{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OT2LECEMNY2V24WUHDMCVOMOJW","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":"c5db7c7e86f2d2ac2393091bc04e358849f9457c1e5bfc48fffb3442ef529180","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-01T05:16:56Z","title_canon_sha256":"9f8c1eec6d8db0d7d66de7a3bae71c8eb36ad97f4bd089eb6f38833e513207c7"},"schema_version":"1.0","source":{"id":"1205.0090","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0090","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0090v1","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0090","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"OT2LECEMNY2V","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OT2LECEMNY2V24WU","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OT2LECEM","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:fb9f369d77d1bed6d8c3a90810e4b1d3962e09d0be8c385fb94d38d0e51e3220","target":"graph","created_at":"2026-05-18T03:56:35Z","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 improve the error term in the van der Corput transform for exponential sums\n  \\sum_{a \\le n \\le b} g(n) exp(2\\pi i f(n)).\n  For many functions g and f, we can extract the next term in the asymptotic, showing that previous results, such as those of Karatsuba and Korolev, are sharp. Of particular note, the methods of this paper avoid the use of the truncated Poisson formula, and thus can be applied to much longer intervals [a,b] with far better results. We provide a detailed analysis of the error term in the case g(x)=1 and f(x)=(x/3)^{3/2}.","authors_text":"Joseph Vandehey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-01T05:16:56Z","title":"Error term improvements for van der Corput transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0090","kind":"arxiv","version":1},"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":"sha256:1d9ceec8b94ba087fdfae5a8ed741369d0f67da1cfca05b34611bea532f12c6e","target":"record","created_at":"2026-05-18T03:56:35Z","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":"c5db7c7e86f2d2ac2393091bc04e358849f9457c1e5bfc48fffb3442ef529180","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-01T05:16:56Z","title_canon_sha256":"9f8c1eec6d8db0d7d66de7a3bae71c8eb36ad97f4bd089eb6f38833e513207c7"},"schema_version":"1.0","source":{"id":"1205.0090","kind":"arxiv","version":1}},"canonical_sha256":"74f4b2088c6e355d72d438d82ab98e4d802cb2afa433830eb84359ed49847c0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74f4b2088c6e355d72d438d82ab98e4d802cb2afa433830eb84359ed49847c0e","first_computed_at":"2026-05-18T03:56:35.889034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:35.889034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PPvOgCh8TAWI4HzPi8p0Ct8ksoS1rvucEHFgkyvGWOhzrVsP0NqMjRQQmPrU/DfPEQX0kpDJIJNGwYw5lCkvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:35.889454Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0090","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d9ceec8b94ba087fdfae5a8ed741369d0f67da1cfca05b34611bea532f12c6e","sha256:fb9f369d77d1bed6d8c3a90810e4b1d3962e09d0be8c385fb94d38d0e51e3220"],"state_sha256":"bf8a410e13785c03ba72810ac0c27ba0845911f0ba33f6004cbdb0247215f86f"}