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Let g : S^p x S^q -> R^m be an embedding such that g |_{a x S^q} : a x S^q -> R^m - g (b x S^q) is null-homotopic for some pair of different points a,b in S^p.\n  Theorem. If h is an autodiffeomorphism of S^p x S^q identical on a neighborhood of a x S^q for some a\\in S^p and p<q and 2m<3p+3q+5, then g h is isotopic to g.\n  Let N be an oriented (p+q)-manifold and f : N -> R^m, "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1402.1853","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-02-08T13:33:13Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"7c16616b345e240a98620919ea4e5ae2fa316dec83484784d75372861998a258","abstract_canon_sha256":"c949619505c55032ef2eac369ab88222a7565ffded5543de149e97a4a40e6d0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:32.994389Z","signature_b64":"Cr/Nf0grNXcHfsuCpCG3My4GzIYzKxDREyOYnK5x44kMtowcFVYmruB7ewxvQ6SFiB8eXc91WvX72t1Xn4W0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fafc2627a04d86fa83428ca231180040a4eb81cc9743fc610735db0435868d2","last_reissued_at":"2026-05-18T00:04:32.993799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:32.993799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"How do autodiffeomorphisms act on embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"A. Skopenkov","submitted_at":"2014-02-08T13:33:13Z","abstract_excerpt":"We work in the smooth category. The following problem was suggested by E. Rees in 2002: describe the precomposition action of self-diffeomorphisms of S^p x S^q on the set of isotopy classes of embeddings S^p x S^q -> R^m. Let g : S^p x S^q -> R^m be an embedding such that g |_{a x S^q} : a x S^q -> R^m - g (b x S^q) is null-homotopic for some pair of different points a,b in S^p.\n  Theorem. If h is an autodiffeomorphism of S^p x S^q identical on a neighborhood of a x S^q for some a\\in S^p and p<q and 2m<3p+3q+5, then g h is isotopic to g.\n  Let N be an oriented (p+q)-manifold and f : N -> R^m, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1853","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1402.1853","created_at":"2026-05-18T00:04:32.993896+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.1853v2","created_at":"2026-05-18T00:04:32.993896+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1853","created_at":"2026-05-18T00:04:32.993896+00:00"},{"alias_kind":"pith_short_12","alias_value":"L6X4EYT2ATMG","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"L6X4EYT2ATMG7KBU","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"L6X4EYT2","created_at":"2026-05-18T12:28:35.611951+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L6X4EYT2ATMG7KBUFDFCGEMAAQ","json":"https://pith.science/pith/L6X4EYT2ATMG7KBUFDFCGEMAAQ.json","graph_json":"https://pith.science/api/pith-number/L6X4EYT2ATMG7KBUFDFCGEMAAQ/graph.json","events_json":"https://pith.science/api/pith-number/L6X4EYT2ATMG7KBUFDFCGEMAAQ/events.json","paper":"https://pith.science/paper/L6X4EYT2"},"agent_actions":{"view_html":"https://pith.science/pith/L6X4EYT2ATMG7KBUFDFCGEMAAQ","download_json":"https://pith.science/pith/L6X4EYT2ATMG7KBUFDFCGEMAAQ.json","view_paper":"https://pith.science/paper/L6X4EYT2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.1853&json=true","fetch_graph":"https://pith.science/api/pith-number/L6X4EYT2ATMG7KBUFDFCGEMAAQ/graph.json","fetch_events":"https://pith.science/api/pith-number/L6X4EYT2ATMG7KBUFDFCGEMAAQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L6X4EYT2ATMG7KBUFDFCGEMAAQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L6X4EYT2ATMG7KBUFDFCGEMAAQ/action/storage_attestation","attest_author":"https://pith.science/pith/L6X4EYT2ATMG7KBUFDFCGEMAAQ/action/author_attestation","sign_citation":"https://pith.science/pith/L6X4EYT2ATMG7KBUFDFCGEMAAQ/action/citation_signature","submit_replication":"https://pith.science/pith/L6X4EYT2ATMG7KBUFDFCGEMAAQ/action/replication_record"}},"created_at":"2026-05-18T00:04:32.993896+00:00","updated_at":"2026-05-18T00:04:32.993896+00:00"}