{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OXWPZ7B4BSVNJ7FW2O7BMLFFVE","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":"e1fb727a4d1781a2c43df2f07e579ea23533d67b27107bd53415ec326c91623c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-11T18:52:06Z","title_canon_sha256":"de3dc12a2c5ed37aaf36c5b78e670be134ef9115826f016d5aabd640c56f873f"},"schema_version":"1.0","source":{"id":"1008.1968","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1968","created_at":"2026-05-18T04:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1968v1","created_at":"2026-05-18T04:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1968","created_at":"2026-05-18T04:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"OXWPZ7B4BSVN","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OXWPZ7B4BSVNJ7FW","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OXWPZ7B4","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:9343385c4c3efcb90e69eed328464f4cdcb95fcc49de0ef5d4b7e9c7de5a33bd","target":"graph","created_at":"2026-05-18T04:42:22Z","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":"Recent work of Borwein, Choi, and the second author examined a collection of polynomials closely related to the Goldbach conjecture: the polynomial $F_N$ is divisible by the $N$th cyclotomic polynomial if and only if there is no representation of $N$ as the sum of two odd primes. The coefficients of these polynomials stabilize, as $N$ grows, to a fixed sequence $a(m)$; they derived upper and lower bounds for $a(m)$, and an asymptotic formula for the summatory function $A(M)$ of the sequence, both under the assumption of a famous conjecture of Hardy and Littlewood. In this article we improve th","authors_text":"Charles L. Samuels, Greg Martin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-11T18:52:06Z","title":"The size of coefficients of certain polynomials related to the Goldbach conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1968","kind":"arxiv","version":1},"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:ce1149645847b2419c8b6cbfe0ecb089917dcd573be7d4e39151630da6f72a5e","target":"record","created_at":"2026-05-18T04:42:22Z","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":"e1fb727a4d1781a2c43df2f07e579ea23533d67b27107bd53415ec326c91623c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-11T18:52:06Z","title_canon_sha256":"de3dc12a2c5ed37aaf36c5b78e670be134ef9115826f016d5aabd640c56f873f"},"schema_version":"1.0","source":{"id":"1008.1968","kind":"arxiv","version":1}},"canonical_sha256":"75ecfcfc3c0caad4fcb6d3be162ca5a91018ac44a708d74d2eea67eb4e1818a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75ecfcfc3c0caad4fcb6d3be162ca5a91018ac44a708d74d2eea67eb4e1818a2","first_computed_at":"2026-05-18T04:42:22.624364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:22.624364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QbXGdJI2Xybn4NJ5aiMOVdw9EpmDOdHIQtmZeiarL1DxlT3s7GTze9/lU4EPGLajDy/dKDDRAFIDYGjvHfveBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:22.624953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1968","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce1149645847b2419c8b6cbfe0ecb089917dcd573be7d4e39151630da6f72a5e","sha256:9343385c4c3efcb90e69eed328464f4cdcb95fcc49de0ef5d4b7e9c7de5a33bd"],"state_sha256":"59da6c7cd6606f30046dcb4a5967d671561268ef3267eced4ce7bc5659826337"}