{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:24GYSV54R5QI3RPTKXSWGS6T4C","short_pith_number":"pith:24GYSV54","canonical_record":{"source":{"id":"1711.11433","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-28T20:17:55Z","cross_cats_sorted":[],"title_canon_sha256":"928c5870b8cf7cefc40937546d4c73b85b6865537005625f8b85e722dc105f60","abstract_canon_sha256":"9c0af5b1a910200547ffaae6bfdb9f77c220418bb1c754f507000530da2b1815"},"schema_version":"1.0"},"canonical_sha256":"d70d8957bc8f608dc5f355e5634bd3e08634fbecf66d7d47ff926ec14c018176","source":{"kind":"arxiv","id":"1711.11433","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:24GYSV54R5QI3RPTKXSWGS6T4C","target":"record","payload":{"canonical_record":{"source":{"id":"1711.11433","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-28T20:17:55Z","cross_cats_sorted":[],"title_canon_sha256":"928c5870b8cf7cefc40937546d4c73b85b6865537005625f8b85e722dc105f60","abstract_canon_sha256":"9c0af5b1a910200547ffaae6bfdb9f77c220418bb1c754f507000530da2b1815"},"schema_version":"1.0"},"canonical_sha256":"d70d8957bc8f608dc5f355e5634bd3e08634fbecf66d7d47ff926ec14c018176","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:55.560749Z","signature_b64":"/A8roBwtGGt148kA6PPajMuxcFh68Iyl2hytvz9lBxPxVNLoS4vuEX1nv9GM7xaboiMZpepjI55JVIXvbyCZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d70d8957bc8f608dc5f355e5634bd3e08634fbecf66d7d47ff926ec14c018176","last_reissued_at":"2026-05-17T23:46:55.560074Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:55.560074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.11433","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xdoS8AvW1SExIjud+IZ0U91MGxxyzCrdMeCUsNyyB/6Rxmbgrds2Lef0pZaQS8ssfqb/NmLMpRotuVRoSajHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:27:08.873471Z"},"content_sha256":"758b2cd436e89f4208174f2da7ee3997ff2c0d2c6b401b9920d6a1f9342fe950","schema_version":"1.0","event_id":"sha256:758b2cd436e89f4208174f2da7ee3997ff2c0d2c6b401b9920d6a1f9342fe950"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:24GYSV54R5QI3RPTKXSWGS6T4C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal Differentiability Sets in Carnot Groups of Arbitrarily High Step","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andrea Pinamonti, Gareth Speight","submitted_at":"2017-11-28T20:17:55Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11433","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XFRe7RD1ygfK3qtbhU3rntRE0oUaTb8H2KEXlzG6kR7cvyJgxygH+eOqL4jsS9VO/ks4EeE1numrNOlymAyGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:27:08.873840Z"},"content_sha256":"ddf9fd3636a84dae7118931e5aa5089e084b9be4a46a916ba5250d96dc64f7f6","schema_version":"1.0","event_id":"sha256:ddf9fd3636a84dae7118931e5aa5089e084b9be4a46a916ba5250d96dc64f7f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/24GYSV54R5QI3RPTKXSWGS6T4C/bundle.json","state_url":"https://pith.science/pith/24GYSV54R5QI3RPTKXSWGS6T4C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/24GYSV54R5QI3RPTKXSWGS6T4C/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T03:27:08Z","links":{"resolver":"https://pith.science/pith/24GYSV54R5QI3RPTKXSWGS6T4C","bundle":"https://pith.science/pith/24GYSV54R5QI3RPTKXSWGS6T4C/bundle.json","state":"https://pith.science/pith/24GYSV54R5QI3RPTKXSWGS6T4C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/24GYSV54R5QI3RPTKXSWGS6T4C/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mDVEJcyKm9mYDgbBeQwOC2W2G8dj6M8L2vxnyrHGTOp+iZTIBGnqCy3SAvgHCuOCGqVWb1ds4hNV1xG2t40NDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T03:27:08.875803Z","bundle_sha256":"81c7962ef1b7085d8166f877d12f65a3b38e519b82f894407837104ac9b1b57e"}}