{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:534MPRWAGFP2SQDTAZXBZPMVGX","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":"4a0f6582408357ec2a1ebe680c4e11de3895d87e4a3f57f1837e911ad3acbbab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-08T10:41:46Z","title_canon_sha256":"61a82f734d88795bc6b6dd92008fa95e4e0363a08733f94097dcf63e80ef122a"},"schema_version":"1.0","source":{"id":"1203.1742","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1742","created_at":"2026-05-18T03:04:22Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1742v1","created_at":"2026-05-18T03:04:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1742","created_at":"2026-05-18T03:04:22Z"},{"alias_kind":"pith_short_12","alias_value":"534MPRWAGFP2","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"534MPRWAGFP2SQDT","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"534MPRWA","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:bd7d3bf9adff67c2b21d448da863758369a808936d34473c60998540b431c77b","target":"graph","created_at":"2026-05-18T03:04:22Z","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"},"paper":{"abstract_excerpt":"Dans un r\\'ecent article, Lagarias et Soundararajan \\'etudient les solutions friables \\`a l'\\'equation a+b=c. Sous l'hypoth\\`ese de Riemann g\\'en\\'eralis\\'ees aux fonctions L de Dirichlet, ils obtiennent une estimation pour le nombre de solutions pond\\'er\\'ees par un poids lisse et une minoration pour le nombre de solutions non pond\\'er\\'ees. Le but de cet article est de pr\\'esenter des arguments qui permettent d'une part de pr\\'eciser les termes d'erreur et d'\\'etendre les domaines de validit\\'e de ces estimations afin de faire le lien avec un travail de la Bret\\`eche et Granville, d'autre pa","authors_text":"Sary Drappeau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-08T10:41:46Z","title":"Sur les solutions friables de l'\\'equation a+b=c"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1742","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":"sha256:5b62da0ad1dc9a14361c30b81cb4ade53964c8cfd719c535647476ad0116e11d","target":"record","created_at":"2026-05-18T03:04:22Z","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":"4a0f6582408357ec2a1ebe680c4e11de3895d87e4a3f57f1837e911ad3acbbab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-08T10:41:46Z","title_canon_sha256":"61a82f734d88795bc6b6dd92008fa95e4e0363a08733f94097dcf63e80ef122a"},"schema_version":"1.0","source":{"id":"1203.1742","kind":"arxiv","version":1}},"canonical_sha256":"eef8c7c6c0315fa94073066e1cbd9535dc561188f3d10dec42cecab29af47b78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eef8c7c6c0315fa94073066e1cbd9535dc561188f3d10dec42cecab29af47b78","first_computed_at":"2026-05-18T03:04:22.741024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:22.741024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aWhv0943COZGEs2FnYoLvMgSh4B0hcIVVjppFagO0anbzWio3jb8w3xfjm0A0zWKALG/Eq4RizNJpmtdN7TVCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:22.741594Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1742","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b62da0ad1dc9a14361c30b81cb4ade53964c8cfd719c535647476ad0116e11d","sha256:bd7d3bf9adff67c2b21d448da863758369a808936d34473c60998540b431c77b"],"state_sha256":"45900ea36f15323c6f411115548792bbf0a757e8109b36afdb25260760597dfb"}