{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:O7M6HYHIBND2XUJ5MAAHVXNPCI","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":"823dab59af2db2a28d0c6b6b2e76e2a6bf59ffc330bc27acf56f13239d6d8e76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-17T16:45:07Z","title_canon_sha256":"97646d0e620b6a5632d6f6a18b93ac3634c9bdc8eb0e8798c0770769c83fe015"},"schema_version":"1.0","source":{"id":"1702.05426","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05426","created_at":"2026-05-18T00:36:43Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05426v4","created_at":"2026-05-18T00:36:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05426","created_at":"2026-05-18T00:36:43Z"},{"alias_kind":"pith_short_12","alias_value":"O7M6HYHIBND2","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O7M6HYHIBND2XUJ5","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O7M6HYHI","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:939663fa6d8a177b5a55b35e9c7693cdbb6df4a362880061c6f08676ddf8d6a8","target":"graph","created_at":"2026-05-18T00:36:43Z","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":"We study the convergence of the parameter family of series $$V_{\\alpha,\\beta}(t)=\\sum_{p}p^{-\\alpha}\\exp(2\\pi i p^{\\beta}t),\\quad \\alpha,\\beta \\in \\mathbb{R}_{>0},\\; t \\in [0,1)$$ defined over prime numbers $p$, and subsequently, their differentiability properties. The visible fractal nature of the graphs as a function of $\\alpha,\\beta$ is analyzed in terms of H\\\"older continuity, self similarity and fractal dimension, backed with numerical results. We also discuss the link of this series to random walks and consequently, explore numerically its random properties.","authors_text":"Dimitris Vartziotis, Doris Bohnet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-17T16:45:07Z","title":"Fractal curves from prime trigonometric series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05426","kind":"arxiv","version":4},"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:b3e1e2ceb15f2adea9d86f651fff319626994bde07512fe65a4a457efe97ceee","target":"record","created_at":"2026-05-18T00:36:43Z","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":"823dab59af2db2a28d0c6b6b2e76e2a6bf59ffc330bc27acf56f13239d6d8e76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-17T16:45:07Z","title_canon_sha256":"97646d0e620b6a5632d6f6a18b93ac3634c9bdc8eb0e8798c0770769c83fe015"},"schema_version":"1.0","source":{"id":"1702.05426","kind":"arxiv","version":4}},"canonical_sha256":"77d9e3e0e80b47abd13d60007addaf12213f6d3190d375cec68a2027cedfa283","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77d9e3e0e80b47abd13d60007addaf12213f6d3190d375cec68a2027cedfa283","first_computed_at":"2026-05-18T00:36:43.444334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:43.444334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"43CmxP6pJpc9YKILj/9ANHRW8Qk95pNAM1oD8CRXVvxw6XXQGW0baF1yOITWVTdnnW4gVOkj3K0ufe3iwrM8CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:43.444946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.05426","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3e1e2ceb15f2adea9d86f651fff319626994bde07512fe65a4a457efe97ceee","sha256:939663fa6d8a177b5a55b35e9c7693cdbb6df4a362880061c6f08676ddf8d6a8"],"state_sha256":"ef52b6045c1aaeecf61ce360b1fb04dc385b257f97705c805c33c668d2b09689"}