{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LNDWUCFKT64DYUB7NQTVHPCUMD","short_pith_number":"pith:LNDWUCFK","schema_version":"1.0","canonical_sha256":"5b476a08aa9fb83c503f6c2753bc5460d13857b30e0b5a3bfebcfcc663c5c656","source":{"kind":"arxiv","id":"1808.06031","version":1},"attestation_state":"computed","paper":{"title":"A stronger connection between the Erd\\H{o}s-Burgess and Davenport constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ashwin Sah, Noah Kravitz","submitted_at":"2018-08-18T02:14:03Z","abstract_excerpt":"The Erd\\H{o}s-Burgess constant of a semigroup $S$ is the smallest positive integer $k$ such that any sequence over $S$ of length $k$ contains a nonempty subsequence whose elements multiply to an idempotent element of $S$. In the case where $S$ is the multiplicative semigroup of $\\mathbb{Z}/n\\mathbb{Z}$, we confirm a conjecture connecting the Erd\\H{o}s-Burgess constant of $S$ and the Davenport constant of $(\\mathbb{Z}/n\\mathbb{Z})^{\\times}$ for $n$ with at most two prime factors. We also discuss the extension of our techniques to other rings."},"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":"1808.06031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-18T02:14:03Z","cross_cats_sorted":[],"title_canon_sha256":"5c2941e03973cda426d9614ac51afef598053cddb7a2bf8c7f7a5f31cdc3095d","abstract_canon_sha256":"678d61ab87f2c8e2d91e7b5df5acd230a38e86ae824147f84f3a3ea69f401a9b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:46.379151Z","signature_b64":"mQMmg5r7BkLgsJ+cQu28xmT8OR6oEab1F4qx6ttAGlx+vBBE3Y9Q436FIeXOqdG2TmEEkL26HROvHrwkCEAfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b476a08aa9fb83c503f6c2753bc5460d13857b30e0b5a3bfebcfcc663c5c656","last_reissued_at":"2026-05-18T00:07:46.378587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:46.378587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A stronger connection between the Erd\\H{o}s-Burgess and Davenport constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ashwin Sah, Noah Kravitz","submitted_at":"2018-08-18T02:14:03Z","abstract_excerpt":"The Erd\\H{o}s-Burgess constant of a semigroup $S$ is the smallest positive integer $k$ such that any sequence over $S$ of length $k$ contains a nonempty subsequence whose elements multiply to an idempotent element of $S$. In the case where $S$ is the multiplicative semigroup of $\\mathbb{Z}/n\\mathbb{Z}$, we confirm a conjecture connecting the Erd\\H{o}s-Burgess constant of $S$ and the Davenport constant of $(\\mathbb{Z}/n\\mathbb{Z})^{\\times}$ for $n$ with at most two prime factors. We also discuss the extension of our techniques to other rings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06031","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":"1808.06031","created_at":"2026-05-18T00:07:46.378696+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.06031v1","created_at":"2026-05-18T00:07:46.378696+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.06031","created_at":"2026-05-18T00:07:46.378696+00:00"},{"alias_kind":"pith_short_12","alias_value":"LNDWUCFKT64D","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LNDWUCFKT64DYUB7","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LNDWUCFK","created_at":"2026-05-18T12:32:37.024351+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/LNDWUCFKT64DYUB7NQTVHPCUMD","json":"https://pith.science/pith/LNDWUCFKT64DYUB7NQTVHPCUMD.json","graph_json":"https://pith.science/api/pith-number/LNDWUCFKT64DYUB7NQTVHPCUMD/graph.json","events_json":"https://pith.science/api/pith-number/LNDWUCFKT64DYUB7NQTVHPCUMD/events.json","paper":"https://pith.science/paper/LNDWUCFK"},"agent_actions":{"view_html":"https://pith.science/pith/LNDWUCFKT64DYUB7NQTVHPCUMD","download_json":"https://pith.science/pith/LNDWUCFKT64DYUB7NQTVHPCUMD.json","view_paper":"https://pith.science/paper/LNDWUCFK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.06031&json=true","fetch_graph":"https://pith.science/api/pith-number/LNDWUCFKT64DYUB7NQTVHPCUMD/graph.json","fetch_events":"https://pith.science/api/pith-number/LNDWUCFKT64DYUB7NQTVHPCUMD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LNDWUCFKT64DYUB7NQTVHPCUMD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LNDWUCFKT64DYUB7NQTVHPCUMD/action/storage_attestation","attest_author":"https://pith.science/pith/LNDWUCFKT64DYUB7NQTVHPCUMD/action/author_attestation","sign_citation":"https://pith.science/pith/LNDWUCFKT64DYUB7NQTVHPCUMD/action/citation_signature","submit_replication":"https://pith.science/pith/LNDWUCFKT64DYUB7NQTVHPCUMD/action/replication_record"}},"created_at":"2026-05-18T00:07:46.378696+00:00","updated_at":"2026-05-18T00:07:46.378696+00:00"}