{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:65ISILK75BUNELNE7ZUWG74LBM","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":"54a736277fa6ecdcd79b2c9a07d66567bac6bff5ff7e7be2858a41be7428a1c4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-20T14:18:08Z","title_canon_sha256":"076e5c65084ebe06651652c95ec17f4b047dfbcf8c08b162cc68c668823375c3"},"schema_version":"1.0","source":{"id":"1707.06528","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06528","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06528v1","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06528","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"65ISILK75BUN","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"65ISILK75BUNELNE","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"65ISILK7","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:3c7fd1d53224282c030f41e890155f5e8f2c2680491a6b3025a2ebe880b0aa8e","target":"graph","created_at":"2026-05-18T00:39:53Z","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":"For nonempty subsets $S_0, \\dots, S_{n-1}$ of a (large enough) finite field $\\mathbb{F}$ satisfying $$|S_1|, \\dots, |S_{n-1}| > 2 \\quad \\mathrm{or} \\quad |S_1|,|S_{n-1}| > n - 1,$$ we show that there exist $a_0 \\in S_0, \\dots, a_{n-1} \\in S_{n-1}$ such that $$ T^n + a_{n-1}T^{n-1} + \\dots + a_1T + a_0 \\in \\mathbb{F}[T] $$ is a squarefree polynomial.","authors_text":"Amotz Oppenheim, Mark Shusterman","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-20T14:18:08Z","title":"Squarefree polynomials with prescribed coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06528","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":"sha256:9607573a721c75991ecbba486070fb9d3c3583536e989ea757032a4bd32284c6","target":"record","created_at":"2026-05-18T00:39:53Z","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":"54a736277fa6ecdcd79b2c9a07d66567bac6bff5ff7e7be2858a41be7428a1c4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-20T14:18:08Z","title_canon_sha256":"076e5c65084ebe06651652c95ec17f4b047dfbcf8c08b162cc68c668823375c3"},"schema_version":"1.0","source":{"id":"1707.06528","kind":"arxiv","version":1}},"canonical_sha256":"f751242d5fe868d22da4fe69637f8b0b22904314467ebeb0ada7ba9ff5c0c55a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f751242d5fe868d22da4fe69637f8b0b22904314467ebeb0ada7ba9ff5c0c55a","first_computed_at":"2026-05-18T00:39:53.621738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:53.621738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sKU50ijxz/uuydwbsuwDdubbFvytyntIMukHuyHgRhPXYPjD1Ot300gjjxQR4qep/XX0A+K0TyliTRikeoRsDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:53.622351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06528","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9607573a721c75991ecbba486070fb9d3c3583536e989ea757032a4bd32284c6","sha256:3c7fd1d53224282c030f41e890155f5e8f2c2680491a6b3025a2ebe880b0aa8e"],"state_sha256":"b77abe9ed0a287bfc7a36014ce08e3f2fffd52a8c34cac50c357f0b92092f3ec"}