{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7XL422HO6QPYEGUYXP7V4UA62C","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":"21fd59ded89c4467eddd7a9227de7bec8c18e36bced8692a42dbc1d53217a5be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-10-10T20:28:41Z","title_canon_sha256":"0bbd922deb776e96794689711d20c1c6c9edc175ce86b3198f17431acc01e7e2"},"schema_version":"1.0","source":{"id":"1610.03084","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03084","created_at":"2026-05-18T01:02:49Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03084v1","created_at":"2026-05-18T01:02:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03084","created_at":"2026-05-18T01:02:49Z"},{"alias_kind":"pith_short_12","alias_value":"7XL422HO6QPY","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7XL422HO6QPYEGUY","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7XL422HO","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:48fbcbf9d6d0bae54f404b4990972a2fff227bb84f2e725547a205c0fea0137d","target":"graph","created_at":"2026-05-18T01:02:49Z","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":"A b-coloring of the vertices of a graph is a proper coloring where each color class contains a vertex which is adjacent to each other color class. The b-chromatic number of $G$ is the maximum integer $\\chi_b(G)$ for which $G$ has a b-coloring with $\\chi_b(G)$ colors. A graph $G$ is b-continuous if $G$ has a b-coloring with $k$ colors, for every integer $k$ in the interval $[\\chi(G),\\chi_b(G)]$. It is known that not all graphs are b-continuous. Here, we investigate whether the lexicographic product $G[H]$ of b-continuous graphs $G$ and $H$ is also b-continuous. Using homomorphisms, we provide a","authors_text":"Ana Silva, Cl\\'audia Linhares Sales, Leonardo Sampaio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-10-10T20:28:41Z","title":"On the b-continuity of the lexicographic product of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03084","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":"sha256:09eed2d5310b7f0519879092229b81103f98a8d0059bde4f12986749cea56947","target":"record","created_at":"2026-05-18T01:02:49Z","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":"21fd59ded89c4467eddd7a9227de7bec8c18e36bced8692a42dbc1d53217a5be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-10-10T20:28:41Z","title_canon_sha256":"0bbd922deb776e96794689711d20c1c6c9edc175ce86b3198f17431acc01e7e2"},"schema_version":"1.0","source":{"id":"1610.03084","kind":"arxiv","version":1}},"canonical_sha256":"fdd7cd68eef41f821a98bbff5e501ed0b6c2c110632b82dd65856e6209c164cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fdd7cd68eef41f821a98bbff5e501ed0b6c2c110632b82dd65856e6209c164cf","first_computed_at":"2026-05-18T01:02:49.643661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:49.643661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U7CYuGcPu4AItfPFuh3SIndLf7FIovqkgXqoRQ1a/gptzynEY2zkWU+6qXvMRaqiMCl4mlbpFpqCNKAXc00FDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:49.644078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03084","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09eed2d5310b7f0519879092229b81103f98a8d0059bde4f12986749cea56947","sha256:48fbcbf9d6d0bae54f404b4990972a2fff227bb84f2e725547a205c0fea0137d"],"state_sha256":"283cb4cad73e9d9c1274dd3dcaf0690bc4cfba3120f4f89fcb235de01aefac5a"}