{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LHSZNSHNZWCTAOVAWMULOJAJBF","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":"cbf1020699805afff8e67435b9e05730d1ee7e8f040deaf97902d24b44980215","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-18T13:26:50Z","title_canon_sha256":"ea797f5178b1e32cf9888aad4af6ac214e0d877ce586546f657e290aabf1ebbf"},"schema_version":"1.0","source":{"id":"1805.07197","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07197","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07197v1","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07197","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"pith_short_12","alias_value":"LHSZNSHNZWCT","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LHSZNSHNZWCTAOVA","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LHSZNSHN","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:ad3ffd773fba363c85dcd1755ecf9b94482476a94ba31be0c738bebd6b36c0fc","target":"graph","created_at":"2026-05-18T00:15:38Z","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":"A result of Rosenthal says that for every $q>1$ and $n \\in \\mathbb{N}$ there is $N \\in \\mathbb{N}$ such that every sequence of $N$ distinct positive numbers contains, after a suitable translation and possible multiplication by $-1$, a subsequence $a_1,\\ldots,a_n$ that is either $q$-increasing (that is, $a_{i+1}>qa_i$ for all $i$) or $1/q$-decreasing ($a_{i+1}<a_i/q$ for all $i$). One of our main theorems extends this result to vector sequences. This theorem is then used to prove the universality theorem for Tverberg partitions which says that, for every $d$ and $r$, every long enough sequence ","authors_text":"Attila Por","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-18T13:26:50Z","title":"Universality of vector sequences and universality of Tverberg partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07197","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:d6a5282af188e9919db108097eae2e41c5fbb65768fd77dc2502d5619e238778","target":"record","created_at":"2026-05-18T00:15:38Z","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":"cbf1020699805afff8e67435b9e05730d1ee7e8f040deaf97902d24b44980215","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-18T13:26:50Z","title_canon_sha256":"ea797f5178b1e32cf9888aad4af6ac214e0d877ce586546f657e290aabf1ebbf"},"schema_version":"1.0","source":{"id":"1805.07197","kind":"arxiv","version":1}},"canonical_sha256":"59e596c8edcd85303aa0b328b7240909553d23d87647652ce19df482f6def781","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59e596c8edcd85303aa0b328b7240909553d23d87647652ce19df482f6def781","first_computed_at":"2026-05-18T00:15:38.956195Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:38.956195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qPOIrDlLJpjWjZi6TCgVveJ2lX4woDyiD2uhxdZh4dg4JG06wo2pJo99hTGLJUNvsA0tcNwq/8PxsKhLKPt1Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:38.956713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07197","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6a5282af188e9919db108097eae2e41c5fbb65768fd77dc2502d5619e238778","sha256:ad3ffd773fba363c85dcd1755ecf9b94482476a94ba31be0c738bebd6b36c0fc"],"state_sha256":"b341c3a6a85a2dca6ca420e90dafc81419d04b452ed149a5e2e0ff9809ae7ccb"}