{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2FA63VAANMKQVTQPY2SFVNSU4H","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":"861def73cdfff0a3e532b80026250da8caeb60540229f052bec390332bac0a22","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-04-05T09:18:08Z","title_canon_sha256":"c1f2d61403678fa2f20d7f759c56ee453f43bd2e3b57024abee3fcc5e6cf2d01"},"schema_version":"1.0","source":{"id":"2504.04117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.04117","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"arxiv_version","alias_value":"2504.04117v1","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.04117","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_12","alias_value":"2FA63VAANMKQ","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_16","alias_value":"2FA63VAANMKQVTQP","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_8","alias_value":"2FA63VAA","created_at":"2026-06-19T16:10:29Z"}],"graph_snapshots":[{"event_id":"sha256:aec74c4164cd4dd00c9ecb7ecec741a29d1e8a6735f2d67d95666d34b50c03ec","target":"graph","created_at":"2026-06-19T16:10:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.04117/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that no matter what subset of a normed space is given, a typical 1-Lipschitz mapping into a Banach space is non-differentiable at a typical point of the set in a very strong sense: the derivative ratio approximates, on arbitrary small scales, every linear operator of norm at most 1.\n  For subsets of finite-dimensional normed spaces which can be covered by a countable union of closed purely unrectifiable sets this extreme non-differentiability holds for a typical Lipschitz mapping at every point.\n  Both results are new even for Lipschitz mappings with a finite-dimensional co-domain.","authors_text":"Michael Dymond, Olga Maleva","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-04-05T09:18:08Z","title":"Extreme non-differentiability of typical Lipschitz mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.04117","kind":"arxiv","version":1},"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":"sha256:04b78ee219896082a87a76b66a19dd3db6ddadb940a0813027cf14c4f7a2d046","target":"record","created_at":"2026-06-19T16:10:29Z","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":"861def73cdfff0a3e532b80026250da8caeb60540229f052bec390332bac0a22","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-04-05T09:18:08Z","title_canon_sha256":"c1f2d61403678fa2f20d7f759c56ee453f43bd2e3b57024abee3fcc5e6cf2d01"},"schema_version":"1.0","source":{"id":"2504.04117","kind":"arxiv","version":1}},"canonical_sha256":"d141edd4006b150ace0fc6a45ab654e1e31fa861b891a825431c925562825c0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d141edd4006b150ace0fc6a45ab654e1e31fa861b891a825431c925562825c0e","first_computed_at":"2026-06-19T16:10:29.583001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:29.583001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xg+kye0Jb72txY7iAMDTZhbbbrM7O2WuA1kp7qMfN+v8VhW7FwZBmu2nyHXi17udYzNyRyZyvBV8r0bWwMeNCw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:29.583434Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.04117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04b78ee219896082a87a76b66a19dd3db6ddadb940a0813027cf14c4f7a2d046","sha256:aec74c4164cd4dd00c9ecb7ecec741a29d1e8a6735f2d67d95666d34b50c03ec"],"state_sha256":"ddff6f0f3c61d6e9efa498a08be5e1afc4a886b5b318da39cfdc53c0da7424ff"}