{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:HBVNZCZJUCFEITOLANCCNR2QI2","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":"115939044ffdd7dec8d2db871bf6d605d079446fb48178da2c1830d7c730f819","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-13T15:41:17Z","title_canon_sha256":"74e2564710f1189b28b5b74494074dbfca203d4d046ce27e909d95c498fe83fe"},"schema_version":"1.0","source":{"id":"1905.05100","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05100","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05100v1","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05100","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"HBVNZCZJUCFE","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"HBVNZCZJUCFEITOL","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"HBVNZCZJ","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:4be3a799ab0e1c7b9e3f3599928ae4bbd5cc8470ba42226a79bd9757d6cbe5e2","target":"graph","created_at":"2026-05-17T23:46:22Z","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":"Extending a result of Rado to hypergraphs, we prove that for all $s, k, t \\in \\mathbb{N}$ with $k \\geq t \\geq 2$, the vertices of every $r = s(k-t+1)$-edge-coloured countably infinite complete $k$-graph can be partitioned into the cores of at most $s$ monochromatic $t$-tight Berge-paths of different colours. We further describe a construction showing that this result is best possible.","authors_text":"Jan Corsten, N\\'ora Frankl, Sebasti\\'an Bustamante","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-13T15:41:17Z","title":"Partitioning infinite hypergraphs into few monochromatic Berge-paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05100","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":"sha256:1769fe7b1efcf88f3e26b6faf681290907d0f574b57feb8bb520086da0c4603b","target":"record","created_at":"2026-05-17T23:46:22Z","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":"115939044ffdd7dec8d2db871bf6d605d079446fb48178da2c1830d7c730f819","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-13T15:41:17Z","title_canon_sha256":"74e2564710f1189b28b5b74494074dbfca203d4d046ce27e909d95c498fe83fe"},"schema_version":"1.0","source":{"id":"1905.05100","kind":"arxiv","version":1}},"canonical_sha256":"386adc8b29a08a444dcb034426c75046aa7d8ddca5cee96b00be215612aa3dc2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"386adc8b29a08a444dcb034426c75046aa7d8ddca5cee96b00be215612aa3dc2","first_computed_at":"2026-05-17T23:46:22.546674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:22.546674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AQYs6B+Lhg6BhSU8wFXx3op7xXMv42WnEntKMirLKqvXcIZjD+1kUbbipE2qVwqX3DxoBW4e2neI/MEFzL/CBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:22.547271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.05100","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1769fe7b1efcf88f3e26b6faf681290907d0f574b57feb8bb520086da0c4603b","sha256:4be3a799ab0e1c7b9e3f3599928ae4bbd5cc8470ba42226a79bd9757d6cbe5e2"],"state_sha256":"d889f426b38f2a93e29ffedb0e336ee93698915f3db97edd0c1759c65e15aac0"}