{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GGKHSYBJUTNYFO4V4VP3HMQ4I5","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":"687a6900da1c4844e4465410d9f2c15d901c7883bf2f5d10d7c2425d35ec728e","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-09-18T16:57:56Z","title_canon_sha256":"b234296accc6b0ad039306a88800904b7dd33d687820f097a10e53f480a79f86"},"schema_version":"1.0","source":{"id":"1809.06829","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06829","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06829v3","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06829","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"pith_short_12","alias_value":"GGKHSYBJUTNY","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GGKHSYBJUTNYFO4V","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GGKHSYBJ","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:48608d7521c5a21d4badf1fd4cc278bf66a05d3712269c478745f9222c2b13d3","target":"graph","created_at":"2026-05-17T23:50:38Z","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 a version of the implicit function theorem for Lipschitz mappings $f:\\mathbb{R}^{n+m}\\supset A \\to X$ into arbitrary metric spaces. As long as the pull-back of the Hausdorff content $\\mathcal{H}_{\\infty}^n$ by $f$ has positive upper $n$-density on a set of positive Lebesgue measure, then, there is a local diffeomorphism $G$ in $\\mathbb{R}^{n+m}$ and a Lipschitz map $\\pi:X\\to \\mathbb{R}^n$ such that $\\pi\\circ f\\circ G^{-1}$, when restricted to a certain subset of $A$ of positive measure, is a the orthogonal projection of $\\mathbb{R}^{n+m}$ onto the first $n$-coordinates. This may be se","authors_text":"Piotr Haj{\\l}asz, Scott Zimmerman","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-09-18T16:57:56Z","title":"An implicit function theorem for Lipschitz mappings into metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06829","kind":"arxiv","version":3},"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":"sha256:1f5308062fc36b31554b3967f725704a6a9d7a5b6900c1f108f41b68b18419de","target":"record","created_at":"2026-05-17T23:50:38Z","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":"687a6900da1c4844e4465410d9f2c15d901c7883bf2f5d10d7c2425d35ec728e","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-09-18T16:57:56Z","title_canon_sha256":"b234296accc6b0ad039306a88800904b7dd33d687820f097a10e53f480a79f86"},"schema_version":"1.0","source":{"id":"1809.06829","kind":"arxiv","version":3}},"canonical_sha256":"3194796029a4db82bb95e55fb3b21c47555eb264355f21d18a2925df07a88522","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3194796029a4db82bb95e55fb3b21c47555eb264355f21d18a2925df07a88522","first_computed_at":"2026-05-17T23:50:38.470875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:38.470875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UiCPVuTqx1VAMATbYTddx5ShnDmRVT7c7OkkqfN3HUSvgLZVPUZbAZfTBrhXRH5E27DIutG4TOlhceYsqmL9Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:38.471329Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.06829","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f5308062fc36b31554b3967f725704a6a9d7a5b6900c1f108f41b68b18419de","sha256:48608d7521c5a21d4badf1fd4cc278bf66a05d3712269c478745f9222c2b13d3"],"state_sha256":"7f2e67cfef96bae0eaddc60971ef1d25696bd0287e926dcb4c2ee90355e393c0"}