{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TOAD2BJKUHUTLOKD2W5IPL2QB7","short_pith_number":"pith:TOAD2BJK","canonical_record":{"source":{"id":"1402.2429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-02-11T10:28:26Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"9841c786661e24434a92623361b46ee1dbdf47677c8bfc5fecd1582df5ee3d89","abstract_canon_sha256":"7c5a5444db2e913af376e8d7f6cc50af56f0bc07ab3ffbba5d9bf6af279ebc77"},"schema_version":"1.0"},"canonical_sha256":"9b803d052aa1e935b943d5ba87af500fc80f2aa5f516c5194e5ed05fbd0ad0df","source":{"kind":"arxiv","id":"1402.2429","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2429","created_at":"2026-05-18T02:51:56Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2429v1","created_at":"2026-05-18T02:51:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2429","created_at":"2026-05-18T02:51:56Z"},{"alias_kind":"pith_short_12","alias_value":"TOAD2BJKUHUT","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TOAD2BJKUHUTLOKD","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TOAD2BJK","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TOAD2BJKUHUTLOKD2W5IPL2QB7","target":"record","payload":{"canonical_record":{"source":{"id":"1402.2429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-02-11T10:28:26Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"9841c786661e24434a92623361b46ee1dbdf47677c8bfc5fecd1582df5ee3d89","abstract_canon_sha256":"7c5a5444db2e913af376e8d7f6cc50af56f0bc07ab3ffbba5d9bf6af279ebc77"},"schema_version":"1.0"},"canonical_sha256":"9b803d052aa1e935b943d5ba87af500fc80f2aa5f516c5194e5ed05fbd0ad0df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:56.670567Z","signature_b64":"thLViR9L98Ge+PcXFOyq1/c0crZcSjYzdUeay0MayP8vrRJejYfGjgKCkxWh+GJ8y3rg567r8mMdjC58++75AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b803d052aa1e935b943d5ba87af500fc80f2aa5f516c5194e5ed05fbd0ad0df","last_reissued_at":"2026-05-18T02:51:56.670110Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:56.670110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.2429","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SUOLea2zqlxOOfVg35Mz1nk7BTWiE9cPJYIS80yfLZLLxp3dLWaMY3taKLhxkNJXzGE4LDzgidO49+PzWV0BCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:10:23.581608Z"},"content_sha256":"d611d3a4e5523f5729a20afc13ebefb65ecf4060e371823e99653fb583162370","schema_version":"1.0","event_id":"sha256:d611d3a4e5523f5729a20afc13ebefb65ecf4060e371823e99653fb583162370"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TOAD2BJKUHUTLOKD2W5IPL2QB7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algorithmic aspects of Lipschitz functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.LO","authors_text":"Andr\\'e Nies, Bj{\\o}rn Kjos-Hanssen, Cameron Freer, Frank Stephan","submitted_at":"2014-02-11T10:28:26Z","abstract_excerpt":"We characterize the variation functions of computable Lipschitz functions. We show that a real z is computably random if and only if every computable Lipschitz function is differentiable at z. Beyond these principal results, we show that a real z is Schnorr random if and only if every Lipschitz function with $L_1$-computable derivative is differentiable at z."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2429","kind":"arxiv","version":1},"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":"2026-05-18T02:51:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wxjBacD9pd1UwZ34idywaZcbrfL/XUrc+3UdCc4bUeTfoy29wnMmlzDfcmRFo+HrYO7OUO2Uc7BnQVwG+SNXDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:10:23.582011Z"},"content_sha256":"ec085e11b22c658c83ac4ad2720b1a816da1c6c03e27c33162eefd8c7fdc3e6b","schema_version":"1.0","event_id":"sha256:ec085e11b22c658c83ac4ad2720b1a816da1c6c03e27c33162eefd8c7fdc3e6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TOAD2BJKUHUTLOKD2W5IPL2QB7/bundle.json","state_url":"https://pith.science/pith/TOAD2BJKUHUTLOKD2W5IPL2QB7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TOAD2BJKUHUTLOKD2W5IPL2QB7/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":"2026-05-27T22:10:23Z","links":{"resolver":"https://pith.science/pith/TOAD2BJKUHUTLOKD2W5IPL2QB7","bundle":"https://pith.science/pith/TOAD2BJKUHUTLOKD2W5IPL2QB7/bundle.json","state":"https://pith.science/pith/TOAD2BJKUHUTLOKD2W5IPL2QB7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TOAD2BJKUHUTLOKD2W5IPL2QB7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TOAD2BJKUHUTLOKD2W5IPL2QB7","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":"7c5a5444db2e913af376e8d7f6cc50af56f0bc07ab3ffbba5d9bf6af279ebc77","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-02-11T10:28:26Z","title_canon_sha256":"9841c786661e24434a92623361b46ee1dbdf47677c8bfc5fecd1582df5ee3d89"},"schema_version":"1.0","source":{"id":"1402.2429","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2429","created_at":"2026-05-18T02:51:56Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2429v1","created_at":"2026-05-18T02:51:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2429","created_at":"2026-05-18T02:51:56Z"},{"alias_kind":"pith_short_12","alias_value":"TOAD2BJKUHUT","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TOAD2BJKUHUTLOKD","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TOAD2BJK","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:ec085e11b22c658c83ac4ad2720b1a816da1c6c03e27c33162eefd8c7fdc3e6b","target":"graph","created_at":"2026-05-18T02:51:56Z","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 characterize the variation functions of computable Lipschitz functions. We show that a real z is computably random if and only if every computable Lipschitz function is differentiable at z. Beyond these principal results, we show that a real z is Schnorr random if and only if every Lipschitz function with $L_1$-computable derivative is differentiable at z.","authors_text":"Andr\\'e Nies, Bj{\\o}rn Kjos-Hanssen, Cameron Freer, Frank Stephan","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-02-11T10:28:26Z","title":"Algorithmic aspects of Lipschitz functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2429","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:d611d3a4e5523f5729a20afc13ebefb65ecf4060e371823e99653fb583162370","target":"record","created_at":"2026-05-18T02:51:56Z","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":"7c5a5444db2e913af376e8d7f6cc50af56f0bc07ab3ffbba5d9bf6af279ebc77","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-02-11T10:28:26Z","title_canon_sha256":"9841c786661e24434a92623361b46ee1dbdf47677c8bfc5fecd1582df5ee3d89"},"schema_version":"1.0","source":{"id":"1402.2429","kind":"arxiv","version":1}},"canonical_sha256":"9b803d052aa1e935b943d5ba87af500fc80f2aa5f516c5194e5ed05fbd0ad0df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b803d052aa1e935b943d5ba87af500fc80f2aa5f516c5194e5ed05fbd0ad0df","first_computed_at":"2026-05-18T02:51:56.670110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:56.670110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"thLViR9L98Ge+PcXFOyq1/c0crZcSjYzdUeay0MayP8vrRJejYfGjgKCkxWh+GJ8y3rg567r8mMdjC58++75AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:56.670567Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.2429","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d611d3a4e5523f5729a20afc13ebefb65ecf4060e371823e99653fb583162370","sha256:ec085e11b22c658c83ac4ad2720b1a816da1c6c03e27c33162eefd8c7fdc3e6b"],"state_sha256":"14a7ca51aff06bf62978c709b5df26727630c8526738d353c0f0fa4dd2ab5952"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R6NeYoMK2MPRLGhMygY+J94TnYmxupjLoaAgvDAFCDT8wtOM/Y5fEDk6FcHjmU6S67G6NgS0vXJW0glSefDXCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:10:23.584195Z","bundle_sha256":"12ace4c3a40b4540a848c763614b563e11147a8405a9c98225705739ef401546"}}