{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MHPANXDYLVASLK2T7MADMHEVUP","short_pith_number":"pith:MHPANXDY","schema_version":"1.0","canonical_sha256":"61de06dc785d4125ab53fb00361c95a3e266f3ebbee46023505e4e967a7ec182","source":{"kind":"arxiv","id":"1507.02463","version":1},"attestation_state":"computed","paper":{"title":"An extremal problem in proper $(r,p)$-coloring of hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Sudebkumar Prasant Pal, Tapas Kumar Mishra","submitted_at":"2015-07-09T11:25:23Z","abstract_excerpt":"Let $G(V,E)$ be a $k$-uniform hypergraph. A hyperedge $e \\in E$ is said to be properly $(r,p)$ colored by an $r$-coloring of vertices in $V$ if $e$ contains vertices of at least $p$ distinct colors in the $r$-coloring. An $r$-coloring of vertices in $V$ is called a {\\it strong $(r,p)$ coloring} if every hyperedge $e \\in E$ is properly $(r,p)$ colored by the $r$-coloring. We study the maximum number of hyperedges that can be properly $(r,p)$ colored by a single $r$-coloring and the structures that maximizes number of properly $(r,p)$ colored hyperedges."},"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":"1507.02463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-07-09T11:25:23Z","cross_cats_sorted":[],"title_canon_sha256":"91644658b236c18503a33b8b4a4882f3f2849afa9b6d009850ef8b537ee6cd5d","abstract_canon_sha256":"7a892b417620b77b85307a326faaa7cc4b11f036c491b80f0e1a4bf47d982ae7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:06.683525Z","signature_b64":"ZX12SDvFcpiPmiRtJx60pej7gdvQTVSrQYco52uBR9qfYKn45LlDupzJ+r4WKNUi71iTaqbynyd4dPxcbNULAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61de06dc785d4125ab53fb00361c95a3e266f3ebbee46023505e4e967a7ec182","last_reissued_at":"2026-05-18T01:37:06.682741Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:06.682741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An extremal problem in proper $(r,p)$-coloring of hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Sudebkumar Prasant Pal, Tapas Kumar Mishra","submitted_at":"2015-07-09T11:25:23Z","abstract_excerpt":"Let $G(V,E)$ be a $k$-uniform hypergraph. A hyperedge $e \\in E$ is said to be properly $(r,p)$ colored by an $r$-coloring of vertices in $V$ if $e$ contains vertices of at least $p$ distinct colors in the $r$-coloring. An $r$-coloring of vertices in $V$ is called a {\\it strong $(r,p)$ coloring} if every hyperedge $e \\in E$ is properly $(r,p)$ colored by the $r$-coloring. We study the maximum number of hyperedges that can be properly $(r,p)$ colored by a single $r$-coloring and the structures that maximizes number of properly $(r,p)$ colored hyperedges."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02463","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1507.02463","created_at":"2026-05-18T01:37:06.682871+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.02463v1","created_at":"2026-05-18T01:37:06.682871+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02463","created_at":"2026-05-18T01:37:06.682871+00:00"},{"alias_kind":"pith_short_12","alias_value":"MHPANXDYLVAS","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MHPANXDYLVASLK2T","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MHPANXDY","created_at":"2026-05-18T12:29:32.376354+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MHPANXDYLVASLK2T7MADMHEVUP","json":"https://pith.science/pith/MHPANXDYLVASLK2T7MADMHEVUP.json","graph_json":"https://pith.science/api/pith-number/MHPANXDYLVASLK2T7MADMHEVUP/graph.json","events_json":"https://pith.science/api/pith-number/MHPANXDYLVASLK2T7MADMHEVUP/events.json","paper":"https://pith.science/paper/MHPANXDY"},"agent_actions":{"view_html":"https://pith.science/pith/MHPANXDYLVASLK2T7MADMHEVUP","download_json":"https://pith.science/pith/MHPANXDYLVASLK2T7MADMHEVUP.json","view_paper":"https://pith.science/paper/MHPANXDY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.02463&json=true","fetch_graph":"https://pith.science/api/pith-number/MHPANXDYLVASLK2T7MADMHEVUP/graph.json","fetch_events":"https://pith.science/api/pith-number/MHPANXDYLVASLK2T7MADMHEVUP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MHPANXDYLVASLK2T7MADMHEVUP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MHPANXDYLVASLK2T7MADMHEVUP/action/storage_attestation","attest_author":"https://pith.science/pith/MHPANXDYLVASLK2T7MADMHEVUP/action/author_attestation","sign_citation":"https://pith.science/pith/MHPANXDYLVASLK2T7MADMHEVUP/action/citation_signature","submit_replication":"https://pith.science/pith/MHPANXDYLVASLK2T7MADMHEVUP/action/replication_record"}},"created_at":"2026-05-18T01:37:06.682871+00:00","updated_at":"2026-05-18T01:37:06.682871+00:00"}