{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:UXZDP4QDWTURMGUBJ67TKK5HD3","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":"d685437a326351207adbf1c5487d64007b119a2dc8f9d4ec77ff34a405b509b5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-11-07T13:53:15Z","title_canon_sha256":"897d15497d8f0e365063767c7a95941cb6f1f2e35c13268e793dd601eb718900"},"schema_version":"1.0","source":{"id":"2311.03997","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.03997","created_at":"2026-07-05T07:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"2311.03997v1","created_at":"2026-07-05T07:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.03997","created_at":"2026-07-05T07:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"UXZDP4QDWTUR","created_at":"2026-07-05T07:10:09Z"},{"alias_kind":"pith_short_16","alias_value":"UXZDP4QDWTURMGUB","created_at":"2026-07-05T07:10:09Z"},{"alias_kind":"pith_short_8","alias_value":"UXZDP4QD","created_at":"2026-07-05T07:10:09Z"}],"graph_snapshots":[{"event_id":"sha256:96c3aabdc24dd88ccb904f0612a1e5db68f5c34af6dd9b2f1b4f5ac71c0ca18a","target":"graph","created_at":"2026-07-05T07:10:09Z","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/2311.03997/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $1<c<d$ be two relatively prime integers. For a non-negative integer $\\ell$, let $g_\\ell(c,d)$ be the largest integer $n$ such that $n=c x+d y$ has at most $\\ell$ non-negative solutions $(x,y)$. In this paper we prove that $$ \\pi_{\\ell,c,d}\\sim\\frac{\\pi\\bigl(g_\\ell(c,d)\\bigr)}{2 \\ell+2}\\quad(\\text{as}~ c\\to\\infty)\\,, $$ where $\\pi_{\\ell,c,d}$ is the number of primes $n$ having more than $\\ell$ distinct non-negative solutions to $n=c x+d y$ with $n\\le g_\\ell(c,d)$, and $\\pi(x)$ denotes the number of all primes up to $x$. The case where $\\ell=0$ has been proved by Ding, Zhai and Zhao recentl","authors_text":"Takao Komatsu, Yuchen Ding","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-11-07T13:53:15Z","title":"On a conjecture of Ram\\'{\\i}rez Alfons\\'{\\i}n and Ska{\\l}ba III"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.03997","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":"sha256:1b72671179697809474b9d00099ede33450d76f72b40064fc0bd58d9504d0b51","target":"record","created_at":"2026-07-05T07:10:09Z","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":"d685437a326351207adbf1c5487d64007b119a2dc8f9d4ec77ff34a405b509b5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-11-07T13:53:15Z","title_canon_sha256":"897d15497d8f0e365063767c7a95941cb6f1f2e35c13268e793dd601eb718900"},"schema_version":"1.0","source":{"id":"2311.03997","kind":"arxiv","version":1}},"canonical_sha256":"a5f237f203b4e9161a814fbf352ba71ed294682544448c6adf8f34d5a956e8d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5f237f203b4e9161a814fbf352ba71ed294682544448c6adf8f34d5a956e8d1","first_computed_at":"2026-07-05T07:10:09.321035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:10:09.321035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VUbIbpAYvV3rgIvqQczZe39TdTOMviT2y6S8DMAPWw6RZpGn+EQkUqNQ8NtZouaS+okwwoqg0qfZTRgIIjiNCg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:10:09.321510Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.03997","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b72671179697809474b9d00099ede33450d76f72b40064fc0bd58d9504d0b51","sha256:96c3aabdc24dd88ccb904f0612a1e5db68f5c34af6dd9b2f1b4f5ac71c0ca18a"],"state_sha256":"2595d7dd30385dd4e0dca66c01436c8741ada6429937ac7b54e645b2396842dc"}