{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LEQEE6LWVFKC6KX7L63KAAR5MX","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":"714ec74e029b557576b8ad12e06bcf097ce16b07741c582f5b26a8b1b89ffa5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-31T22:27:58Z","title_canon_sha256":"dc7cf671df02ba3dce98d60c732b34e6ec6c1846a814c066de617be0a2be4ca5"},"schema_version":"1.0","source":{"id":"1804.00221","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00221","created_at":"2026-07-05T06:23:23Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00221v5","created_at":"2026-07-05T06:23:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00221","created_at":"2026-07-05T06:23:23Z"},{"alias_kind":"pith_short_12","alias_value":"LEQEE6LWVFKC","created_at":"2026-07-05T06:23:23Z"},{"alias_kind":"pith_short_16","alias_value":"LEQEE6LWVFKC6KX7","created_at":"2026-07-05T06:23:23Z"},{"alias_kind":"pith_short_8","alias_value":"LEQEE6LW","created_at":"2026-07-05T06:23:23Z"}],"graph_snapshots":[{"event_id":"sha256:20e4a6d6bd27f59e15bbdcd7c37c11d4b965784ec8e83072b220c57856166350","target":"graph","created_at":"2026-07-05T06:23:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1804.00221/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $S_{a,b}$ denote the sequence of leading digits of $a^n$ in base $b$. It is well known that if $a$ is not a rational power of $b$, then the sequence $S_{a,b}$ satisfies Benford's Law; that is, digit $d$ occurs in $S_{a,b}$ with frequency $\\log_{b}(1+1/d)$, for $d=1,2,\\dots,b-1$.\n  In this paper, we investigate the \\emph{complexity} of such sequences. We focus mainly on the \\emph{block complexity}, $p_{a,b}(n)$, defined as the number of distinct blocks of length $n$ appearing in $S_{a,b}$. In our main result we determine $p_{a,b}(n)$ for all squarefree bases $b\\ge 5$ and all rational number","authors_text":"A.J. Hildebrand, Xinwei He, Yuchen Li, Yunyi Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-31T22:27:58Z","title":"Complexity of Leading Digit Sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00221","kind":"arxiv","version":5},"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":"sha256:9bc9455195b3c635b2a83711e0fd37db8ab4444a92d74aced12524975650239b","target":"record","created_at":"2026-07-05T06:23:23Z","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":"714ec74e029b557576b8ad12e06bcf097ce16b07741c582f5b26a8b1b89ffa5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-31T22:27:58Z","title_canon_sha256":"dc7cf671df02ba3dce98d60c732b34e6ec6c1846a814c066de617be0a2be4ca5"},"schema_version":"1.0","source":{"id":"1804.00221","kind":"arxiv","version":5}},"canonical_sha256":"5920427976a9542f2aff5fb6a0023d65cf7fda9519f59cf3e185457df085c9bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5920427976a9542f2aff5fb6a0023d65cf7fda9519f59cf3e185457df085c9bc","first_computed_at":"2026-07-05T06:23:23.880037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:23:23.880037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5q2tqOn4/opE80cOcS+b0mXS9rq4FyryVlmG/bOndQp+xkTWL1poKLOS6P+qRmgL7yyAU011brc6q/FGWTcpBw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:23:23.880394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.00221","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bc9455195b3c635b2a83711e0fd37db8ab4444a92d74aced12524975650239b","sha256:20e4a6d6bd27f59e15bbdcd7c37c11d4b965784ec8e83072b220c57856166350"],"state_sha256":"564ae47a0a195cfe0d4c9170dbd387cc93459d730ad9b3989443de0b7a8f3ccd"}