{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HGSGRJAYX4DBUUIIZHXK5ITZXI","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":"8cbfc4b58820a432baaa54d9820eaee9e25232b8781ae17f8183ca30b2fee0b0","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-06-01T18:08:16Z","title_canon_sha256":"f967b18eaacf8caccf1c923a717afac89b2a034c81d3a3b4e6bbf3fcd4d475c6"},"schema_version":"1.0","source":{"id":"1006.0205","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.0205","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"1006.0205v4","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.0205","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"HGSGRJAYX4DB","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HGSGRJAYX4DBUUII","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HGSGRJAY","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:57db2f51006c2d2f5a46b6d8899151b652a4e917f349144a9c1c877d33e3a27a","target":"graph","created_at":"2026-05-18T04:21:10Z","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":"In this note we announce the proof of the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s => 3; this is new for s => 4, the cases s = 1,2,3 having been previously established. More precisely we outline a proof (details of which will appear in a forthcoming paper) that if f : [N] -> [-1,1] is a function with || f ||_{U^{s+1}[N]} => \\delta then there is a bounded-complexity s-step nilsequence F(g(n)\\Gamma) which correlates with f, where the bounds on the complexity and correlation depend only on s and \\delta. From previous results, this conjecture implies the Hardy-Littlewood prime t","authors_text":"Ben Green, Tamar Ziegler, Terence Tao","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-06-01T18:08:16Z","title":"An inverse theorem for the Gowers U^{s+1}[N]-norm (announcement)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0205","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":"sha256:3a2a788aeee47968a55a3f054ff3fb1e1df8b778cac4d94cc80b027c2e352f91","target":"record","created_at":"2026-05-18T04:21:10Z","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":"8cbfc4b58820a432baaa54d9820eaee9e25232b8781ae17f8183ca30b2fee0b0","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-06-01T18:08:16Z","title_canon_sha256":"f967b18eaacf8caccf1c923a717afac89b2a034c81d3a3b4e6bbf3fcd4d475c6"},"schema_version":"1.0","source":{"id":"1006.0205","kind":"arxiv","version":4}},"canonical_sha256":"39a468a418bf061a5108c9eeaea279ba1962260e8d0c02fa697a44f1f42d76bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39a468a418bf061a5108c9eeaea279ba1962260e8d0c02fa697a44f1f42d76bf","first_computed_at":"2026-05-18T04:21:10.851085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:10.851085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hsBT77NMLOANwOQ2as3uhcGikC/fhndpPCRGJ8P7OswDOPX2p6YUC8lD9/1jzJpxYfIIFuasDMJeDW1oWQnnBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:10.851761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.0205","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a2a788aeee47968a55a3f054ff3fb1e1df8b778cac4d94cc80b027c2e352f91","sha256:57db2f51006c2d2f5a46b6d8899151b652a4e917f349144a9c1c877d33e3a27a"],"state_sha256":"a1b4e242731b43ff27d62480cdab370a61435fbc3aff50c2a75a474abe848afd"}