{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:GV5W5WZB4QNTN2VGSKPL4G6NVH","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":"2c27c16af750275750842fccecf8fdc9182b97b348712a335fab63757911613f","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2006-06-04T10:37:47Z","title_canon_sha256":"e83691131202cdde9947f568a79792d361515755539bedf5a657cc2e29ead124"},"schema_version":"1.0","source":{"id":"math/0606087","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606087","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606087v2","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606087","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"pith_short_12","alias_value":"GV5W5WZB4QNT","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"GV5W5WZB4QNTN2VG","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"GV5W5WZB","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:2e8afda1093ee7d32d6ccab311769687b0868ec2cb5da6ba9f478af9e2056c6d","target":"graph","created_at":"2026-05-18T04:08:53Z","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":"This paper is a part of our programme to generalise the Hardy-Littlewood method to handle systems of linear questions in primes. This programme is laid out in our paper Linear Equations in Primes [LEP], which accompanies this submission. In particular, the results of this paper may be used, together with the machinery of [LEP], to establish an asymptotic for the number of four-term progressions p_1 < p_2 < p_3 < p_4 <= N of primes, and more generally any problem counting prime points inside a ``non-degenerate'' affine lattice of codimension at most 2.\n  The main result of this paper is a proof","authors_text":"Ben Green, Terence Tao","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2006-06-04T10:37:47Z","title":"Quadratic Uniformity of the Mobius Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606087","kind":"arxiv","version":2},"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":"sha256:567bc4295e03a2b2da9272f89cf2219f00b9e6b5f63451c3da5d1ce16ae4e3eb","target":"record","created_at":"2026-05-18T04:08:53Z","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":"2c27c16af750275750842fccecf8fdc9182b97b348712a335fab63757911613f","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2006-06-04T10:37:47Z","title_canon_sha256":"e83691131202cdde9947f568a79792d361515755539bedf5a657cc2e29ead124"},"schema_version":"1.0","source":{"id":"math/0606087","kind":"arxiv","version":2}},"canonical_sha256":"357b6edb21e41b36eaa6929ebe1bcda9f293767803afc66b49da3870d543c88b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"357b6edb21e41b36eaa6929ebe1bcda9f293767803afc66b49da3870d543c88b","first_computed_at":"2026-05-18T04:08:53.457844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:53.457844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZX0FCexW3b+NH6uP+2TdZmMggX7mvIHHDSNOU40H1kfe21Zf71w6Fu6sEHe8u2CY5v3pa1elZXRFL3Rupo5bDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:53.458275Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606087","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:567bc4295e03a2b2da9272f89cf2219f00b9e6b5f63451c3da5d1ce16ae4e3eb","sha256:2e8afda1093ee7d32d6ccab311769687b0868ec2cb5da6ba9f478af9e2056c6d"],"state_sha256":"fab454fbda9201cc7f082276a38de1e95d08b665b929f5f21fb2500ae1260451"}