{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:EEAMHI37ZCFNEQ344EPI4QPEBA","short_pith_number":"pith:EEAMHI37","schema_version":"1.0","canonical_sha256":"2100c3a37fc88ad2437ce11e8e41e4083ae655056c1adb3783bcb524c8e4ee97","source":{"kind":"arxiv","id":"2607.21950","version":1},"attestation_state":"computed","paper":{"title":"Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Zhicheng Tong","submitted_at":"2026-07-24T03:53:25Z","abstract_excerpt":"Since Krengel's work [Kre78] in 1978, it has been widely known that no effective rate of convergence exists in the ergodic theorem. For toral translations, however, by choosing appropriate weights one can accelerate the convergence of ergodic averages to an exponential rate, but this intuitively requires both highly nonresonant frequencies and very regular observables. In this paper, we uncover a new phenomenon: even for any given nonresonant frequency, there exists a non-trivial family of weights and observables of low regularity such that the weighted Birkhoff averages along quasi-periodic o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.21950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-24T03:53:25Z","cross_cats_sorted":[],"title_canon_sha256":"3707719fafa1ff57e2c4c46b8b119cd1e14a484d29b95f384fb3f807abc42318","abstract_canon_sha256":"6edee6673c1f875e27ee6e61b3499dd422eb6a025909287490cf82d854d3da01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-27T00:20:29.372064Z","signature_b64":"wNUxxyjuguwLu8Q7LGYfK6xjSqGdMRXfeOlyMImTApciTnJ1BWVl0mzx9HOnW5JJvjAgLDir1hohL5fwM3UABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2100c3a37fc88ad2437ce11e8e41e4083ae655056c1adb3783bcb524c8e4ee97","last_reissued_at":"2026-07-27T00:20:29.371290Z","signature_status":"signed_v1","first_computed_at":"2026-07-27T00:20:29.371290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Zhicheng Tong","submitted_at":"2026-07-24T03:53:25Z","abstract_excerpt":"Since Krengel's work [Kre78] in 1978, it has been widely known that no effective rate of convergence exists in the ergodic theorem. For toral translations, however, by choosing appropriate weights one can accelerate the convergence of ergodic averages to an exponential rate, but this intuitively requires both highly nonresonant frequencies and very regular observables. In this paper, we uncover a new phenomenon: even for any given nonresonant frequency, there exists a non-trivial family of weights and observables of low regularity such that the weighted Birkhoff averages along quasi-periodic o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21950","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.21950/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.21950","created_at":"2026-07-27T00:20:29.371688+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.21950v1","created_at":"2026-07-27T00:20:29.371688+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21950","created_at":"2026-07-27T00:20:29.371688+00:00"},{"alias_kind":"pith_short_12","alias_value":"EEAMHI37ZCFN","created_at":"2026-07-27T00:20:29.371688+00:00"},{"alias_kind":"pith_short_16","alias_value":"EEAMHI37ZCFNEQ34","created_at":"2026-07-27T00:20:29.371688+00:00"},{"alias_kind":"pith_short_8","alias_value":"EEAMHI37","created_at":"2026-07-27T00:20:29.371688+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.02182","citing_title":"Laskar's frequency map analysis revisited","ref_index":64,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EEAMHI37ZCFNEQ344EPI4QPEBA","json":"https://pith.science/pith/EEAMHI37ZCFNEQ344EPI4QPEBA.json","graph_json":"https://pith.science/api/pith-number/EEAMHI37ZCFNEQ344EPI4QPEBA/graph.json","events_json":"https://pith.science/api/pith-number/EEAMHI37ZCFNEQ344EPI4QPEBA/events.json","paper":"https://pith.science/paper/EEAMHI37"},"agent_actions":{"view_html":"https://pith.science/pith/EEAMHI37ZCFNEQ344EPI4QPEBA","download_json":"https://pith.science/pith/EEAMHI37ZCFNEQ344EPI4QPEBA.json","view_paper":"https://pith.science/paper/EEAMHI37","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.21950&json=true","fetch_graph":"https://pith.science/api/pith-number/EEAMHI37ZCFNEQ344EPI4QPEBA/graph.json","fetch_events":"https://pith.science/api/pith-number/EEAMHI37ZCFNEQ344EPI4QPEBA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EEAMHI37ZCFNEQ344EPI4QPEBA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EEAMHI37ZCFNEQ344EPI4QPEBA/action/storage_attestation","attest_author":"https://pith.science/pith/EEAMHI37ZCFNEQ344EPI4QPEBA/action/author_attestation","sign_citation":"https://pith.science/pith/EEAMHI37ZCFNEQ344EPI4QPEBA/action/citation_signature","submit_replication":"https://pith.science/pith/EEAMHI37ZCFNEQ344EPI4QPEBA/action/replication_record"}},"created_at":"2026-07-27T00:20:29.371688+00:00","updated_at":"2026-07-27T00:20:29.371688+00:00"}