{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:DOWOLM6K4PRN46SOLB2IBKYZJW","short_pith_number":"pith:DOWOLM6K","schema_version":"1.0","canonical_sha256":"1bace5b3cae3e2de7a4e587480ab194d845e26843f3d2660b2e4a1a33a4e1776","source":{"kind":"arxiv","id":"1406.2485","version":3},"attestation_state":"computed","paper":{"title":"Lifting differentiable curves from orbit spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DG","authors_text":"Adam Parusinski, Armin Rainer","submitted_at":"2014-06-10T09:49:10Z","abstract_excerpt":"Let $\\rho : G \\rightarrow \\operatorname{O}(V)$ be a real finite dimensional orthogonal representation of a compact Lie group, let $\\sigma = (\\sigma_1,\\ldots,\\sigma_n) : V \\to \\mathbb R^n$, where $\\sigma_1,\\ldots,\\sigma_n$ form a minimal system of homogeneous generators of the $G$-invariant polynomials on $V$, and set $d = \\max_i \\operatorname{deg} \\sigma_i$. We prove that for each $C^{d-1,1}$-curve $c$ in $\\sigma(V) \\subseteq \\mathbb R^n$ there exits a locally Lipschitz lift over $\\sigma$, i.e., a locally Lipschitz curve $\\overline c$ in $V$ so that $c = \\sigma \\circ \\overline c$, and we obtai"},"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":"1406.2485","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-06-10T09:49:10Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"a3920e641eaf79e931d00bdc14cc5b0d337ebe9d0228f65e7ad869cbfed2a08c","abstract_canon_sha256":"941aea374c18e6556e8e8752326c9299b66011aef95173b738a18955c3b905e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:33.939204Z","signature_b64":"iDBekLYgT5nUXP3jQ4n7QTBtrlw43WFpPImnBAZrJGW8+P46/RxliLJCnf30vro1WgGTu7aT0DALT1719VNEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bace5b3cae3e2de7a4e587480ab194d845e26843f3d2660b2e4a1a33a4e1776","last_reissued_at":"2026-05-18T00:29:33.938622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:33.938622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lifting differentiable curves from orbit spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DG","authors_text":"Adam Parusinski, Armin Rainer","submitted_at":"2014-06-10T09:49:10Z","abstract_excerpt":"Let $\\rho : G \\rightarrow \\operatorname{O}(V)$ be a real finite dimensional orthogonal representation of a compact Lie group, let $\\sigma = (\\sigma_1,\\ldots,\\sigma_n) : V \\to \\mathbb R^n$, where $\\sigma_1,\\ldots,\\sigma_n$ form a minimal system of homogeneous generators of the $G$-invariant polynomials on $V$, and set $d = \\max_i \\operatorname{deg} \\sigma_i$. We prove that for each $C^{d-1,1}$-curve $c$ in $\\sigma(V) \\subseteq \\mathbb R^n$ there exits a locally Lipschitz lift over $\\sigma$, i.e., a locally Lipschitz curve $\\overline c$ in $V$ so that $c = \\sigma \\circ \\overline c$, and we obtai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2485","kind":"arxiv","version":3},"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":"1406.2485","created_at":"2026-05-18T00:29:33.938747+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.2485v3","created_at":"2026-05-18T00:29:33.938747+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2485","created_at":"2026-05-18T00:29:33.938747+00:00"},{"alias_kind":"pith_short_12","alias_value":"DOWOLM6K4PRN","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"DOWOLM6K4PRN46SO","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"DOWOLM6K","created_at":"2026-05-18T12:28:25.294606+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/DOWOLM6K4PRN46SOLB2IBKYZJW","json":"https://pith.science/pith/DOWOLM6K4PRN46SOLB2IBKYZJW.json","graph_json":"https://pith.science/api/pith-number/DOWOLM6K4PRN46SOLB2IBKYZJW/graph.json","events_json":"https://pith.science/api/pith-number/DOWOLM6K4PRN46SOLB2IBKYZJW/events.json","paper":"https://pith.science/paper/DOWOLM6K"},"agent_actions":{"view_html":"https://pith.science/pith/DOWOLM6K4PRN46SOLB2IBKYZJW","download_json":"https://pith.science/pith/DOWOLM6K4PRN46SOLB2IBKYZJW.json","view_paper":"https://pith.science/paper/DOWOLM6K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.2485&json=true","fetch_graph":"https://pith.science/api/pith-number/DOWOLM6K4PRN46SOLB2IBKYZJW/graph.json","fetch_events":"https://pith.science/api/pith-number/DOWOLM6K4PRN46SOLB2IBKYZJW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DOWOLM6K4PRN46SOLB2IBKYZJW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DOWOLM6K4PRN46SOLB2IBKYZJW/action/storage_attestation","attest_author":"https://pith.science/pith/DOWOLM6K4PRN46SOLB2IBKYZJW/action/author_attestation","sign_citation":"https://pith.science/pith/DOWOLM6K4PRN46SOLB2IBKYZJW/action/citation_signature","submit_replication":"https://pith.science/pith/DOWOLM6K4PRN46SOLB2IBKYZJW/action/replication_record"}},"created_at":"2026-05-18T00:29:33.938747+00:00","updated_at":"2026-05-18T00:29:33.938747+00:00"}