{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:G4YAGMPXEK4LPAXNMCRZ5VBVAG","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":"87453cc8a837d4f81ada6c945710da08c8885ccb12d0d08a7f7e1aa70ad11142","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-06T21:36:49Z","title_canon_sha256":"0d058ed00de101e947e6d17c759d6c71ed626d04908543bafd59d15662b7f923"},"schema_version":"1.0","source":{"id":"1807.02573","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.02573","created_at":"2026-05-18T00:11:16Z"},{"alias_kind":"arxiv_version","alias_value":"1807.02573v1","created_at":"2026-05-18T00:11:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02573","created_at":"2026-05-18T00:11:16Z"},{"alias_kind":"pith_short_12","alias_value":"G4YAGMPXEK4L","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G4YAGMPXEK4LPAXN","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G4YAGMPX","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:9c17cf40a40342aa13bc8e79ca7a5e90ff882d1eb43f13565fbfd2955500c61b","target":"graph","created_at":"2026-05-18T00:11:16Z","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":"Let $b$ be a numeration base. A $b$-Niven number is one that is divisible by the sum of its base $b$ digits. We introduce high degree $b$-Niven numbers. These are $b$-Niven numbers that have a power greater than $1$ that is $b$-Niven number. Our main result shows that for each degree there exists an infinite set of bases $b$ for which $b$-Niven numbers of that degree exist. The high degree $b$-Niven numbers are given by explicit formulas and have all digits different from zero.","authors_text":"Viorel Nitica","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-06T21:36:49Z","title":"High degree $b$-Niven numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02573","kind":"arxiv","version":1},"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":"sha256:6adf4b82bffe9af8673b9fc98b12c6f455361a91795be96bc75054c759052eb2","target":"record","created_at":"2026-05-18T00:11:16Z","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":"87453cc8a837d4f81ada6c945710da08c8885ccb12d0d08a7f7e1aa70ad11142","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-06T21:36:49Z","title_canon_sha256":"0d058ed00de101e947e6d17c759d6c71ed626d04908543bafd59d15662b7f923"},"schema_version":"1.0","source":{"id":"1807.02573","kind":"arxiv","version":1}},"canonical_sha256":"37300331f722b8b782ed60a39ed4350195adc72a64451f99176cd3220ce54e57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37300331f722b8b782ed60a39ed4350195adc72a64451f99176cd3220ce54e57","first_computed_at":"2026-05-18T00:11:16.685650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:16.685650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8ahVBaM8CSP9zLA1CHYwbsxvkfxytSWUFciGuRWcuYdHGLJYu9UWI7zGB6dNuVGXZIfxfMlB8LhnTTcbC4vlDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:16.686380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.02573","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6adf4b82bffe9af8673b9fc98b12c6f455361a91795be96bc75054c759052eb2","sha256:9c17cf40a40342aa13bc8e79ca7a5e90ff882d1eb43f13565fbfd2955500c61b"],"state_sha256":"e7993642900c720db784ecc1b71c85492e1794913314c0fbc70662b95f073891"}