{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MHPANXDYLVASLK2T7MADMHEVUP","short_pith_number":"pith:MHPANXDY","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"},"canonical_sha256":"61de06dc785d4125ab53fb00361c95a3e266f3ebbee46023505e4e967a7ec182","source":{"kind":"arxiv","id":"1507.02463","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02463","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02463v1","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02463","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"MHPANXDYLVAS","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MHPANXDYLVASLK2T","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MHPANXDY","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MHPANXDYLVASLK2T7MADMHEVUP","target":"record","payload":{"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"},"canonical_sha256":"61de06dc785d4125ab53fb00361c95a3e266f3ebbee46023505e4e967a7ec182","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"},"source_kind":"arxiv","source_id":"1507.02463","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":"2026-05-18T01:37:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ejkx189KZr+HhcajPnB/VTCNbPRYHE4iIVRCnzsgMwbT5oZBNJ5un5hfm84qiqkvuPJ23CM0ZNnp59g6MoUtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:42:42.736831Z"},"content_sha256":"477434cfd25fcdbe75af8e9b4d82c7668c470751885770979a1e886667c54152","schema_version":"1.0","event_id":"sha256:477434cfd25fcdbe75af8e9b4d82c7668c470751885770979a1e886667c54152"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MHPANXDYLVASLK2T7MADMHEVUP","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6enrBXi6CiC4fDMuTPH9dxls1701FiDfV4FFeAMFr576O2NikVJin3T4gROG4dToEPnZli7cK9ZFWBKpApezBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:42:42.737165Z"},"content_sha256":"3946340d8c98c663079ec71965770e0f4ac1607e3e1b0d4a432fdfecfba0fe5f","schema_version":"1.0","event_id":"sha256:3946340d8c98c663079ec71965770e0f4ac1607e3e1b0d4a432fdfecfba0fe5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MHPANXDYLVASLK2T7MADMHEVUP/bundle.json","state_url":"https://pith.science/pith/MHPANXDYLVASLK2T7MADMHEVUP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MHPANXDYLVASLK2T7MADMHEVUP/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":"2026-06-29T19:42:42Z","links":{"resolver":"https://pith.science/pith/MHPANXDYLVASLK2T7MADMHEVUP","bundle":"https://pith.science/pith/MHPANXDYLVASLK2T7MADMHEVUP/bundle.json","state":"https://pith.science/pith/MHPANXDYLVASLK2T7MADMHEVUP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MHPANXDYLVASLK2T7MADMHEVUP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MHPANXDYLVASLK2T7MADMHEVUP","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":"7a892b417620b77b85307a326faaa7cc4b11f036c491b80f0e1a4bf47d982ae7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-07-09T11:25:23Z","title_canon_sha256":"91644658b236c18503a33b8b4a4882f3f2849afa9b6d009850ef8b537ee6cd5d"},"schema_version":"1.0","source":{"id":"1507.02463","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02463","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02463v1","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02463","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"MHPANXDYLVAS","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MHPANXDYLVASLK2T","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MHPANXDY","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:3946340d8c98c663079ec71965770e0f4ac1607e3e1b0d4a432fdfecfba0fe5f","target":"graph","created_at":"2026-05-18T01:37:06Z","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":"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.","authors_text":"Sudebkumar Prasant Pal, Tapas Kumar Mishra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-07-09T11:25:23Z","title":"An extremal problem in proper $(r,p)$-coloring of hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02463","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":"sha256:477434cfd25fcdbe75af8e9b4d82c7668c470751885770979a1e886667c54152","target":"record","created_at":"2026-05-18T01:37:06Z","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":"7a892b417620b77b85307a326faaa7cc4b11f036c491b80f0e1a4bf47d982ae7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-07-09T11:25:23Z","title_canon_sha256":"91644658b236c18503a33b8b4a4882f3f2849afa9b6d009850ef8b537ee6cd5d"},"schema_version":"1.0","source":{"id":"1507.02463","kind":"arxiv","version":1}},"canonical_sha256":"61de06dc785d4125ab53fb00361c95a3e266f3ebbee46023505e4e967a7ec182","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61de06dc785d4125ab53fb00361c95a3e266f3ebbee46023505e4e967a7ec182","first_computed_at":"2026-05-18T01:37:06.682741Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:06.682741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZX12SDvFcpiPmiRtJx60pej7gdvQTVSrQYco52uBR9qfYKn45LlDupzJ+r4WKNUi71iTaqbynyd4dPxcbNULAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:06.683525Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02463","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:477434cfd25fcdbe75af8e9b4d82c7668c470751885770979a1e886667c54152","sha256:3946340d8c98c663079ec71965770e0f4ac1607e3e1b0d4a432fdfecfba0fe5f"],"state_sha256":"3e5c2b3929dc3d91586de38e92f0814844c4baac3cd0daf20db1cbfbd35bcc81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tiZH7MPVItYVCwPHrRQhsri4gt3ORNKEEygVJpieq4NLUB1lK0J/2MD65D+DojFuZIrlUV/UgBabqIwyVbWWDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T19:42:42.739207Z","bundle_sha256":"b84161fbee27aa446965de74e9c377e2bbbcb92e08a14ebed8a93fb8da0a5497"}}