{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:24GYSV54R5QI3RPTKXSWGS6T4C","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":"9c0af5b1a910200547ffaae6bfdb9f77c220418bb1c754f507000530da2b1815","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-28T20:17:55Z","title_canon_sha256":"928c5870b8cf7cefc40937546d4c73b85b6865537005625f8b85e722dc105f60"},"schema_version":"1.0","source":{"id":"1711.11433","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11433","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11433v2","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11433","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"pith_short_12","alias_value":"24GYSV54R5QI","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"24GYSV54R5QI3RPT","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"24GYSV54","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:ddf9fd3636a84dae7118931e5aa5089e084b9be4a46a916ba5250d96dc64f7f6","target":"graph","created_at":"2026-05-17T23:46:55Z","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 show that every model filiform group $\\mathbb{E}_{n}$ contains a measure zero set $N$ such that every Lipschitz map $f\\colon \\mathbb{E}_{n}\\to \\mathbb{R}$ is differentiable at some point of $N$. Model filiform groups are a class of Carnot groups which can have arbitrarily high step. Essential to our work is the question of whether existence of an (almost) maximal directional derivative $Ef(x)$ in a Carnot group implies differentiability of a Lipschitz map $f$ at $x$. We show that such an implication is valid in model Filiform groups except for a one-dimensional subspace of horizontal direct","authors_text":"Andrea Pinamonti, Gareth Speight","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-28T20:17:55Z","title":"Universal Differentiability Sets in Carnot Groups of Arbitrarily High Step"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11433","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":"sha256:758b2cd436e89f4208174f2da7ee3997ff2c0d2c6b401b9920d6a1f9342fe950","target":"record","created_at":"2026-05-17T23:46:55Z","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":"9c0af5b1a910200547ffaae6bfdb9f77c220418bb1c754f507000530da2b1815","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-28T20:17:55Z","title_canon_sha256":"928c5870b8cf7cefc40937546d4c73b85b6865537005625f8b85e722dc105f60"},"schema_version":"1.0","source":{"id":"1711.11433","kind":"arxiv","version":2}},"canonical_sha256":"d70d8957bc8f608dc5f355e5634bd3e08634fbecf66d7d47ff926ec14c018176","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d70d8957bc8f608dc5f355e5634bd3e08634fbecf66d7d47ff926ec14c018176","first_computed_at":"2026-05-17T23:46:55.560074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:55.560074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/A8roBwtGGt148kA6PPajMuxcFh68Iyl2hytvz9lBxPxVNLoS4vuEX1nv9GM7xaboiMZpepjI55JVIXvbyCZDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:55.560749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.11433","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:758b2cd436e89f4208174f2da7ee3997ff2c0d2c6b401b9920d6a1f9342fe950","sha256:ddf9fd3636a84dae7118931e5aa5089e084b9be4a46a916ba5250d96dc64f7f6"],"state_sha256":"d5e9a5933e0b9bd66b10792469a2566366f4f0019aa6c1d3059456c6373502c0"}