{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:G2PPG5KNVZG2TLVLQT4OPXBKZ2","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":"1818c9891a14b513e74e5a0cb2ac23d5c4e07b46ee5ba9d245b2ed6de612156f","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-01-07T15:09:13Z","title_canon_sha256":"9bb5eb0ad2207a523e944c3e27ce830a950db2abdb9407bfa895365578f69609"},"schema_version":"1.0","source":{"id":"2601.03999","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.03999","created_at":"2026-06-09T02:07:16Z"},{"alias_kind":"arxiv_version","alias_value":"2601.03999v2","created_at":"2026-06-09T02:07:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.03999","created_at":"2026-06-09T02:07:16Z"},{"alias_kind":"pith_short_12","alias_value":"G2PPG5KNVZG2","created_at":"2026-06-09T02:07:16Z"},{"alias_kind":"pith_short_16","alias_value":"G2PPG5KNVZG2TLVL","created_at":"2026-06-09T02:07:16Z"},{"alias_kind":"pith_short_8","alias_value":"G2PPG5KN","created_at":"2026-06-09T02:07:16Z"}],"graph_snapshots":[{"event_id":"sha256:a5ee36a19bfd114dd6668ea289bfe58f337d5178ebb0c0c0ecb8a7d0412a5594","target":"graph","created_at":"2026-06-09T02:07:16Z","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/2601.03999/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove quantitative polynomial Wiener-Wintner theorems in a very general setup, including measure-preserving actions of nilpotent Lie groups. Our results apply both to ergodic averages and to averages with singular integral weights. The proof relies on the generalized polynomial Carleson theorem developed in the companion paper by van Doorn, Srivastava, and the authors.","authors_text":"Asgar Jamneshan, Christoph Thiele, Lars Becker","cross_cats":["math.CA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-01-07T15:09:13Z","title":"Quantitative Polynomial Wiener-Wintner Theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.03999","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":"sha256:9ee9e483f2964bb15092d0d74562ba605d0a9b44681e0523e3a89d3bdb47e4cd","target":"record","created_at":"2026-06-09T02:07:16Z","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":"1818c9891a14b513e74e5a0cb2ac23d5c4e07b46ee5ba9d245b2ed6de612156f","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-01-07T15:09:13Z","title_canon_sha256":"9bb5eb0ad2207a523e944c3e27ce830a950db2abdb9407bfa895365578f69609"},"schema_version":"1.0","source":{"id":"2601.03999","kind":"arxiv","version":2}},"canonical_sha256":"369ef3754dae4da9aeab84f8e7dc2ace82377a8d4eccf72b7c401c4ceee4a747","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"369ef3754dae4da9aeab84f8e7dc2ace82377a8d4eccf72b7c401c4ceee4a747","first_computed_at":"2026-06-09T02:07:16.685224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:07:16.685224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TvZk8OwK8SDusjY41d1ZJ79rVHu4kJPyr6XcwW97NqvCSsMXa9tgDDGQ0SHqNJzhsZiN8CGyem5dauF6BzGkBw==","signature_status":"signed_v1","signed_at":"2026-06-09T02:07:16.686040Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.03999","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ee9e483f2964bb15092d0d74562ba605d0a9b44681e0523e3a89d3bdb47e4cd","sha256:a5ee36a19bfd114dd6668ea289bfe58f337d5178ebb0c0c0ecb8a7d0412a5594"],"state_sha256":"b96646533928e3e27e85dd53c9dd17ab7099cda25d64f1eaf6ae5efae6fae7f6"}