{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:QVSOKJKEVD3RZOZEEP2WHFLPYQ","short_pith_number":"pith:QVSOKJKE","schema_version":"1.0","canonical_sha256":"8564e52544a8f71cbb2423f563956fc4395039b633ef777a2539fe7a14bc99dd","source":{"kind":"arxiv","id":"2508.18793","version":1},"attestation_state":"computed","paper":{"title":"Hoffman colorability of (strongly) regular graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aida Abiad, Bart De Bruyn, Thijs van Veluw","submitted_at":"2025-08-26T08:18:28Z","abstract_excerpt":"Hoffman's bound is a well-known eigenvalue bound on the chromatic number of a graph. By interpreting this bound as a parameter, we show multiple applications of colorings attaining the bound (Hoffman colorings) for several notions of graph regularity: regular, (co-)edge-regular, and strongly regular. For strongly regular graphs, we prove that Hoffman colorability implies pseudo-geometricity, and we strengthen Haemers' finiteness result on strongly regular graphs with a bounded chromatic number by considering the Hoffman bound instead of the chromatic number. Furthermore, by using Hoffman color"},"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":"2508.18793","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-08-26T08:18:28Z","cross_cats_sorted":[],"title_canon_sha256":"44e1508f45d7856bd6ca597b193fe8b13d74c69838ffd6d3c62073e2f15b8a76","abstract_canon_sha256":"90a01e0c6bb449863489204e1dbeea01e33d21b4d851976afbcaad0601207581"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:59:31.140438Z","signature_b64":"Wn1gTN874/G4ixY9JtOxj6aM2Y31qNcetsiY9LlhbTQrAL2j0NfHe2wAMN0FajW+9rx1I7enaGABg1E60ZxFCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8564e52544a8f71cbb2423f563956fc4395039b633ef777a2539fe7a14bc99dd","last_reissued_at":"2026-07-05T11:59:31.139887Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:59:31.139887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hoffman colorability of (strongly) regular graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aida Abiad, Bart De Bruyn, Thijs van Veluw","submitted_at":"2025-08-26T08:18:28Z","abstract_excerpt":"Hoffman's bound is a well-known eigenvalue bound on the chromatic number of a graph. By interpreting this bound as a parameter, we show multiple applications of colorings attaining the bound (Hoffman colorings) for several notions of graph regularity: regular, (co-)edge-regular, and strongly regular. For strongly regular graphs, we prove that Hoffman colorability implies pseudo-geometricity, and we strengthen Haemers' finiteness result on strongly regular graphs with a bounded chromatic number by considering the Hoffman bound instead of the chromatic number. Furthermore, by using Hoffman color"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.18793","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.18793/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":"2508.18793","created_at":"2026-07-05T11:59:31.139958+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.18793v1","created_at":"2026-07-05T11:59:31.139958+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.18793","created_at":"2026-07-05T11:59:31.139958+00:00"},{"alias_kind":"pith_short_12","alias_value":"QVSOKJKEVD3R","created_at":"2026-07-05T11:59:31.139958+00:00"},{"alias_kind":"pith_short_16","alias_value":"QVSOKJKEVD3RZOZE","created_at":"2026-07-05T11:59:31.139958+00:00"},{"alias_kind":"pith_short_8","alias_value":"QVSOKJKE","created_at":"2026-07-05T11:59:31.139958+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.05814","citing_title":"A graph energy conjecture through the lenses of semidefinite programming","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QVSOKJKEVD3RZOZEEP2WHFLPYQ","json":"https://pith.science/pith/QVSOKJKEVD3RZOZEEP2WHFLPYQ.json","graph_json":"https://pith.science/api/pith-number/QVSOKJKEVD3RZOZEEP2WHFLPYQ/graph.json","events_json":"https://pith.science/api/pith-number/QVSOKJKEVD3RZOZEEP2WHFLPYQ/events.json","paper":"https://pith.science/paper/QVSOKJKE"},"agent_actions":{"view_html":"https://pith.science/pith/QVSOKJKEVD3RZOZEEP2WHFLPYQ","download_json":"https://pith.science/pith/QVSOKJKEVD3RZOZEEP2WHFLPYQ.json","view_paper":"https://pith.science/paper/QVSOKJKE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.18793&json=true","fetch_graph":"https://pith.science/api/pith-number/QVSOKJKEVD3RZOZEEP2WHFLPYQ/graph.json","fetch_events":"https://pith.science/api/pith-number/QVSOKJKEVD3RZOZEEP2WHFLPYQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QVSOKJKEVD3RZOZEEP2WHFLPYQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QVSOKJKEVD3RZOZEEP2WHFLPYQ/action/storage_attestation","attest_author":"https://pith.science/pith/QVSOKJKEVD3RZOZEEP2WHFLPYQ/action/author_attestation","sign_citation":"https://pith.science/pith/QVSOKJKEVD3RZOZEEP2WHFLPYQ/action/citation_signature","submit_replication":"https://pith.science/pith/QVSOKJKEVD3RZOZEEP2WHFLPYQ/action/replication_record"}},"created_at":"2026-07-05T11:59:31.139958+00:00","updated_at":"2026-07-05T11:59:31.139958+00:00"}