{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:W6YLRGQWYGBUSRDM5DLHKQZEPV","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":"4b67b9546b00c15b9a39b00ae0de2cfdc9f4b641fe524ac9e79b44e4bd2ac2d2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-11-14T13:49:13Z","title_canon_sha256":"920464c0e0c0ce56802763e103cd1c0278b678267676a97cb6d5af7b6860a003"},"schema_version":"1.0","source":{"id":"2411.09446","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.09446","created_at":"2026-07-05T10:51:28Z"},{"alias_kind":"arxiv_version","alias_value":"2411.09446v4","created_at":"2026-07-05T10:51:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.09446","created_at":"2026-07-05T10:51:28Z"},{"alias_kind":"pith_short_12","alias_value":"W6YLRGQWYGBU","created_at":"2026-07-05T10:51:28Z"},{"alias_kind":"pith_short_16","alias_value":"W6YLRGQWYGBUSRDM","created_at":"2026-07-05T10:51:28Z"},{"alias_kind":"pith_short_8","alias_value":"W6YLRGQW","created_at":"2026-07-05T10:51:28Z"}],"graph_snapshots":[{"event_id":"sha256:f120eb75bfabb579d97a9653d4d9d91efc3a755c64050715318e3b8268e9588c","target":"graph","created_at":"2026-07-05T10:51:28Z","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/2411.09446/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $2< a<b$ be two relatively prime integers and $g=ab-a-b$. It is proved that there exists at least one prime $p\\le g$ of the form $p=ax+by~(x,y\\in \\mathbb{Z}_{\\ge 0})$, which confirms a 2020 conjecture of Ram\\'{\\i}rez Alfons\\'{\\i}n and Ska{\\l}ba.","authors_text":"Hui Wang, Tianhan Dai, Yuchen Ding","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-11-14T13:49:13Z","title":"Note on a conjecture of Ram\\'{\\i}rez Alfons\\'{\\i}n and Ska{\\l}ba"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09446","kind":"arxiv","version":4},"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":"sha256:57e6d06205e28f4c891209f685ab3926c72aae1a7b90f9cbc6ee7e08811d777d","target":"record","created_at":"2026-07-05T10:51:28Z","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":"4b67b9546b00c15b9a39b00ae0de2cfdc9f4b641fe524ac9e79b44e4bd2ac2d2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-11-14T13:49:13Z","title_canon_sha256":"920464c0e0c0ce56802763e103cd1c0278b678267676a97cb6d5af7b6860a003"},"schema_version":"1.0","source":{"id":"2411.09446","kind":"arxiv","version":4}},"canonical_sha256":"b7b0b89a16c18349446ce8d67543247d659d6dd3143b90353b54b51069d0a394","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7b0b89a16c18349446ce8d67543247d659d6dd3143b90353b54b51069d0a394","first_computed_at":"2026-07-05T10:51:28.284879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:51:28.284879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"evvzsB5DVW9ZUJ+sxF4k7q7uG7TgqkoLW7ID2AmrD/sdCm7CVUjbUt8Gnfc1PSyRZl4c56yMKGWkQuroudM5CA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:51:28.285391Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.09446","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57e6d06205e28f4c891209f685ab3926c72aae1a7b90f9cbc6ee7e08811d777d","sha256:f120eb75bfabb579d97a9653d4d9d91efc3a755c64050715318e3b8268e9588c"],"state_sha256":"663639f2c02630b2894a27edccf77ec1c0d2aac56f114a8f633d5ee6716e503b"}