{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:XU2AF6YV67YOLEUF5MMBSJK2KV","short_pith_number":"pith:XU2AF6YV","canonical_record":{"source":{"id":"1906.10192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-24T19:35:40Z","cross_cats_sorted":[],"title_canon_sha256":"83485aba696b5d3be2dabb763fc25473c0c6b641d8d8335d9853c15c776fa8e9","abstract_canon_sha256":"c16129788ee5b11e0b5ff11275c33143ab21b13bdfb27f024ccbdfa16eb6805b"},"schema_version":"1.0"},"canonical_sha256":"bd3402fb15f7f0e59285eb1819255a55619a9308e64cf15801ff826692b17693","source":{"kind":"arxiv","id":"1906.10192","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.10192","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"arxiv_version","alias_value":"1906.10192v1","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10192","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"pith_short_12","alias_value":"XU2AF6YV67YO","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XU2AF6YV67YOLEUF","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XU2AF6YV","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:XU2AF6YV67YOLEUF5MMBSJK2KV","target":"record","payload":{"canonical_record":{"source":{"id":"1906.10192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-24T19:35:40Z","cross_cats_sorted":[],"title_canon_sha256":"83485aba696b5d3be2dabb763fc25473c0c6b641d8d8335d9853c15c776fa8e9","abstract_canon_sha256":"c16129788ee5b11e0b5ff11275c33143ab21b13bdfb27f024ccbdfa16eb6805b"},"schema_version":"1.0"},"canonical_sha256":"bd3402fb15f7f0e59285eb1819255a55619a9308e64cf15801ff826692b17693","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:31.969608Z","signature_b64":"ph/yAI+f5mnbfcgtkkssqgylc+3iYFCz9eIS6m6wz122ukL4g+t+qkDoMhyWRSH8hyn43M2G57DicDfKd1/cCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd3402fb15f7f0e59285eb1819255a55619a9308e64cf15801ff826692b17693","last_reissued_at":"2026-05-17T23:42:31.969014Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:31.969014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.10192","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":"2026-05-17T23:42:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JNp689LvY6ulpIZ3hQRt+YnJbb7WIt1WvgwcOWVBw2AJTa8Kb9uAG5Ncx3KxIDb0uLiYWPZAKwLLTOJhhkPmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:10:18.228536Z"},"content_sha256":"3a421e20c23669be0196e0d47db22e2dc2d3809b4b6fe38cf7018081bf1e7022","schema_version":"1.0","event_id":"sha256:3a421e20c23669be0196e0d47db22e2dc2d3809b4b6fe38cf7018081bf1e7022"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:XU2AF6YV67YOLEUF5MMBSJK2KV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Superdifferential of the Takagi function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Javier G\\'omez Gil, Juan Ferrera","submitted_at":"2019-06-24T19:35:40Z","abstract_excerpt":"The Takagi function is a classical example of a continuous nowhere differentiable function. It has empty subdifferential except in a countable set where its subdifferential is $\\mathbb{R}$. In this paper we characterize its superdifferential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10192","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":"2026-05-17T23:42:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b+xJIQJdxKvi0nKCPLLNLFHuGnROaxbU5xm7UJ/6mkT1lzj9keML3fD6sF6y0GM4enNwAmIZ8gExt4HwW8PCAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:10:18.229240Z"},"content_sha256":"fc32bcdf7944b5492b33277dbb693f1510569bacf5d43abddc0aa798dccbe0b2","schema_version":"1.0","event_id":"sha256:fc32bcdf7944b5492b33277dbb693f1510569bacf5d43abddc0aa798dccbe0b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XU2AF6YV67YOLEUF5MMBSJK2KV/bundle.json","state_url":"https://pith.science/pith/XU2AF6YV67YOLEUF5MMBSJK2KV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XU2AF6YV67YOLEUF5MMBSJK2KV/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":"2026-06-06T08:10:18Z","links":{"resolver":"https://pith.science/pith/XU2AF6YV67YOLEUF5MMBSJK2KV","bundle":"https://pith.science/pith/XU2AF6YV67YOLEUF5MMBSJK2KV/bundle.json","state":"https://pith.science/pith/XU2AF6YV67YOLEUF5MMBSJK2KV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XU2AF6YV67YOLEUF5MMBSJK2KV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XU2AF6YV67YOLEUF5MMBSJK2KV","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":"c16129788ee5b11e0b5ff11275c33143ab21b13bdfb27f024ccbdfa16eb6805b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-24T19:35:40Z","title_canon_sha256":"83485aba696b5d3be2dabb763fc25473c0c6b641d8d8335d9853c15c776fa8e9"},"schema_version":"1.0","source":{"id":"1906.10192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.10192","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"arxiv_version","alias_value":"1906.10192v1","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10192","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"pith_short_12","alias_value":"XU2AF6YV67YO","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XU2AF6YV67YOLEUF","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XU2AF6YV","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:fc32bcdf7944b5492b33277dbb693f1510569bacf5d43abddc0aa798dccbe0b2","target":"graph","created_at":"2026-05-17T23:42:31Z","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":"The Takagi function is a classical example of a continuous nowhere differentiable function. It has empty subdifferential except in a countable set where its subdifferential is $\\mathbb{R}$. In this paper we characterize its superdifferential.","authors_text":"Javier G\\'omez Gil, Juan Ferrera","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-24T19:35:40Z","title":"Superdifferential of the Takagi function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10192","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":"sha256:3a421e20c23669be0196e0d47db22e2dc2d3809b4b6fe38cf7018081bf1e7022","target":"record","created_at":"2026-05-17T23:42:31Z","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":"c16129788ee5b11e0b5ff11275c33143ab21b13bdfb27f024ccbdfa16eb6805b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-24T19:35:40Z","title_canon_sha256":"83485aba696b5d3be2dabb763fc25473c0c6b641d8d8335d9853c15c776fa8e9"},"schema_version":"1.0","source":{"id":"1906.10192","kind":"arxiv","version":1}},"canonical_sha256":"bd3402fb15f7f0e59285eb1819255a55619a9308e64cf15801ff826692b17693","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd3402fb15f7f0e59285eb1819255a55619a9308e64cf15801ff826692b17693","first_computed_at":"2026-05-17T23:42:31.969014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:31.969014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ph/yAI+f5mnbfcgtkkssqgylc+3iYFCz9eIS6m6wz122ukL4g+t+qkDoMhyWRSH8hyn43M2G57DicDfKd1/cCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:31.969608Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.10192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a421e20c23669be0196e0d47db22e2dc2d3809b4b6fe38cf7018081bf1e7022","sha256:fc32bcdf7944b5492b33277dbb693f1510569bacf5d43abddc0aa798dccbe0b2"],"state_sha256":"c0e8b2631f213ea0b388c478d32a8fee32adf633ac58ad71dcc6b50ce2b1635d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eKfBPeD4u0bDiVa9LflNwp7oX3unrfxLA7Y1fXOOwc3tDgFl6BeR7VZHszwwnsdFvRAXEnp3q2wYQRTJSIclBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T08:10:18.233104Z","bundle_sha256":"e103788e765385b083838c09d9771d4d6023bdf7bb304495006910a1b8d89803"}}