{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HVHGKIMAT5324B5ODRGCPNUGXV","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":"35eb99b5433060877603bf30e8015119d8cd2b0456864f1669987ad7a964e8fd","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-20T00:26:07Z","title_canon_sha256":"5416607771cc25ec1f37122e7a2833599de0eb821f1ca7a68461e78ecbe23244"},"schema_version":"1.0","source":{"id":"1702.05823","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05823","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05823v2","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05823","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"pith_short_12","alias_value":"HVHGKIMAT532","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"HVHGKIMAT5324B5O","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"HVHGKIMA","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:f36f1f89ca8b96fe0c6c17a747554287237447aab14dac4e0674c5f878974966","target":"graph","created_at":"2026-05-17T23:54:07Z","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 $n_1 < n_2 < \\cdots < n_N$ be non-negative integers. In a private communication Brian Conrey asked how fast the number of real zeros of the trigonometric polynomials $T_N(\\theta) = \\sum_{j=1}^N {\\cos (n_j\\theta)}$ tends to $\\infty$ as a function of $N$. Conrey's question in general does not appear to be easy.Let ${\\mathcal P}_n(S)$ be the set of all algebraic polynomials of degree at most $n$ with each of their coefficients in $S$. For a finite set $S \\subset {\\mathbb C}$ let $M = M(S) := \\max\\{|z|: z \\in S\\}$. It has been shown recently that if $S \\subset {\\mathbb R}$ is a finite set and ","authors_text":"Tam\\'as Erd\\'elyi","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-20T00:26:07Z","title":"Improved lower bound for the number of unimodular zeros of self-reciprocal polynomials with coefficients in a finite set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05823","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":"sha256:1d105fdccbe56975545fe7489ac8372d55a23af08348f597374d419219397bc6","target":"record","created_at":"2026-05-17T23:54:07Z","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":"35eb99b5433060877603bf30e8015119d8cd2b0456864f1669987ad7a964e8fd","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-20T00:26:07Z","title_canon_sha256":"5416607771cc25ec1f37122e7a2833599de0eb821f1ca7a68461e78ecbe23244"},"schema_version":"1.0","source":{"id":"1702.05823","kind":"arxiv","version":2}},"canonical_sha256":"3d4e6521809f77ae07ae1c4c27b686bd63fc480ee908878feecb93db60e8d1f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d4e6521809f77ae07ae1c4c27b686bd63fc480ee908878feecb93db60e8d1f3","first_computed_at":"2026-05-17T23:54:07.704249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:07.704249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gd3dXsEJUYTZuFvgp69kHwAC8LApaClDeKH/avahjtJMJ7tRn50OAYAyN5UUbpdEtT5MboePHQlZf9rFMcbtAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:07.704660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.05823","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d105fdccbe56975545fe7489ac8372d55a23af08348f597374d419219397bc6","sha256:f36f1f89ca8b96fe0c6c17a747554287237447aab14dac4e0674c5f878974966"],"state_sha256":"4c8c4045999e7d13b178925a8e1e9873277ede4d7ef8406d8ec97719d6400896"}