{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2PRCA43AOHPGP43RF5MZ2DP6K2","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":"6561dd5337ae0948afd2aa3faac21b6cde0a970e228eff4012753188d2876693","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-29T16:01:42Z","title_canon_sha256":"73ca5345764e3a2bedb52d2c9865b94a36d04c2e4376c67306aa15fb4d011b30"},"schema_version":"1.0","source":{"id":"1603.03467","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03467","created_at":"2026-05-18T01:19:15Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03467v1","created_at":"2026-05-18T01:19:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03467","created_at":"2026-05-18T01:19:15Z"},{"alias_kind":"pith_short_12","alias_value":"2PRCA43AOHPG","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2PRCA43AOHPGP43R","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2PRCA43A","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:da8bd9b4108edd58ce79fb8d7367e29ff13b91bd3ae8b5a1685c02f247df27bb","target":"graph","created_at":"2026-05-18T01:19:15Z","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 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","authors_text":"Simon Blatt","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-29T16:01:42Z","title":"Curves between Lipschitz and $C^1$ and their relation to geometric knot theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03467","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:dd3711dcdc65f5b0985b0ba7c62811bce9ba5effb826a4619c82715240833100","target":"record","created_at":"2026-05-18T01:19:15Z","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":"6561dd5337ae0948afd2aa3faac21b6cde0a970e228eff4012753188d2876693","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-29T16:01:42Z","title_canon_sha256":"73ca5345764e3a2bedb52d2c9865b94a36d04c2e4376c67306aa15fb4d011b30"},"schema_version":"1.0","source":{"id":"1603.03467","kind":"arxiv","version":1}},"canonical_sha256":"d3e220736071de67f3712f599d0dfe568d28f0a2f671d34aa69b9bb0d6a6daad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3e220736071de67f3712f599d0dfe568d28f0a2f671d34aa69b9bb0d6a6daad","first_computed_at":"2026-05-18T01:19:15.557259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:15.557259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZAIBKTvO3Y48WxBcEeXRSQ9D9rG2yireGFUjTPM/q+VQu/Suq+EuiMvoB68N4X7Rwzy6uXK/nUf1fThUrmmTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:15.557643Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.03467","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd3711dcdc65f5b0985b0ba7c62811bce9ba5effb826a4619c82715240833100","sha256:da8bd9b4108edd58ce79fb8d7367e29ff13b91bd3ae8b5a1685c02f247df27bb"],"state_sha256":"ea349c4ebce336fb93c219e2c5986a738d0807a85e84f2b7155ac1fa13ee5d63"}