBG","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"S356XZGMJZBGYIJL","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"S356XZGM","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:0d120f32d8da9d37f4672a31fa4456e1691185c78001c9bb9618c5e8eafc6f46","target":"graph","created_at":"2026-05-18T00:40:08Z","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":"An \\textit{$r$-dynamic $k$-coloring} of a graph $G$ is a proper $k$-coloring of $G$ such that every vertex in $V(G)$ has neighbors in at least $\\min\\{d(v),r\\}$ different color classes. The \\textit{$r$-dynamic chromatic number} of a graph $G$, written $\\chi_r(G)$, is the least $k$ such that $G$ has such a coloring. 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 $r,m,n$.","authors_text":"Douglas B. West, Ross Kang, Tobias Muller","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-13T19:51:17Z","title":"On r-dynamic Coloring of Grids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3504","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:e57593abf9e7660861054b5536e59209920b1a461e7740526e9f6d8112efb8f8","target":"record","created_at":"2026-05-18T00:40:08Z","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":"cbfb97294ec1a4ac10f701e5788fcc4ede3a09949fc6767ff036b5365f6e95b8","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-13T19:51:17Z","title_canon_sha256":"d85f1a39d9f709d25c8200ebbb11e0d21e33524e853361a8f904870499fc06c4"},"schema_version":"1.0","source":{"id":"1407.3504","kind":"arxiv","version":1}},"canonical_sha256":"96fbebe4cc4e426c212bb5dbb95992486d411826e2e782945182447a76f6536d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96fbebe4cc4e426c212bb5dbb95992486d411826e2e782945182447a76f6536d","first_computed_at":"2026-05-18T00:40:08.728385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:08.728385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qPMB2M5EpSdLwjvwHpy1NNmvwnUa17qSd/XP/Bsp66BjpIvb/QDWNczxBkIjgIdYot8NdtADc/dtdB45n126AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:08.728852Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.3504","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e57593abf9e7660861054b5536e59209920b1a461e7740526e9f6d8112efb8f8","sha256:0d120f32d8da9d37f4672a31fa4456e1691185c78001c9bb9618c5e8eafc6f46"],"state_sha256":"d6b73a3937bd672bb0e17b66b6e348591c7f2406a0583a5e0130ba1b4b474e12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FGt1uDAzsShG9WuzTA7XEYId8BqZT9KTVkiIl+Lz/wUsexweyD3hmlrCTNUIiEZO8qBWeHa4OOcSC1OrCvYhDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:26:58.045200Z","bundle_sha256":"ab822c1a3061523bacb28546668bcb749f6f645997905ed6b1a452e77d75ec57"}}