{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:RKGT6GL5H3O7CQLNWKDSM4IUZL","short_pith_number":"pith:RKGT6GL5","schema_version":"1.0","canonical_sha256":"8a8d3f197d3eddf1416db287267114cae6aff98e7d79f921e2e56dc2b0f7ece1","source":{"kind":"arxiv","id":"2501.08698","version":3},"attestation_state":"computed","paper":{"title":"On the generalized coloring numbers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO","math.CO"],"primary_cat":"cs.DM","authors_text":"Sebastian Siebertz","submitted_at":"2025-01-15T10:17:52Z","abstract_excerpt":"The \\emph{coloring number} $\\mathrm{col}(G)$ of a graph $G$, which is equal to the \\emph{degeneracy} of $G$ plus one, provides a very useful measure for the uniform sparsity of $G$. The coloring number is generalized by three series of measures, the \\emph{generalized coloring numbers}. These are the \\emph{$r$-admissibility} $\\mathrm{adm}_r(G)$, the \\emph{strong $r$-coloring number} $\\mathrm{col}_r(G)$ and the \\emph{weak $r$-coloring number} $\\mathrm{wcol}_r(G)$, where $r$ is an integer parameter. The generalized coloring numbers measure the edge density of bounded-depth minors and thereby prov"},"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":"2501.08698","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2025-01-15T10:17:52Z","cross_cats_sorted":["cs.LO","math.CO"],"title_canon_sha256":"730d715ca8078331507025068c5baa56636810526ce9f8307216ff4584882bdf","abstract_canon_sha256":"4cb89e5035ee092c42b6ab2fa8a710a878f99de688666d5c24d7dd14325ea0e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:42:25.058984Z","signature_b64":"YytUAc8Bbg9jAz6dJ8pygUkGq2j79UPmq/XQe5lgU7br9BWcnE3bm++MmDZp9wKJCWRq62FzqhTEBJsfXeoVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a8d3f197d3eddf1416db287267114cae6aff98e7d79f921e2e56dc2b0f7ece1","last_reissued_at":"2026-07-05T11:42:25.058528Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:42:25.058528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the generalized coloring numbers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO","math.CO"],"primary_cat":"cs.DM","authors_text":"Sebastian Siebertz","submitted_at":"2025-01-15T10:17:52Z","abstract_excerpt":"The \\emph{coloring number} $\\mathrm{col}(G)$ of a graph $G$, which is equal to the \\emph{degeneracy} of $G$ plus one, provides a very useful measure for the uniform sparsity of $G$. The coloring number is generalized by three series of measures, the \\emph{generalized coloring numbers}. These are the \\emph{$r$-admissibility} $\\mathrm{adm}_r(G)$, the \\emph{strong $r$-coloring number} $\\mathrm{col}_r(G)$ and the \\emph{weak $r$-coloring number} $\\mathrm{wcol}_r(G)$, where $r$ is an integer parameter. The generalized coloring numbers measure the edge density of bounded-depth minors and thereby prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08698","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.08698/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2501.08698","created_at":"2026-07-05T11:42:25.058585+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.08698v3","created_at":"2026-07-05T11:42:25.058585+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.08698","created_at":"2026-07-05T11:42:25.058585+00:00"},{"alias_kind":"pith_short_12","alias_value":"RKGT6GL5H3O7","created_at":"2026-07-05T11:42:25.058585+00:00"},{"alias_kind":"pith_short_16","alias_value":"RKGT6GL5H3O7CQLN","created_at":"2026-07-05T11:42:25.058585+00:00"},{"alias_kind":"pith_short_8","alias_value":"RKGT6GL5","created_at":"2026-07-05T11:42:25.058585+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.15655","citing_title":"First-order transducibility among classes of sparse graphs","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RKGT6GL5H3O7CQLNWKDSM4IUZL","json":"https://pith.science/pith/RKGT6GL5H3O7CQLNWKDSM4IUZL.json","graph_json":"https://pith.science/api/pith-number/RKGT6GL5H3O7CQLNWKDSM4IUZL/graph.json","events_json":"https://pith.science/api/pith-number/RKGT6GL5H3O7CQLNWKDSM4IUZL/events.json","paper":"https://pith.science/paper/RKGT6GL5"},"agent_actions":{"view_html":"https://pith.science/pith/RKGT6GL5H3O7CQLNWKDSM4IUZL","download_json":"https://pith.science/pith/RKGT6GL5H3O7CQLNWKDSM4IUZL.json","view_paper":"https://pith.science/paper/RKGT6GL5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.08698&json=true","fetch_graph":"https://pith.science/api/pith-number/RKGT6GL5H3O7CQLNWKDSM4IUZL/graph.json","fetch_events":"https://pith.science/api/pith-number/RKGT6GL5H3O7CQLNWKDSM4IUZL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RKGT6GL5H3O7CQLNWKDSM4IUZL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RKGT6GL5H3O7CQLNWKDSM4IUZL/action/storage_attestation","attest_author":"https://pith.science/pith/RKGT6GL5H3O7CQLNWKDSM4IUZL/action/author_attestation","sign_citation":"https://pith.science/pith/RKGT6GL5H3O7CQLNWKDSM4IUZL/action/citation_signature","submit_replication":"https://pith.science/pith/RKGT6GL5H3O7CQLNWKDSM4IUZL/action/replication_record"}},"created_at":"2026-07-05T11:42:25.058585+00:00","updated_at":"2026-07-05T11:42:25.058585+00:00"}