{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TVOH3E7JMZGOCRVYN5OP27T4TD","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":"b2a90f0080b6a0698504c54497120f18406b46eebd7b15ccc313bc634ca283cb","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-11-26T15:22:58Z","title_canon_sha256":"089888cb075f9390a988b0cefa8376dfd83d83d652213acde3025aa4f3962217"},"schema_version":"1.0","source":{"id":"1711.10349","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10349","created_at":"2026-05-18T00:25:36Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10349v2","created_at":"2026-05-18T00:25:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10349","created_at":"2026-05-18T00:25:36Z"},{"alias_kind":"pith_short_12","alias_value":"TVOH3E7JMZGO","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TVOH3E7JMZGOCRVY","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TVOH3E7J","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:757dab489aea34af365bcb55c3689cd2e34e446735e21924658b1e8e5fbc0ee6","target":"graph","created_at":"2026-05-18T00:25:36Z","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":"In the following, bypassing dynamical systems tools, we propose a simple means of computing the box dimension of the graph of the classical Weierstrass function defined, for any real number~$x$, by~$ {\\cal W}(x)=\\displaystyle \\sum_{n=0}^{+\\infty} \\lambda^n\\,\\cos \\left ( 2\\, \\pi\\,N_b^n\\,x \\right)\n  $, where~$\\lambda$ and~$N_b$ are two real numbers such that~\\mbox{$0 <\\lambda<1$},~\\mbox{$ N_b\\,\\in\\,\\N$} and~$ \\lambda\\,N_b > 1 $, using a sequence a graphs that approximate the studied one.","authors_text":"Claire David","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-11-26T15:22:58Z","title":"Bypassing dynamical systems : A simple way to get the box-counting dimension of the graph of the Weierstrass function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10349","kind":"arxiv","version":2},"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":"sha256:7592cd4c267a0c7a7ab47ff0f0c343b16c91b86a7340630c0e9ae44c5ce685d4","target":"record","created_at":"2026-05-18T00:25:36Z","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":"b2a90f0080b6a0698504c54497120f18406b46eebd7b15ccc313bc634ca283cb","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-11-26T15:22:58Z","title_canon_sha256":"089888cb075f9390a988b0cefa8376dfd83d83d652213acde3025aa4f3962217"},"schema_version":"1.0","source":{"id":"1711.10349","kind":"arxiv","version":2}},"canonical_sha256":"9d5c7d93e9664ce146b86f5cfd7e7c98c0ca4a4b5709f6cb1e5a544b8d8384db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d5c7d93e9664ce146b86f5cfd7e7c98c0ca4a4b5709f6cb1e5a544b8d8384db","first_computed_at":"2026-05-18T00:25:36.754591Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:36.754591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KEeEGKllJp0PCFTXXiP4RPVeR8bqxPeBhrNNtrVv60TBIK7U4AC4WRJJFGmqlXO4XmFBafHnTsxWibgFhERZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:36.755236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.10349","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7592cd4c267a0c7a7ab47ff0f0c343b16c91b86a7340630c0e9ae44c5ce685d4","sha256:757dab489aea34af365bcb55c3689cd2e34e446735e21924658b1e8e5fbc0ee6"],"state_sha256":"03f900f971cb7b88924eedfc18f020cff4fb25ca6dc89c86bd1ee7dfe45a450a"}