{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:35RYOVLXN7N5GZB7PYZNHCY4WJ","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":"5b9e64be09d6b5532d0ef491b69686690ef2679e22d5188ac8c16529d7539e7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-09T20:04:52Z","title_canon_sha256":"0f25baad498d47505c4649858567e280d74713e37f549acfe40b3e1e733002ed"},"schema_version":"1.0","source":{"id":"1802.03437","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03437","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03437v1","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03437","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"pith_short_12","alias_value":"35RYOVLXN7N5","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"35RYOVLXN7N5GZB7","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"35RYOVLX","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:0872f3793b9aec2a5c3315e06c57838d657ae0d97ba3786b6431eabdcdf787d4","target":"graph","created_at":"2026-05-18T00:23:51Z","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 $Q$ be a positive-definite quaternary quadratic form with integer coefficients. We study the problem of giving bounds on the largest positive integer $n$ that is locally represented by $Q$ but not represented. Assuming that $n$ is relatively prime to $D(Q)$, the determinant of the Gram matrix of $Q$, we show that $n$ is represented provided that \\[\n  n \\gg \\max \\{ N(Q)^{3/2 + \\epsilon} D(Q)^{5/4 + \\epsilon}, N(Q)^{2 + \\epsilon} D(Q)^{1 + \\epsilon} \\}. \\] Here $N(Q)$ is the level of $Q$. We give three other bounds that hold under successively weaker local conditions on $n$.\n  These results ","authors_text":"Jeremy Rouse","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-09T20:04:52Z","title":"Integers represented by positive-definite quadratic forms and Petersson inner products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03437","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:cc9bc9718c70c9bfd400dd42ec6f8366d3e2c2042cff255b019c8f1247209632","target":"record","created_at":"2026-05-18T00:23:51Z","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":"5b9e64be09d6b5532d0ef491b69686690ef2679e22d5188ac8c16529d7539e7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-09T20:04:52Z","title_canon_sha256":"0f25baad498d47505c4649858567e280d74713e37f549acfe40b3e1e733002ed"},"schema_version":"1.0","source":{"id":"1802.03437","kind":"arxiv","version":1}},"canonical_sha256":"df638755776fdbd3643f7e32d38b1cb2770d9e5277c8ae8c19a7d23a66dd1945","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df638755776fdbd3643f7e32d38b1cb2770d9e5277c8ae8c19a7d23a66dd1945","first_computed_at":"2026-05-18T00:23:51.648666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:51.648666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QwWdMq1MAJJcJAjj7F2kzj7wT8K+tpG1Nh5Q44+mp9/OdrclwUy5Zpkh2idCNK2dYMwGj7g8bHs4KaeVM6uGBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:51.649406Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.03437","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc9bc9718c70c9bfd400dd42ec6f8366d3e2c2042cff255b019c8f1247209632","sha256:0872f3793b9aec2a5c3315e06c57838d657ae0d97ba3786b6431eabdcdf787d4"],"state_sha256":"5da42bc50baf4346038e70d9f33a1692af639a5b76993d1f0d0bfe338e68c1cc"}