{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BUHSIRFXUMWXUUWTPKEPLTVXCF","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":"0bb5628f37ad6965af95b1a8c031a2a58f576572da49a7655a43b66c374a3db5","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-22T14:45:49Z","title_canon_sha256":"ad042986da7763d5f2d70637cb4457de1a7cf757c7b27c4b9df4e5e836874f68"},"schema_version":"1.0","source":{"id":"1109.4831","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4831","created_at":"2026-05-18T04:12:32Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4831v1","created_at":"2026-05-18T04:12:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4831","created_at":"2026-05-18T04:12:32Z"},{"alias_kind":"pith_short_12","alias_value":"BUHSIRFXUMWX","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BUHSIRFXUMWXUUWT","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BUHSIRFX","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:e74c4fa895f8860b74b8f094bc424085a289ee999497ebc509f1498f75d38530","target":"graph","created_at":"2026-05-18T04:12:32Z","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":"In the paper we investigate the degree and the homotopy theory of Orlicz-Sobolev mappings $W^{1,P}(M,N)$ between manifolds, where the Young function $P$ satisfies a divergence condition and forms a slightly larger space than $W^{1,n}$, $n=\\dim M$. In particular, we prove that if $M$ and $N$ are compact oriented manifolds without boundary and $\\dim M=\\dim N=n$, then the degree is well defined in $W^{1,P}(M,N)$ if and only if the universal cover of $N$ is not a rational homology sphere, and in the case $n=4$, if and only if $N$ is not homeomorphic to $S^4$.","authors_text":"Pawel Goldstein, Piotr Hajlasz","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-22T14:45:49Z","title":"Sobolev mappings, degree, homotopy classes and rational homology spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4831","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":"sha256:83ab05a96875972484e282b3be36c8472b364b2ff8d2d643844426a7e689cfd4","target":"record","created_at":"2026-05-18T04:12:32Z","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":"0bb5628f37ad6965af95b1a8c031a2a58f576572da49a7655a43b66c374a3db5","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-22T14:45:49Z","title_canon_sha256":"ad042986da7763d5f2d70637cb4457de1a7cf757c7b27c4b9df4e5e836874f68"},"schema_version":"1.0","source":{"id":"1109.4831","kind":"arxiv","version":1}},"canonical_sha256":"0d0f2444b7a32d7a52d37a88f5ceb7116639df4b5938fd1fefc5902b895c6f83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d0f2444b7a32d7a52d37a88f5ceb7116639df4b5938fd1fefc5902b895c6f83","first_computed_at":"2026-05-18T04:12:32.827530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:32.827530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KyK2uR2MvnQHiBUSDq6+zsPlM5G81fRdJ1dxF5OixpYi1aYdrZzh10bTPO/LLoBTKbd51nNFGdUKw3oMK0O2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:32.828045Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4831","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83ab05a96875972484e282b3be36c8472b364b2ff8d2d643844426a7e689cfd4","sha256:e74c4fa895f8860b74b8f094bc424085a289ee999497ebc509f1498f75d38530"],"state_sha256":"5de69b9b31d4bef324e5c19fc5ce577de4c7c7a28d3e4b600ad32670a9e720d8"}