{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JPTRRLWUCUXOWK7IFI7I5OGL2M","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":"69da8a578a787aa645f686b93b1b33c2b899cce1727ba543d107831c0e0c9ef4","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-06-03T10:45:46Z","title_canon_sha256":"6ddd783f844e7550e54410e09c891a86c0abc76839812b0305a3da5d1be0c789"},"schema_version":"1.0","source":{"id":"1006.0613","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.0613","created_at":"2026-05-18T04:19:13Z"},{"alias_kind":"arxiv_version","alias_value":"1006.0613v3","created_at":"2026-05-18T04:19:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.0613","created_at":"2026-05-18T04:19:13Z"},{"alias_kind":"pith_short_12","alias_value":"JPTRRLWUCUXO","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JPTRRLWUCUXOWK7I","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JPTRRLWU","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:0fa03092e14533983b743414b2604803c08a7282678f6670aaab2771f72837d2","target":"graph","created_at":"2026-05-18T04:19:13Z","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":"For a topological space $X$ we study continuous maps $f : X\\to \\mathbb R^m$ such that images of every pairwise distinct $k$ points are affinely (linearly) independent. Such maps are called affinely (linearly) $k$-regular embeddings.\n  We investigate the cohomology obstructions to existence of regular embeddings and give some new lower bounds on the dimension $m$ as function of $X$ and $k$, for the cases $X$ is $\\mathbb R^n$ or $X$ is an $n$-dimensional manifold. In the latter case, some nonzero Stiefel--Whitney classes of $X$ help to improve the bound.","authors_text":"R.N. Karasev","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-06-03T10:45:46Z","title":"Regular embeddings of manifolds and topology of configuration spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0613","kind":"arxiv","version":3},"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":"sha256:89f48e66ff3a849ae4042cf975b72720714b4aabdcc6c5db925aae99a74bf81c","target":"record","created_at":"2026-05-18T04:19:13Z","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":"69da8a578a787aa645f686b93b1b33c2b899cce1727ba543d107831c0e0c9ef4","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-06-03T10:45:46Z","title_canon_sha256":"6ddd783f844e7550e54410e09c891a86c0abc76839812b0305a3da5d1be0c789"},"schema_version":"1.0","source":{"id":"1006.0613","kind":"arxiv","version":3}},"canonical_sha256":"4be718aed4152eeb2be82a3e8eb8cbd31aa179b15c566ef5e75d9afab9f59f4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4be718aed4152eeb2be82a3e8eb8cbd31aa179b15c566ef5e75d9afab9f59f4d","first_computed_at":"2026-05-18T04:19:13.341545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:13.341545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K8R8ZBYSU9UMxti2O+Mt9HQ6UbNTil5N/t7FfZK1t7l/wDWTxtEo3lydJMvQOrmu62KQCOrzqx+vK0ZlFOBSDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:13.342113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.0613","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89f48e66ff3a849ae4042cf975b72720714b4aabdcc6c5db925aae99a74bf81c","sha256:0fa03092e14533983b743414b2604803c08a7282678f6670aaab2771f72837d2"],"state_sha256":"43956df3084f4056dc691b3f75196a752f87026f9bedd61a2c233d074be6097b"}