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The collection of functions with the form are called the Takagi class. In this paper, we show that in the case that $\\varlimsup_{n \\to \\infty} b^n |c_n|<\\infty$, the Assouad dimension of the graph ${\\mathcal G} f_{{\\mathbf c},b}=\\{(x,f_{{\\mathbf c},b}(x)):x\\in[0,1]\\}$ fo"},"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":"2502.01140","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-02-03T08:16:47Z","cross_cats_sorted":[],"title_canon_sha256":"76746d54b4445b603d0fdeda0f9cad85c5d2b9681f90e9e6804be32eda3d9e99","abstract_canon_sha256":"fd77607a3851b3a7946f89bc945d55644bff29ffc5b438bef4ea17dc4d7d026d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:31:26.544065Z","signature_b64":"4eH99bJ1rVgyjhdhQcwSIFK+IWKzW/M7vNElqa8j8LNPWT/vkJZfV7jWKm+2I1Ph8i+Wm8Gwds1XkanOfPHhDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a1230af16ab47caea09448078de343378bca8ca0951108712047dcd285eb382","last_reissued_at":"2026-07-05T10:31:26.543597Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:31:26.543597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Assouad dimension of the Takagi function","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Lai Jiang","submitted_at":"2025-02-03T08:16:47Z","abstract_excerpt":"For any integer $b\\geq2$ and real series $\\{c_n\\}$ such that $\\sum_{n=0}^\\infty|c_n|<\\infty$, the generalized Takagi function $f_{{\\mathbf c},b}(x)$ is defined by $$\n  f_{{\\mathbf c},b}(x):=\\sum_{n=0}^\\infty c_n\\phi(b^n x), \\quad x\\in [0,1], $$ where $\\phi(x)=dist(x,\\mathbb{Z})$ is the distance from $x$ to the nearest integer. The collection of functions with the form are called the Takagi class. In this paper, we show that in the case that $\\varlimsup_{n \\to \\infty} b^n |c_n|<\\infty$, the Assouad dimension of the graph ${\\mathcal G} f_{{\\mathbf c},b}=\\{(x,f_{{\\mathbf c},b}(x)):x\\in[0,1]\\}$ fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01140","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.01140/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2502.01140","created_at":"2026-07-05T10:31:26.543656+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.01140v2","created_at":"2026-07-05T10:31:26.543656+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.01140","created_at":"2026-07-05T10:31:26.543656+00:00"},{"alias_kind":"pith_short_12","alias_value":"JIJDBLYWVND4","created_at":"2026-07-05T10:31:26.543656+00:00"},{"alias_kind":"pith_short_16","alias_value":"JIJDBLYWVND4V2QJ","created_at":"2026-07-05T10:31:26.543656+00:00"},{"alias_kind":"pith_short_8","alias_value":"JIJDBLYW","created_at":"2026-07-05T10:31:26.543656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.11145","citing_title":"On the Assouad dimension of Weierstrass function graphs","ref_index":28,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JIJDBLYWVND4V2QJISAHRXRUGN","json":"https://pith.science/pith/JIJDBLYWVND4V2QJISAHRXRUGN.json","graph_json":"https://pith.science/api/pith-number/JIJDBLYWVND4V2QJISAHRXRUGN/graph.json","events_json":"https://pith.science/api/pith-number/JIJDBLYWVND4V2QJISAHRXRUGN/events.json","paper":"https://pith.science/paper/JIJDBLYW"},"agent_actions":{"view_html":"https://pith.science/pith/JIJDBLYWVND4V2QJISAHRXRUGN","download_json":"https://pith.science/pith/JIJDBLYWVND4V2QJISAHRXRUGN.json","view_paper":"https://pith.science/paper/JIJDBLYW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.01140&json=true","fetch_graph":"https://pith.science/api/pith-number/JIJDBLYWVND4V2QJISAHRXRUGN/graph.json","fetch_events":"https://pith.science/api/pith-number/JIJDBLYWVND4V2QJISAHRXRUGN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JIJDBLYWVND4V2QJISAHRXRUGN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JIJDBLYWVND4V2QJISAHRXRUGN/action/storage_attestation","attest_author":"https://pith.science/pith/JIJDBLYWVND4V2QJISAHRXRUGN/action/author_attestation","sign_citation":"https://pith.science/pith/JIJDBLYWVND4V2QJISAHRXRUGN/action/citation_signature","submit_replication":"https://pith.science/pith/JIJDBLYWVND4V2QJISAHRXRUGN/action/replication_record"}},"created_at":"2026-07-05T10:31:26.543656+00:00","updated_at":"2026-07-05T10:31:26.543656+00:00"}