{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MQRZRDV4M6UAP2LITLHZCMNZJI","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":"c7456f609abbaa690273664b18f44b30fd06b9e4b06dd80bf9340d696497f096","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-10-20T18:32:21Z","title_canon_sha256":"32efef7e931ef2e19f37209d5167821dfaae27bf9323157a1dd89cfc7ef8a089"},"schema_version":"1.0","source":{"id":"1010.4271","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4271","created_at":"2026-05-18T04:38:59Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4271v1","created_at":"2026-05-18T04:38:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4271","created_at":"2026-05-18T04:38:59Z"},{"alias_kind":"pith_short_12","alias_value":"MQRZRDV4M6UA","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MQRZRDV4M6UAP2LI","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MQRZRDV4","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:5e8b3112de3eb1f4e6cfe92c5a1e451cd55335b88233cbffc8ac447c9740d568","target":"graph","created_at":"2026-05-18T04:38:59Z","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 $N$ be a closed orientable connected $n$-manifold, $n\\ge 4$. We classify embeddings of the punctured manifold $N_0$ into $\\R^{2n-1}$ up to isotopy. Our result in some sense extends results of J.C. Becker -- H.H. Glover (1971) and O. Saeki (1999).","authors_text":"Dmitry Tonkonog","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-10-20T18:32:21Z","title":"Embedding punctured n-manifolds in Euclidean (2n-1)-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4271","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":"sha256:67d91be57ca4da5aeea357452f7c9a71c09abf5d95d9a93df23798b124b3b5d3","target":"record","created_at":"2026-05-18T04:38:59Z","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":"c7456f609abbaa690273664b18f44b30fd06b9e4b06dd80bf9340d696497f096","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-10-20T18:32:21Z","title_canon_sha256":"32efef7e931ef2e19f37209d5167821dfaae27bf9323157a1dd89cfc7ef8a089"},"schema_version":"1.0","source":{"id":"1010.4271","kind":"arxiv","version":1}},"canonical_sha256":"6423988ebc67a807e9689acf9131b94a2a81e611addb042ea075b68253263614","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6423988ebc67a807e9689acf9131b94a2a81e611addb042ea075b68253263614","first_computed_at":"2026-05-18T04:38:59.530169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:59.530169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j9uOZIYt4AWwjLPytRqd54vEUNR6ex7sZiQBpInAsHMkzTfAvnN/A9U6bDKqGxuYkQMHHg0gI40OiJzw7a27BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:59.530841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.4271","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67d91be57ca4da5aeea357452f7c9a71c09abf5d95d9a93df23798b124b3b5d3","sha256:5e8b3112de3eb1f4e6cfe92c5a1e451cd55335b88233cbffc8ac447c9740d568"],"state_sha256":"9197a7aab2912a7f92a818bedeaaf8cf42cf6d496614b7ba6eb981f9bfbab35d"}