{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:MQ24TMGDAHLEWU4B2ATNTOYIBX","short_pith_number":"pith:MQ24TMGD","schema_version":"1.0","canonical_sha256":"6435c9b0c301d64b5381d026d9bb080de32aa5700e74fc48858234985fef5f87","source":{"kind":"arxiv","id":"1105.4960","version":1},"attestation_state":"computed","paper":{"title":"On the dimension of graphs of Weierstrass-type functions with rapidly growing frequencies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.MG","authors_text":"Krzysztof Baranski","submitted_at":"2011-05-25T08:04:30Z","abstract_excerpt":"We determine the Hausdorff and box dimension of the fractal graphs for a general class of Weierstrass-type functions of the form $f(x) = \\sum_{n=1}^\\infty a_n \\, g(b_n x + \\theta_n)$, where $g$ is a periodic Lipschitz real function and $a_{n+1}/a_n \\to 0$, $b_{n+1}/b_n \\to \\infty$ as $n \\to \\infty$. Moreover, for any $H, B \\in [1, 2]$, $H \\leq B$ we provide examples of such functions with $\\dim_H(\\graph f) = \\underline{\\dim}_B(\\graph f) = H$, $\\bar{\\dim}_B(\\graph f) = B$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1105.4960","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-05-25T08:04:30Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"c1ddadbe7a7ab5e995433e9a1914df96268d37a71e633e895ec665d7b58b1d7b","abstract_canon_sha256":"45e26c625e69aa797cc9b747e89c21e4c58a219f5e8af53bf554141d903fcc45"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:17.620518Z","signature_b64":"ac8DPOa9in8bsPKam3Ej+0C97bHzRLuHbD8O8mOv/erzmm0ddXmcIlW4hJjKvEwccUdVRqsE6P7trfVgqxP2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6435c9b0c301d64b5381d026d9bb080de32aa5700e74fc48858234985fef5f87","last_reissued_at":"2026-05-18T03:53:17.619914Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:17.619914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the dimension of graphs of Weierstrass-type functions with rapidly growing frequencies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.MG","authors_text":"Krzysztof Baranski","submitted_at":"2011-05-25T08:04:30Z","abstract_excerpt":"We determine the Hausdorff and box dimension of the fractal graphs for a general class of Weierstrass-type functions of the form $f(x) = \\sum_{n=1}^\\infty a_n \\, g(b_n x + \\theta_n)$, where $g$ is a periodic Lipschitz real function and $a_{n+1}/a_n \\to 0$, $b_{n+1}/b_n \\to \\infty$ as $n \\to \\infty$. Moreover, for any $H, B \\in [1, 2]$, $H \\leq B$ we provide examples of such functions with $\\dim_H(\\graph f) = \\underline{\\dim}_B(\\graph f) = H$, $\\bar{\\dim}_B(\\graph f) = B$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4960","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1105.4960","created_at":"2026-05-18T03:53:17.620016+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.4960v1","created_at":"2026-05-18T03:53:17.620016+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4960","created_at":"2026-05-18T03:53:17.620016+00:00"},{"alias_kind":"pith_short_12","alias_value":"MQ24TMGDAHLE","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"MQ24TMGDAHLEWU4B","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"MQ24TMGD","created_at":"2026-05-18T12:26:34.985390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MQ24TMGDAHLEWU4B2ATNTOYIBX","json":"https://pith.science/pith/MQ24TMGDAHLEWU4B2ATNTOYIBX.json","graph_json":"https://pith.science/api/pith-number/MQ24TMGDAHLEWU4B2ATNTOYIBX/graph.json","events_json":"https://pith.science/api/pith-number/MQ24TMGDAHLEWU4B2ATNTOYIBX/events.json","paper":"https://pith.science/paper/MQ24TMGD"},"agent_actions":{"view_html":"https://pith.science/pith/MQ24TMGDAHLEWU4B2ATNTOYIBX","download_json":"https://pith.science/pith/MQ24TMGDAHLEWU4B2ATNTOYIBX.json","view_paper":"https://pith.science/paper/MQ24TMGD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.4960&json=true","fetch_graph":"https://pith.science/api/pith-number/MQ24TMGDAHLEWU4B2ATNTOYIBX/graph.json","fetch_events":"https://pith.science/api/pith-number/MQ24TMGDAHLEWU4B2ATNTOYIBX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MQ24TMGDAHLEWU4B2ATNTOYIBX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MQ24TMGDAHLEWU4B2ATNTOYIBX/action/storage_attestation","attest_author":"https://pith.science/pith/MQ24TMGDAHLEWU4B2ATNTOYIBX/action/author_attestation","sign_citation":"https://pith.science/pith/MQ24TMGDAHLEWU4B2ATNTOYIBX/action/citation_signature","submit_replication":"https://pith.science/pith/MQ24TMGDAHLEWU4B2ATNTOYIBX/action/replication_record"}},"created_at":"2026-05-18T03:53:17.620016+00:00","updated_at":"2026-05-18T03:53:17.620016+00:00"}