{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2MQ3CONEAT3SLCTNMPOUCFB6IV","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":"2db5c39efe8468daf852576a5c0a2ef7c5bb6917709f7a3cc2a6430f1360158c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-18T17:47:38Z","title_canon_sha256":"ef32ca04cbcc43930654972a5d515f437be4a75fc78bff5bc866015bbe8a28e7"},"schema_version":"1.0","source":{"id":"1707.05764","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05764","created_at":"2026-05-18T00:27:00Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05764v2","created_at":"2026-05-18T00:27:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05764","created_at":"2026-05-18T00:27:00Z"},{"alias_kind":"pith_short_12","alias_value":"2MQ3CONEAT3S","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2MQ3CONEAT3SLCTN","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2MQ3CONE","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:08a0b6b1dfe227950f977c379d0904749a35b8eb9355434df4b426128c8fd658","target":"graph","created_at":"2026-05-18T00:27:00Z","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 every $p\\in(1,\\infty)$ there is a natural notion of topological degree for maps in $W^{1/p,p}({\\mathbb S}^1;{\\mathbb S}^1)$ which allows us to write that space as a disjoint union of classes, $W^{1/p,p}({\\mathbb S}^1;{\\mathbb S}^1)=\\bigcup_{d\\in{\\mathbb Z}}\\mathcal{E}_d$. For every pair $d_1,d_2\\in {\\mathbb Z}$, we show that the distance $\\text{Dist}_{W^{1/p,p}}({\\mathcal\n  E}_{d_1}, {\\mathcal E}_{d_2}):=\\sup_{f\\in{\\mathcal E}_{d_1}}\\ \\inf_{g\\in{\\mathcal E}_{d_2}}\\ d_{W^{1/p,p}}(f, g)$ equals the minimal $W^{1/p,p}$-energy in $\\mathcal{E}_{d_1-d_2}$. In the special case $p=2$ we deduce fro","authors_text":"Itai Shafrir","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-18T17:47:38Z","title":"On the distance between homotopy classes in $W^{1/p,p}({\\mathbb S}^1;{\\mathbb S}^1)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05764","kind":"arxiv","version":2},"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":"sha256:35390a0d22a1c3fb7d77e08e2463b2a0ef7f8e0a91de36db99348170d3439d9a","target":"record","created_at":"2026-05-18T00:27:00Z","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":"2db5c39efe8468daf852576a5c0a2ef7c5bb6917709f7a3cc2a6430f1360158c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-18T17:47:38Z","title_canon_sha256":"ef32ca04cbcc43930654972a5d515f437be4a75fc78bff5bc866015bbe8a28e7"},"schema_version":"1.0","source":{"id":"1707.05764","kind":"arxiv","version":2}},"canonical_sha256":"d321b139a404f7258a6d63dd41143e45597c54e740b6f4a040ad3a274ca667c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d321b139a404f7258a6d63dd41143e45597c54e740b6f4a040ad3a274ca667c5","first_computed_at":"2026-05-18T00:27:00.402745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:00.402745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9KdAZAN5e+dIjidehMBD4ti/dgIz9XCMm54S94TIlts1twQav+qiRZJSD2NJoTQqRIlMd0T2zTzze3D/zcPFDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:00.403473Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.05764","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35390a0d22a1c3fb7d77e08e2463b2a0ef7f8e0a91de36db99348170d3439d9a","sha256:08a0b6b1dfe227950f977c379d0904749a35b8eb9355434df4b426128c8fd658"],"state_sha256":"54ddf5f612d39ea468a1b0a113037f4674f434a4e1e777dedcf779b6c176e63a"}