{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KZEIF3TG5VUGAHJCD7UR54YDAT","short_pith_number":"pith:KZEIF3TG","canonical_record":{"source":{"id":"1010.0881","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-05T13:33:12Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"ef1e6afa2819b82cc4a49e40afd09127e6705b92c552b109e02d3d9083c3c25b","abstract_canon_sha256":"12d119d73d86d8b18ef0c02a633bcb8904701f5472ebcdb5e5674f392bd0567a"},"schema_version":"1.0"},"canonical_sha256":"564882ee66ed68601d221fe91ef30304f6cc47abda5314020d400675d1ea854b","source":{"kind":"arxiv","id":"1010.0881","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0881","created_at":"2026-05-18T03:57:50Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0881v1","created_at":"2026-05-18T03:57:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0881","created_at":"2026-05-18T03:57:50Z"},{"alias_kind":"pith_short_12","alias_value":"KZEIF3TG5VUG","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KZEIF3TG5VUGAHJC","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KZEIF3TG","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KZEIF3TG5VUGAHJCD7UR54YDAT","target":"record","payload":{"canonical_record":{"source":{"id":"1010.0881","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-05T13:33:12Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"ef1e6afa2819b82cc4a49e40afd09127e6705b92c552b109e02d3d9083c3c25b","abstract_canon_sha256":"12d119d73d86d8b18ef0c02a633bcb8904701f5472ebcdb5e5674f392bd0567a"},"schema_version":"1.0"},"canonical_sha256":"564882ee66ed68601d221fe91ef30304f6cc47abda5314020d400675d1ea854b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:50.713721Z","signature_b64":"ZrmyaTg50BPn+9iX50ekSvD3nevbo+nH1ph8YsP66oYQ9Xn95JLpia2iuoMmiPFGcBboghOP5KEmI/OqSNZZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"564882ee66ed68601d221fe91ef30304f6cc47abda5314020d400675d1ea854b","last_reissued_at":"2026-05-18T03:57:50.712855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:50.712855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.0881","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":"2026-05-18T03:57:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U1DXVgd5aT48/dnL+/BLP1/mHg8t/zSAUZhsGL1YQGXhdq/zjfgbeDd40RRjkeY5wTv+bdyQjNdWnZEfCVdTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:57:14.186094Z"},"content_sha256":"355b7ec3171024b019001d3aa6531cef27db367425bccae900736df163d5541e","schema_version":"1.0","event_id":"sha256:355b7ec3171024b019001d3aa6531cef27db367425bccae900736df163d5541e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KZEIF3TG5VUGAHJCD7UR54YDAT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differentiability of fractal curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DS","authors_text":"Alexey Kravchenko, Christoph Bandt","submitted_at":"2010-10-05T13:33:12Z","abstract_excerpt":"While self-similar sets have no tangents at any single point, self-affine curves can be smooth. We consider plane self-affine curves without double points and with two pieces. There is an open subset of parameter space for which the curve is differentiable at all points except for a countable set. For a parameter set of codimension one, the curve is continuously differentiable. However, there are no twice differentiable self-affine curves in the plane, except for parabolic arcs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0881","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":"2026-05-18T03:57:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fOB3pB4pWTZq3srmh+tLOnZ2/Ei9oTggfqgWc2LtyjbZBXFf+cYGNc0nINSGvD/mATzLhR8VmnHtXjDa4vUdBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:57:14.186861Z"},"content_sha256":"34ba901568e203ccbeb0238ec325d7fcc620607f2a505cae7a5f889c726b5f0f","schema_version":"1.0","event_id":"sha256:34ba901568e203ccbeb0238ec325d7fcc620607f2a505cae7a5f889c726b5f0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KZEIF3TG5VUGAHJCD7UR54YDAT/bundle.json","state_url":"https://pith.science/pith/KZEIF3TG5VUGAHJCD7UR54YDAT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KZEIF3TG5VUGAHJCD7UR54YDAT/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":"2026-06-07T16:57:14Z","links":{"resolver":"https://pith.science/pith/KZEIF3TG5VUGAHJCD7UR54YDAT","bundle":"https://pith.science/pith/KZEIF3TG5VUGAHJCD7UR54YDAT/bundle.json","state":"https://pith.science/pith/KZEIF3TG5VUGAHJCD7UR54YDAT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KZEIF3TG5VUGAHJCD7UR54YDAT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KZEIF3TG5VUGAHJCD7UR54YDAT","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":"12d119d73d86d8b18ef0c02a633bcb8904701f5472ebcdb5e5674f392bd0567a","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-05T13:33:12Z","title_canon_sha256":"ef1e6afa2819b82cc4a49e40afd09127e6705b92c552b109e02d3d9083c3c25b"},"schema_version":"1.0","source":{"id":"1010.0881","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0881","created_at":"2026-05-18T03:57:50Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0881v1","created_at":"2026-05-18T03:57:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0881","created_at":"2026-05-18T03:57:50Z"},{"alias_kind":"pith_short_12","alias_value":"KZEIF3TG5VUG","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KZEIF3TG5VUGAHJC","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KZEIF3TG","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:34ba901568e203ccbeb0238ec325d7fcc620607f2a505cae7a5f889c726b5f0f","target":"graph","created_at":"2026-05-18T03:57:50Z","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":"While self-similar sets have no tangents at any single point, self-affine curves can be smooth. We consider plane self-affine curves without double points and with two pieces. There is an open subset of parameter space for which the curve is differentiable at all points except for a countable set. For a parameter set of codimension one, the curve is continuously differentiable. However, there are no twice differentiable self-affine curves in the plane, except for parabolic arcs.","authors_text":"Alexey Kravchenko, Christoph Bandt","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-05T13:33:12Z","title":"Differentiability of fractal curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0881","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":"sha256:355b7ec3171024b019001d3aa6531cef27db367425bccae900736df163d5541e","target":"record","created_at":"2026-05-18T03:57:50Z","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":"12d119d73d86d8b18ef0c02a633bcb8904701f5472ebcdb5e5674f392bd0567a","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-05T13:33:12Z","title_canon_sha256":"ef1e6afa2819b82cc4a49e40afd09127e6705b92c552b109e02d3d9083c3c25b"},"schema_version":"1.0","source":{"id":"1010.0881","kind":"arxiv","version":1}},"canonical_sha256":"564882ee66ed68601d221fe91ef30304f6cc47abda5314020d400675d1ea854b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"564882ee66ed68601d221fe91ef30304f6cc47abda5314020d400675d1ea854b","first_computed_at":"2026-05-18T03:57:50.712855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:50.712855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZrmyaTg50BPn+9iX50ekSvD3nevbo+nH1ph8YsP66oYQ9Xn95JLpia2iuoMmiPFGcBboghOP5KEmI/OqSNZZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:50.713721Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0881","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:355b7ec3171024b019001d3aa6531cef27db367425bccae900736df163d5541e","sha256:34ba901568e203ccbeb0238ec325d7fcc620607f2a505cae7a5f889c726b5f0f"],"state_sha256":"46a8ccde0c43197f6a3f617c64b73003d1a7d93890357096f751d3ded0c5a9ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m8lVX9gs/5C+hNtQuV3ictp/7CAeFfqNvPW4IXdgjq15O+MankKMISN9Jfr37vWUxtkbdTF6by0h/d+3HXJ0BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:57:14.191453Z","bundle_sha256":"8aa031a2e5f063b77ec7f34980e310435d53e6ec3fa6f40b5eb2c5c8bc6e0039"}}