{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:63W4IGDE6BS4STAF2NP7633O32","short_pith_number":"pith:63W4IGDE","canonical_record":{"source":{"id":"1705.09133","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-25T11:39:22Z","cross_cats_sorted":[],"title_canon_sha256":"b99a99844f5a301f628812e7f55574d7201a3cfe2bd321e238a34e2d89be25d2","abstract_canon_sha256":"458aeccb00eb7772cd20801138f242da88cbc0d0c02eec15bad0d715c3aa551a"},"schema_version":"1.0"},"canonical_sha256":"f6edc41864f065c94c05d35fff6f6ede9f90904b36bc612d70c5867e09dfa190","source":{"kind":"arxiv","id":"1705.09133","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:63W4IGDE6BS4STAF2NP7633O32","target":"record","payload":{"canonical_record":{"source":{"id":"1705.09133","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-25T11:39:22Z","cross_cats_sorted":[],"title_canon_sha256":"b99a99844f5a301f628812e7f55574d7201a3cfe2bd321e238a34e2d89be25d2","abstract_canon_sha256":"458aeccb00eb7772cd20801138f242da88cbc0d0c02eec15bad0d715c3aa551a"},"schema_version":"1.0"},"canonical_sha256":"f6edc41864f065c94c05d35fff6f6ede9f90904b36bc612d70c5867e09dfa190","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:33.912800Z","signature_b64":"tUzUxqtSve7twG9H/kpmNxmUsplySQfKCJH8pSjiF3mX/BJnCLHtn5X4rHsIcPK1iu48De5E6+CyU3nfN1mSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6edc41864f065c94c05d35fff6f6ede9f90904b36bc612d70c5867e09dfa190","last_reissued_at":"2026-05-17T23:53:33.911988Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:33.911988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.09133","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fKOOwOyBXwNUJoOsEIg9HOQGHk7iR/ZYUAhibQJO5qulCWMATUAM6nzmA1Pgdf+sLBonyX3KxgCWscxGUMbDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:31:12.448433Z"},"content_sha256":"2676fbec7c9972873f4721a87b865ddf1aa211a090151cb612e84d27f54409e3","schema_version":"1.0","event_id":"sha256:2676fbec7c9972873f4721a87b865ddf1aa211a090151cb612e84d27f54409e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:63W4IGDE6BS4STAF2NP7633O32","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sarnak's saturation problem for complete intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Damaris Schindler, Efthymios Sofos","submitted_at":"2017-05-25T11:39:22Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09133","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ta7EFtg1VMGPQ+OhO5gIBytrcVEOXbKVUuy+wAuV4lWsD69XZMWjINOxkzf+yqXDGSYh0We8MoD13ysHAfSdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:31:12.449169Z"},"content_sha256":"9d2c3bed3c2a2676f7fee1d9829e540cce306b692dbc9710f09e0c6f3fa34596","schema_version":"1.0","event_id":"sha256:9d2c3bed3c2a2676f7fee1d9829e540cce306b692dbc9710f09e0c6f3fa34596"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63W4IGDE6BS4STAF2NP7633O32/bundle.json","state_url":"https://pith.science/pith/63W4IGDE6BS4STAF2NP7633O32/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63W4IGDE6BS4STAF2NP7633O32/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T21:31:12Z","links":{"resolver":"https://pith.science/pith/63W4IGDE6BS4STAF2NP7633O32","bundle":"https://pith.science/pith/63W4IGDE6BS4STAF2NP7633O32/bundle.json","state":"https://pith.science/pith/63W4IGDE6BS4STAF2NP7633O32/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63W4IGDE6BS4STAF2NP7633O32/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5qjfD6Le1+WHoiJPDQYh6v8KGMLeZrzSD6TkfFVqlgiPBUVri1oHPz2rqQkOphH6JOPhUq//Bv7eU2i7XnBqCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:31:12.453069Z","bundle_sha256":"6335098c438fd98a52f4f32e59505d9ab24ecdbe76446d772e57907cf4fd58cd"}}