{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:2PRCA43AOHPGP43RF5MZ2DP6K2","short_pith_number":"pith:2PRCA43A","schema_version":"1.0","canonical_sha256":"d3e220736071de67f3712f599d0dfe568d28f0a2f671d34aa69b9bb0d6a6daad","source":{"kind":"arxiv","id":"1603.03467","version":1},"attestation_state":"computed","paper":{"title":"Curves between Lipschitz and $C^1$ and their relation to geometric knot theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Simon Blatt","submitted_at":"2016-02-29T16:01:42Z","abstract_excerpt":"In this article we investigate regular curves whose derivatives have vanishing mean oscillations. We show that smoothing these curves using a standard mollifier one gets regular curves again.\n  We apply this result to solve a couple of open problems. We show that curves with finite M\\\"obius energy can be approximated by smooth curves in the energy space $W^{\\frac 32,2}$ such that the energy converges which answers a question of He. Furthermore, we extend the result of Scholtes on the $\\Gamma$-convergence of the discrete M\\\"obius energies towards the M\\\"obius energy and prove conjectures of Ish"},"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":"1603.03467","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-29T16:01:42Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"73ca5345764e3a2bedb52d2c9865b94a36d04c2e4376c67306aa15fb4d011b30","abstract_canon_sha256":"6561dd5337ae0948afd2aa3faac21b6cde0a970e228eff4012753188d2876693"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:15.557643Z","signature_b64":"ZAIBKTvO3Y48WxBcEeXRSQ9D9rG2yireGFUjTPM/q+VQu/Suq+EuiMvoB68N4X7Rwzy6uXK/nUf1fThUrmmTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3e220736071de67f3712f599d0dfe568d28f0a2f671d34aa69b9bb0d6a6daad","last_reissued_at":"2026-05-18T01:19:15.557259Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:15.557259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Curves between Lipschitz and $C^1$ and their relation to geometric knot theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Simon Blatt","submitted_at":"2016-02-29T16:01:42Z","abstract_excerpt":"In this article we investigate regular curves whose derivatives have vanishing mean oscillations. We show that smoothing these curves using a standard mollifier one gets regular curves again.\n  We apply this result to solve a couple of open problems. We show that curves with finite M\\\"obius energy can be approximated by smooth curves in the energy space $W^{\\frac 32,2}$ such that the energy converges which answers a question of He. Furthermore, we extend the result of Scholtes on the $\\Gamma$-convergence of the discrete M\\\"obius energies towards the M\\\"obius energy and prove conjectures of Ish"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03467","kind":"arxiv","version":1},"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":"1603.03467","created_at":"2026-05-18T01:19:15.557325+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.03467v1","created_at":"2026-05-18T01:19:15.557325+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03467","created_at":"2026-05-18T01:19:15.557325+00:00"},{"alias_kind":"pith_short_12","alias_value":"2PRCA43AOHPG","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"2PRCA43AOHPGP43R","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"2PRCA43A","created_at":"2026-05-18T12:29:55.572404+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/2PRCA43AOHPGP43RF5MZ2DP6K2","json":"https://pith.science/pith/2PRCA43AOHPGP43RF5MZ2DP6K2.json","graph_json":"https://pith.science/api/pith-number/2PRCA43AOHPGP43RF5MZ2DP6K2/graph.json","events_json":"https://pith.science/api/pith-number/2PRCA43AOHPGP43RF5MZ2DP6K2/events.json","paper":"https://pith.science/paper/2PRCA43A"},"agent_actions":{"view_html":"https://pith.science/pith/2PRCA43AOHPGP43RF5MZ2DP6K2","download_json":"https://pith.science/pith/2PRCA43AOHPGP43RF5MZ2DP6K2.json","view_paper":"https://pith.science/paper/2PRCA43A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.03467&json=true","fetch_graph":"https://pith.science/api/pith-number/2PRCA43AOHPGP43RF5MZ2DP6K2/graph.json","fetch_events":"https://pith.science/api/pith-number/2PRCA43AOHPGP43RF5MZ2DP6K2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2PRCA43AOHPGP43RF5MZ2DP6K2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2PRCA43AOHPGP43RF5MZ2DP6K2/action/storage_attestation","attest_author":"https://pith.science/pith/2PRCA43AOHPGP43RF5MZ2DP6K2/action/author_attestation","sign_citation":"https://pith.science/pith/2PRCA43AOHPGP43RF5MZ2DP6K2/action/citation_signature","submit_replication":"https://pith.science/pith/2PRCA43AOHPGP43RF5MZ2DP6K2/action/replication_record"}},"created_at":"2026-05-18T01:19:15.557325+00:00","updated_at":"2026-05-18T01:19:15.557325+00:00"}