{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GVCMPGEXXPBIZ2LNW3G3FESQD4","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":"16704305844f7c3caccc7b93c20a7141150fa2ca6cfd7109ed692594b5163bbc","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-07T14:20:17Z","title_canon_sha256":"3fd1a7ff6b129080fad995f3591f5965f845abb379e561c892173cec8ff0e806"},"schema_version":"1.0","source":{"id":"1510.01954","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01954","created_at":"2026-05-18T01:17:07Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01954v2","created_at":"2026-05-18T01:17:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01954","created_at":"2026-05-18T01:17:07Z"},{"alias_kind":"pith_short_12","alias_value":"GVCMPGEXXPBI","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GVCMPGEXXPBIZ2LN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GVCMPGEX","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:08ef7c000f72fedb4ab93ebfea52c9f990a671600875eb156340103ae630df7e","target":"graph","created_at":"2026-05-18T01:17:07Z","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 prove that every immersed $C^2$-curve $\\gamma$ in $\\mathbb R^n$, $n\\geqslant 3$ with curvature $k_{\\gamma}$ can be $C^1$-approximated by immersed $C^2$-curves having prescribed curvature $k>k_{\\gamma}$. The approximating curves satisfy a $C^1$-dense $h$-principle. As an application we obtain the existence of $C^2$-knots of arbitrary positive curvature in each isotopy class, which generalizes a similar result by McAtee for $C^2$-knots of constant curvature.","authors_text":"Micha Wasem","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-07T14:20:17Z","title":"$h$-Principle for Curves with Prescribed Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01954","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:ac8259e857f9cdc5d3375aa1614eeaaf764670cf790dc3d24657466e6c76c99e","target":"record","created_at":"2026-05-18T01:17:07Z","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":"16704305844f7c3caccc7b93c20a7141150fa2ca6cfd7109ed692594b5163bbc","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-07T14:20:17Z","title_canon_sha256":"3fd1a7ff6b129080fad995f3591f5965f845abb379e561c892173cec8ff0e806"},"schema_version":"1.0","source":{"id":"1510.01954","kind":"arxiv","version":2}},"canonical_sha256":"3544c79897bbc28ce96db6cdb292501f357a1d940bb1b4c17b158b12bb2cc6ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3544c79897bbc28ce96db6cdb292501f357a1d940bb1b4c17b158b12bb2cc6ba","first_computed_at":"2026-05-18T01:17:07.912675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:07.912675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HgPy90xTZ42gsfy4ulZl1GT2kAXVcnarYlc8pQ+PfCT2ytmmsOR3i8w8ynAAIKy/9I4wvcA39zHWZfOz6eNsAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:07.913239Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.01954","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac8259e857f9cdc5d3375aa1614eeaaf764670cf790dc3d24657466e6c76c99e","sha256:08ef7c000f72fedb4ab93ebfea52c9f990a671600875eb156340103ae630df7e"],"state_sha256":"c1e7fb7d410256a5f04460d3a4df665ec75ffcce71e54503a15f7ffef2ae2ada"}