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The main ϕ-mixing estimate is obtained by a residue-class blocking argument and a one-sided approximate-independence inequality; it has a free spacing parameter L≥0, spacing coefficient 1/(L+1), and residual terms governed by ϕ(L+1).","weakest_assumption":"The event sequence satisfies quantitative ϕ-mixing or α-mixing bounds (i.e., the mixing coefficients decay at a known rate), which is invoked to control the residual terms after blocking."}},"verdict_id":"736a4d75-11f8-4369-a765-a4683a8dbe2a"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b2416d0375090810711fa0044a21dcffd503b5006473d7e21dbc71434ba53294","target":"record","created_at":"2026-06-09T02:07:27Z","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":"0b11bf877f8545b6380a16bcaa05eb70b48c6d950e2a9dc6f966df93400982f8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-04-26T16:31:01Z","title_canon_sha256":"ccd8604ababa03f9470973a1c13ed8dcebc9e9e33ec901793340142004994508"},"schema_version":"1.0","source":{"id":"2604.23791","kind":"arxiv","version":2}},"canonical_sha256":"4f295ae9b76d1f326474449529e13424b5e7d05eea865645b36e80d97a9009c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f295ae9b76d1f326474449529e13424b5e7d05eea865645b36e80d97a9009c3","first_computed_at":"2026-06-09T02:07:27.351187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:07:27.351187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iGPMP1NqbLwskgmp7WRqd69Up0WWYFERjQiRTDMGRZMoc5NeSzqOKUkCJAyN4jBNlxGYwA2Hq/cuDMn1Z69ZBg==","signature_status":"signed_v1","signed_at":"2026-06-09T02:07:27.352072Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.23791","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4209ff6ccd94ecdc627710f26a06e7a116543b68394188c94845a8c7afd0557","sha256:b2416d0375090810711fa0044a21dcffd503b5006473d7e21dbc71434ba53294","sha256:f37113a5449869eb1dbb6b38cc48faf49480994f53eeaaf0c5c006c5542367d5"],"state_sha256":"b050ad0e19af874fab13807b55f00a44639fa06d7f8d9c52e7f68e42fc9f4ae3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"64YzogLrDp38GncN6bNG+rFz7IPHQ9DiwQw0K8dzyCEuI93w9Jpsq2EG4FMLmL6JxbrI0HFtK1rWa/1RwUOTDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T05:31:32.876586Z","bundle_sha256":"2105e0176f8a43f57b765d53dc62bb0e9548b5c7ea6e2e6d7a6d301febc418c3"}}