{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:63W4IGDE6BS4STAF2NP7633O32","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":"458aeccb00eb7772cd20801138f242da88cbc0d0c02eec15bad0d715c3aa551a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-25T11:39:22Z","title_canon_sha256":"b99a99844f5a301f628812e7f55574d7201a3cfe2bd321e238a34e2d89be25d2"},"schema_version":"1.0","source":{"id":"1705.09133","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09133","created_at":"2026-05-17T23:53:33Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09133v3","created_at":"2026-05-17T23:53:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09133","created_at":"2026-05-17T23:53:33Z"},{"alias_kind":"pith_short_12","alias_value":"63W4IGDE6BS4","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"63W4IGDE6BS4STAF","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"63W4IGDE","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:9d2c3bed3c2a2676f7fee1d9829e540cce306b692dbc9710f09e0c6f3fa34596","target":"graph","created_at":"2026-05-17T23:53:33Z","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":"We study almost prime solutions of systems of Diophantine equations in the Birch setting. Previous work shows that there exist integer solutions of size B with each component having no prime divisors below $B^{1/u}$, where $u=c_0n^{3/2}$, $n$ is the number of variables and $c_0$ is a constant depending on the degree and the number of equations. We improve the polynomial growth $$n^{3/2}$$ to the logarithmic $$\\frac{\\log n}{\\log \\log n}.$$ Our main new ingredients are the generalisation of the Br\\\"udern-Fouvry vector sieve in any dimension and the incorporation of smooth weights into the Davenp","authors_text":"Damaris Schindler, Efthymios Sofos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-25T11:39:22Z","title":"Sarnak's saturation problem for complete intersections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09133","kind":"arxiv","version":3},"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":"sha256:2676fbec7c9972873f4721a87b865ddf1aa211a090151cb612e84d27f54409e3","target":"record","created_at":"2026-05-17T23:53:33Z","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":"458aeccb00eb7772cd20801138f242da88cbc0d0c02eec15bad0d715c3aa551a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-25T11:39:22Z","title_canon_sha256":"b99a99844f5a301f628812e7f55574d7201a3cfe2bd321e238a34e2d89be25d2"},"schema_version":"1.0","source":{"id":"1705.09133","kind":"arxiv","version":3}},"canonical_sha256":"f6edc41864f065c94c05d35fff6f6ede9f90904b36bc612d70c5867e09dfa190","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6edc41864f065c94c05d35fff6f6ede9f90904b36bc612d70c5867e09dfa190","first_computed_at":"2026-05-17T23:53:33.911988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:33.911988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tUzUxqtSve7twG9H/kpmNxmUsplySQfKCJH8pSjiF3mX/BJnCLHtn5X4rHsIcPK1iu48De5E6+CyU3nfN1mSCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:33.912800Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.09133","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2676fbec7c9972873f4721a87b865ddf1aa211a090151cb612e84d27f54409e3","sha256:9d2c3bed3c2a2676f7fee1d9829e540cce306b692dbc9710f09e0c6f3fa34596"],"state_sha256":"e67fd275d063865a6aab67383709ea1ca560840e4be05e62e95f2795e2d78f88"}