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Let $b$ be a positive integer($\\geq 2$). Let $A_{b}$ be the set of all natural numbers which contain only 0's and 1's in b-ary expansion and $S^{(b)}_{q,i}(n)$ be the difference between the corresponding number of $k_e<n$, $k_e\\equiv i \\mod q$, $k_e\\in A_{b}$ and $k_e$ has even n"},"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":"1511.03236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-10T19:42:02Z","cross_cats_sorted":[],"title_canon_sha256":"4f90f5899fd2216395440a342040c7130dbd15f32753e286687bf92409a62ea3","abstract_canon_sha256":"8975fb7784257fdc6116230ba057aadb6465e72f3a0ff7a3bc7afd4902c64f84"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:16.716221Z","signature_b64":"T2B10m1rgsni7FFPYKjyTDO2cUt76rY6ucf38wsZKZngNPz6p4ByuxwnJF3eZB397UQvluYMaqj5Qn5ETV8DDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8caed42ba8eafbd82eb2687336196b8dcf6b5d17c9b8ac7fcd1b119c737f2088","last_reissued_at":"2026-05-18T01:27:16.715729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:16.715729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Newman's phenomenon in higher bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sai Teja Somu","submitted_at":"2015-11-10T19:42:02Z","abstract_excerpt":"A well known result of Newman says that upto a limit, multiples of $3$ with even number of 1's in binary representation always exceed multiples of $3$ with odd number of 1's. The phenomenon of preponderance of even number of 1's is now known as Newman's phenomenon. We show that this phenomenon exists for higher bases. Let $b$ be a positive integer($\\geq 2$). Let $A_{b}$ be the set of all natural numbers which contain only 0's and 1's in b-ary expansion and $S^{(b)}_{q,i}(n)$ be the difference between the corresponding number of $k_e<n$, $k_e\\equiv i \\mod q$, $k_e\\in A_{b}$ and $k_e$ has even n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03236","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":"1511.03236","created_at":"2026-05-18T01:27:16.715810+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.03236v1","created_at":"2026-05-18T01:27:16.715810+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03236","created_at":"2026-05-18T01:27:16.715810+00:00"},{"alias_kind":"pith_short_12","alias_value":"RSXNIK5I5L55","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RSXNIK5I5L55QLVS","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RSXNIK5I","created_at":"2026-05-18T12:29:39.896362+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/RSXNIK5I5L55QLVSNBZTMGLLRX","json":"https://pith.science/pith/RSXNIK5I5L55QLVSNBZTMGLLRX.json","graph_json":"https://pith.science/api/pith-number/RSXNIK5I5L55QLVSNBZTMGLLRX/graph.json","events_json":"https://pith.science/api/pith-number/RSXNIK5I5L55QLVSNBZTMGLLRX/events.json","paper":"https://pith.science/paper/RSXNIK5I"},"agent_actions":{"view_html":"https://pith.science/pith/RSXNIK5I5L55QLVSNBZTMGLLRX","download_json":"https://pith.science/pith/RSXNIK5I5L55QLVSNBZTMGLLRX.json","view_paper":"https://pith.science/paper/RSXNIK5I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.03236&json=true","fetch_graph":"https://pith.science/api/pith-number/RSXNIK5I5L55QLVSNBZTMGLLRX/graph.json","fetch_events":"https://pith.science/api/pith-number/RSXNIK5I5L55QLVSNBZTMGLLRX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RSXNIK5I5L55QLVSNBZTMGLLRX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RSXNIK5I5L55QLVSNBZTMGLLRX/action/storage_attestation","attest_author":"https://pith.science/pith/RSXNIK5I5L55QLVSNBZTMGLLRX/action/author_attestation","sign_citation":"https://pith.science/pith/RSXNIK5I5L55QLVSNBZTMGLLRX/action/citation_signature","submit_replication":"https://pith.science/pith/RSXNIK5I5L55QLVSNBZTMGLLRX/action/replication_record"}},"created_at":"2026-05-18T01:27:16.715810+00:00","updated_at":"2026-05-18T01:27:16.715810+00:00"}