{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6ARVVCN3CJCRZCE6MNBSACMB4F","short_pith_number":"pith:6ARVVCN3","schema_version":"1.0","canonical_sha256":"f0235a89bb12451c889e6343200981e175380e568749e623e2a1f302fc6a9d40","source":{"kind":"arxiv","id":"1511.02404","version":1},"attestation_state":"computed","paper":{"title":"Minimizing the frequency of carries in modular addition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Francesco Monopoli","submitted_at":"2015-11-07T21:18:40Z","abstract_excerpt":"When adding integers in base $m$, carries occur. The same happens modulo a generic integer $q$ when the set of digits is a complete set of residues modulo $m$ for some positive integer $m$ dividing $q$. In this paper we prove that asymptotically every digital set in this setting induces carries with frequency at least $1/4$, thus generalizing results of Alon, Diaconis, Shao and Soundararajan."},"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":"1511.02404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-07T21:18:40Z","cross_cats_sorted":[],"title_canon_sha256":"90dc1e76a894c4270fc50f7dcfe87ab8b80de39e3c3ddc9555e987ced9230497","abstract_canon_sha256":"1e0bd1351362b5d4a87314e7ffc616440fc223bca1ba85ed62ad9ce90d5807c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:30.383271Z","signature_b64":"D/crKyGZNsPBBqcHo8juWkIfDswKoT0exdQ9/wPoZRYGuTFZyBF3nBJZnsL7Fh8/OjtcN3zTb/+A+Js9GtE4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0235a89bb12451c889e6343200981e175380e568749e623e2a1f302fc6a9d40","last_reissued_at":"2026-05-18T01:27:30.382777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:30.382777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimizing the frequency of carries in modular addition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Francesco Monopoli","submitted_at":"2015-11-07T21:18:40Z","abstract_excerpt":"When adding integers in base $m$, carries occur. The same happens modulo a generic integer $q$ when the set of digits is a complete set of residues modulo $m$ for some positive integer $m$ dividing $q$. In this paper we prove that asymptotically every digital set in this setting induces carries with frequency at least $1/4$, thus generalizing results of Alon, Diaconis, Shao and Soundararajan."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02404","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":"1511.02404","created_at":"2026-05-18T01:27:30.382857+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.02404v1","created_at":"2026-05-18T01:27:30.382857+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02404","created_at":"2026-05-18T01:27:30.382857+00:00"},{"alias_kind":"pith_short_12","alias_value":"6ARVVCN3CJCR","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6ARVVCN3CJCRZCE6","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6ARVVCN3","created_at":"2026-05-18T12:29:07.941421+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/6ARVVCN3CJCRZCE6MNBSACMB4F","json":"https://pith.science/pith/6ARVVCN3CJCRZCE6MNBSACMB4F.json","graph_json":"https://pith.science/api/pith-number/6ARVVCN3CJCRZCE6MNBSACMB4F/graph.json","events_json":"https://pith.science/api/pith-number/6ARVVCN3CJCRZCE6MNBSACMB4F/events.json","paper":"https://pith.science/paper/6ARVVCN3"},"agent_actions":{"view_html":"https://pith.science/pith/6ARVVCN3CJCRZCE6MNBSACMB4F","download_json":"https://pith.science/pith/6ARVVCN3CJCRZCE6MNBSACMB4F.json","view_paper":"https://pith.science/paper/6ARVVCN3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.02404&json=true","fetch_graph":"https://pith.science/api/pith-number/6ARVVCN3CJCRZCE6MNBSACMB4F/graph.json","fetch_events":"https://pith.science/api/pith-number/6ARVVCN3CJCRZCE6MNBSACMB4F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6ARVVCN3CJCRZCE6MNBSACMB4F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6ARVVCN3CJCRZCE6MNBSACMB4F/action/storage_attestation","attest_author":"https://pith.science/pith/6ARVVCN3CJCRZCE6MNBSACMB4F/action/author_attestation","sign_citation":"https://pith.science/pith/6ARVVCN3CJCRZCE6MNBSACMB4F/action/citation_signature","submit_replication":"https://pith.science/pith/6ARVVCN3CJCRZCE6MNBSACMB4F/action/replication_record"}},"created_at":"2026-05-18T01:27:30.382857+00:00","updated_at":"2026-05-18T01:27:30.382857+00:00"}