{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FYH5LSEQV3ZVYUKOL7LCH2RCWH","short_pith_number":"pith:FYH5LSEQ","canonical_record":{"source":{"id":"1610.06354","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-20T11:02:40Z","cross_cats_sorted":[],"title_canon_sha256":"6cf60f95edb09169a3df8fd63bcccb0b2250ce63487e9f2f0c3037175782dd6a","abstract_canon_sha256":"0d17e0fc07e45a674eaf5243f2bccc00f245fc07d77254bd6cfc2162b451d969"},"schema_version":"1.0"},"canonical_sha256":"2e0fd5c890aef35c514e5fd623ea22b1dbfa65ea45d05004a3caa4ddd9ea954a","source":{"kind":"arxiv","id":"1610.06354","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06354","created_at":"2026-05-18T01:01:43Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06354v1","created_at":"2026-05-18T01:01:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06354","created_at":"2026-05-18T01:01:43Z"},{"alias_kind":"pith_short_12","alias_value":"FYH5LSEQV3ZV","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FYH5LSEQV3ZVYUKO","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FYH5LSEQ","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FYH5LSEQV3ZVYUKOL7LCH2RCWH","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06354","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-20T11:02:40Z","cross_cats_sorted":[],"title_canon_sha256":"6cf60f95edb09169a3df8fd63bcccb0b2250ce63487e9f2f0c3037175782dd6a","abstract_canon_sha256":"0d17e0fc07e45a674eaf5243f2bccc00f245fc07d77254bd6cfc2162b451d969"},"schema_version":"1.0"},"canonical_sha256":"2e0fd5c890aef35c514e5fd623ea22b1dbfa65ea45d05004a3caa4ddd9ea954a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:43.480416Z","signature_b64":"xdKsYKO5ZV7cORUtKiKjee9TJLfYf0mIFgITUW/2P1M6R8bCwies7vWCrkT27rnMzuWUX9DXsRIAqLRKR5IXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e0fd5c890aef35c514e5fd623ea22b1dbfa65ea45d05004a3caa4ddd9ea954a","last_reissued_at":"2026-05-18T01:01:43.479583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:43.479583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06354","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":"2026-05-18T01:01:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OMHxssjZmyvmHlz81vwGhH4pvErS/8Bzc3/+l0Ws5VyYIxTWy5bpQrEnkoyzF8FFrzivikzO9B3R8MPh+2kuCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:15:50.322007Z"},"content_sha256":"4fe5fecfef29edf6c345aa320d2de3839ffb71b32f6d73fe3d5f516059c6bf81","schema_version":"1.0","event_id":"sha256:4fe5fecfef29edf6c345aa320d2de3839ffb71b32f6d73fe3d5f516059c6bf81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FYH5LSEQV3ZVYUKOL7LCH2RCWH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simple proofs of nowhere-differentiability for Weierstrass's function and cases of slow growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jon Johnsen","submitted_at":"2016-10-20T11:02:40Z","abstract_excerpt":"Using a few basics from integration theory, a short proof of nowhere-differentiability of Weierstrass functions is given. Restated in terms of the Fourier transformation, the method consists in principle of a second microlocalisation, which is used to derive two general results on existence of nowhere differentiable functions. Examples are given in which the frequencies are of polynomial growth and of almost quadratic growth as a borderline case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06354","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":"2026-05-18T01:01:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eh0P95Z+7nQCdaawX53HKDvvf6a8PqdciL8/20nfK6v6PFAlf9LK6TRlSMNWVuvDx05yvdTZd1viFOYcpbq/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:15:50.322354Z"},"content_sha256":"1a4036b47db45a8fe9b54d55bc667a07d95355b9c89d0b87b017246a29bc835a","schema_version":"1.0","event_id":"sha256:1a4036b47db45a8fe9b54d55bc667a07d95355b9c89d0b87b017246a29bc835a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FYH5LSEQV3ZVYUKOL7LCH2RCWH/bundle.json","state_url":"https://pith.science/pith/FYH5LSEQV3ZVYUKOL7LCH2RCWH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FYH5LSEQV3ZVYUKOL7LCH2RCWH/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":"2026-06-26T00:15:50Z","links":{"resolver":"https://pith.science/pith/FYH5LSEQV3ZVYUKOL7LCH2RCWH","bundle":"https://pith.science/pith/FYH5LSEQV3ZVYUKOL7LCH2RCWH/bundle.json","state":"https://pith.science/pith/FYH5LSEQV3ZVYUKOL7LCH2RCWH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FYH5LSEQV3ZVYUKOL7LCH2RCWH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FYH5LSEQV3ZVYUKOL7LCH2RCWH","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":"0d17e0fc07e45a674eaf5243f2bccc00f245fc07d77254bd6cfc2162b451d969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-20T11:02:40Z","title_canon_sha256":"6cf60f95edb09169a3df8fd63bcccb0b2250ce63487e9f2f0c3037175782dd6a"},"schema_version":"1.0","source":{"id":"1610.06354","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06354","created_at":"2026-05-18T01:01:43Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06354v1","created_at":"2026-05-18T01:01:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06354","created_at":"2026-05-18T01:01:43Z"},{"alias_kind":"pith_short_12","alias_value":"FYH5LSEQV3ZV","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FYH5LSEQV3ZVYUKO","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FYH5LSEQ","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:1a4036b47db45a8fe9b54d55bc667a07d95355b9c89d0b87b017246a29bc835a","target":"graph","created_at":"2026-05-18T01:01:43Z","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":"Using a few basics from integration theory, a short proof of nowhere-differentiability of Weierstrass functions is given. Restated in terms of the Fourier transformation, the method consists in principle of a second microlocalisation, which is used to derive two general results on existence of nowhere differentiable functions. Examples are given in which the frequencies are of polynomial growth and of almost quadratic growth as a borderline case.","authors_text":"Jon Johnsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-20T11:02:40Z","title":"Simple proofs of nowhere-differentiability for Weierstrass's function and cases of slow growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06354","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":"sha256:4fe5fecfef29edf6c345aa320d2de3839ffb71b32f6d73fe3d5f516059c6bf81","target":"record","created_at":"2026-05-18T01:01:43Z","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":"0d17e0fc07e45a674eaf5243f2bccc00f245fc07d77254bd6cfc2162b451d969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-20T11:02:40Z","title_canon_sha256":"6cf60f95edb09169a3df8fd63bcccb0b2250ce63487e9f2f0c3037175782dd6a"},"schema_version":"1.0","source":{"id":"1610.06354","kind":"arxiv","version":1}},"canonical_sha256":"2e0fd5c890aef35c514e5fd623ea22b1dbfa65ea45d05004a3caa4ddd9ea954a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e0fd5c890aef35c514e5fd623ea22b1dbfa65ea45d05004a3caa4ddd9ea954a","first_computed_at":"2026-05-18T01:01:43.479583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:43.479583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xdKsYKO5ZV7cORUtKiKjee9TJLfYf0mIFgITUW/2P1M6R8bCwies7vWCrkT27rnMzuWUX9DXsRIAqLRKR5IXBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:43.480416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06354","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fe5fecfef29edf6c345aa320d2de3839ffb71b32f6d73fe3d5f516059c6bf81","sha256:1a4036b47db45a8fe9b54d55bc667a07d95355b9c89d0b87b017246a29bc835a"],"state_sha256":"628729d83595611f0356828a2205a30ab2aeccc08fa7b380941f199718826772"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zF7z+AejGHzFYAaWrkKXHWySYdyd0Emzy8y/tdJfHIMf1z2NQNdX3d0ZPlKS/5uSU0wA9v0Gn9Jj0Q7bOFpdAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:15:50.324293Z","bundle_sha256":"132154f0d5fde3696f5d7e0c742cdc3ad68d90b37a145b37c58ad4894364421c"}}