{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YGUCXJGWKNHPXGBBKST2FMT7H7","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":"4711450b8560e29ba8cad6abb20439a255747d0a6d3ef815cbfb56411c331955","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-15T09:06:56Z","title_canon_sha256":"9d30757846e9de7a663178fe82d0b2fc52354c3c592ffec1a1f216ffc115700c"},"schema_version":"1.0","source":{"id":"1606.04687","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04687","created_at":"2026-05-18T01:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04687v1","created_at":"2026-05-18T01:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04687","created_at":"2026-05-18T01:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"YGUCXJGWKNHP","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YGUCXJGWKNHPXGBB","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YGUCXJGW","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:31daaa3f1969f3f61d0c46f54a89b9fa52a9ae63f52eaaa6809610385acba4bb","target":"graph","created_at":"2026-05-18T01:12:24Z","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":"We introduce an equivalence relation on $W^{s,p}({\\mathbb S}^N;{\\mathbb S}^N)$ involving the topological degree, and we evaluate the distances (in the usual sense and in the Hausdorff sense) between the equivalence classes. In some special cases we even obtain exact formulas.","authors_text":"Haim Brezis, Itai Shafrir, Petru Mironescu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-15T09:06:56Z","title":"Distances between homotopy classes of $W^{s,p}({\\mathbb S}^N;{\\mathbb S}^N)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04687","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":"sha256:4794cdb94b9cbedb86ec8bca482b2be56d8b1330425b79f6815115f98c402f7f","target":"record","created_at":"2026-05-18T01:12:24Z","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":"4711450b8560e29ba8cad6abb20439a255747d0a6d3ef815cbfb56411c331955","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-15T09:06:56Z","title_canon_sha256":"9d30757846e9de7a663178fe82d0b2fc52354c3c592ffec1a1f216ffc115700c"},"schema_version":"1.0","source":{"id":"1606.04687","kind":"arxiv","version":1}},"canonical_sha256":"c1a82ba4d6534efb982154a7a2b27f3ff30ea2cc4c277d1d40dafa544bcc1150","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1a82ba4d6534efb982154a7a2b27f3ff30ea2cc4c277d1d40dafa544bcc1150","first_computed_at":"2026-05-18T01:12:24.580603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:24.580603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V+0u8tXCkgqeZusOPi9Wsd62AEB0bgmOKwcWTjRmRIW0Mw4MiRINpzFAmJtoWB9JcrAnCk8jAD6/44e8sps0Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:24.580932Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.04687","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4794cdb94b9cbedb86ec8bca482b2be56d8b1330425b79f6815115f98c402f7f","sha256:31daaa3f1969f3f61d0c46f54a89b9fa52a9ae63f52eaaa6809610385acba4bb"],"state_sha256":"ed24589a9e9fbf68ca1a50d4cacf9e2f11fc4e36cfed506c89442a907250d94e"}