{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Z66MPSYSSATW2DTPESVRAF7WMJ","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":"b48246e4ef6a801a61c1f6bb2d24b1048ec19126a63077096d9947f9710f9fa7","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2018-02-07T17:12:26Z","title_canon_sha256":"d35e697d789382fdcec7acfd5167fad8d46550a0abc9e4ca93e1dfb39db741db"},"schema_version":"1.0","source":{"id":"1802.02906","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02906","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02906v2","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02906","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"pith_short_12","alias_value":"Z66MPSYSSATW","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Z66MPSYSSATW2DTP","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Z66MPSYS","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:ec84281fce3aa4dd15d35d418ae0007307f35e2144d6a383fbf2f05036197a9f","target":"graph","created_at":"2026-05-18T00:05:14Z","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":"Let either $R_k(t) := |P_k(e^{it})|^2$ or $R_k(t) := |Q_k(e^{it})|^2$, where $P_k$ and $Q_k$ are the usual Rudin-Shapiro polynomials of degree $n-1$ with $n=2^k$. In a recent paper we combined close to sharp upper bounds for the modulus of the autocorrelation coefficients of the Rudin-Shapiro polynomials with a deep theorem of Littlewood to prove that there is an absolute constant $A>0$ such that the equation $R_k(t) = (1+\\eta )n$ has at least $An^{0.5394282}$ distinct zeros in $[0,2\\pi)$ whenever $\\eta$ is real and $|\\eta| < 2^{-11}$. In this paper we show that the equation $R_k(t)=(1+\\eta)n$","authors_text":"Tam\\'as Erd\\'elyi","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2018-02-07T17:12:26Z","title":"Improved results on the oscillation of the modulus of the Rudin-Shapiro polynomials on the unit circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02906","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:c5551bdd5c44e8c771b41fa30cdbd8f9d0ce74bc036e69acdb9f34667d076a94","target":"record","created_at":"2026-05-18T00:05:14Z","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":"b48246e4ef6a801a61c1f6bb2d24b1048ec19126a63077096d9947f9710f9fa7","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2018-02-07T17:12:26Z","title_canon_sha256":"d35e697d789382fdcec7acfd5167fad8d46550a0abc9e4ca93e1dfb39db741db"},"schema_version":"1.0","source":{"id":"1802.02906","kind":"arxiv","version":2}},"canonical_sha256":"cfbcc7cb1290276d0e6f24ab1017f6626245d6397c6f16b025708bc5c7a92f01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfbcc7cb1290276d0e6f24ab1017f6626245d6397c6f16b025708bc5c7a92f01","first_computed_at":"2026-05-18T00:05:14.287175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:14.287175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fM4i7l8SuaCvf4+3r5GyDxYqXkQQACRRb6KwvgsAPtaow5RSkQcbw0NME1V2lXr4yjrJnAi1Ify591DeC/fzBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:14.287670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.02906","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5551bdd5c44e8c771b41fa30cdbd8f9d0ce74bc036e69acdb9f34667d076a94","sha256:ec84281fce3aa4dd15d35d418ae0007307f35e2144d6a383fbf2f05036197a9f"],"state_sha256":"06c5437c96a950f8c0927a073a48f523b1c080e590bf0b0738c9fb64193efd00"}