{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ECIIWRRK4AZ5OGCQKUC4J4SD2N","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":"d4e3904059a6f9f22a9caccc7f3d84acce806be4b9fab3ee003ca192e82e8393","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-02T03:00:45Z","title_canon_sha256":"32fa8583d3e40442bae0e583c3c9a17fd2eee300a60e343bbe18d8a655fee565"},"schema_version":"1.0","source":{"id":"1811.00718","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.00718","created_at":"2026-07-05T07:45:42Z"},{"alias_kind":"arxiv_version","alias_value":"1811.00718v2","created_at":"2026-07-05T07:45:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00718","created_at":"2026-07-05T07:45:42Z"},{"alias_kind":"pith_short_12","alias_value":"ECIIWRRK4AZ5","created_at":"2026-07-05T07:45:42Z"},{"alias_kind":"pith_short_16","alias_value":"ECIIWRRK4AZ5OGCQ","created_at":"2026-07-05T07:45:42Z"},{"alias_kind":"pith_short_8","alias_value":"ECIIWRRK","created_at":"2026-07-05T07:45:42Z"}],"graph_snapshots":[{"event_id":"sha256:ae243d10fd97bfe344f6b80559751fd949c2ba1ba917bef4da66acd67973c25f","target":"graph","created_at":"2026-07-05T07:45:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1811.00718/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a new proof of the inverse theorem for the Gowers $U^{s+1}$-norm over groups $H=\\mathbb Z/N\\mathbb Z$ for $N$ prime. This proof gives reasonable quantitative bounds (the worst parameters are double-exponential), and in particular does not make use of regularity or non-standard analysis, both of which are new for $s \\ge 3$ in this setting.","authors_text":"Frederick Manners","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-02T03:00:45Z","title":"Quantitative bounds in the inverse theorem for the Gowers $U^{s+1}$-norms over cyclic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00718","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":"sha256:8c28fbeee2bd99a314e023765ec1c1ab05ad551a1c9f186aac72fbbbe9d3f4c5","target":"record","created_at":"2026-07-05T07:45:42Z","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":"d4e3904059a6f9f22a9caccc7f3d84acce806be4b9fab3ee003ca192e82e8393","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-02T03:00:45Z","title_canon_sha256":"32fa8583d3e40442bae0e583c3c9a17fd2eee300a60e343bbe18d8a655fee565"},"schema_version":"1.0","source":{"id":"1811.00718","kind":"arxiv","version":2}},"canonical_sha256":"20908b462ae033d718505505c4f243d353448ec2843a3115d76c71872fbf75ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20908b462ae033d718505505c4f243d353448ec2843a3115d76c71872fbf75ad","first_computed_at":"2026-07-05T07:45:42.942661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:45:42.942661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e5bZoyFF1/9986DcPe5jk7Xa5taZWcOaKzzabvPQl9UgzZ8PM/zmYb3841bUubSNqA3E10O/jTkz/PKlHd9/CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:45:42.943095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.00718","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c28fbeee2bd99a314e023765ec1c1ab05ad551a1c9f186aac72fbbbe9d3f4c5","sha256:ae243d10fd97bfe344f6b80559751fd949c2ba1ba917bef4da66acd67973c25f"],"state_sha256":"f69f273eaf0c4ec3f23d1d5c61187a4350b8aa905d110e2aa89655a128555b4d"}