{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:N7D77FVUNB5H6MQ364BC65SPCG","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":"ec295312cf9a69da80bff22deb64008b929721b40e9a7b0180e5f639e245a744","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-22T12:51:22Z","title_canon_sha256":"420b3b98bc58e5f56720965224b9b579f389426cf044bd3bf409f8f7994904c4"},"schema_version":"1.0","source":{"id":"1609.06947","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06947","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06947v2","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06947","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"pith_short_12","alias_value":"N7D77FVUNB5H","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"N7D77FVUNB5H6MQ3","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"N7D77FVU","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:c3c5e09d4945121080a5afebc4b2e9be82bec6f48832c678ae68465aa4644cc6","target":"graph","created_at":"2026-05-18T00:46:02Z","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 $d \\in \\mathbb{N}$ the well-known Schur-Cohn region $\\mathcal{E}_d$ consists of all $d$-dimensional vectors $(a_1,\\ldots,a_d)\\in\\mathbb{R}^d$ corresponding to monic polynomials $X^d+a_1X^{d-1}+\\cdots+a_{d-1}X+a_d$ whose roots all lie in the open unit disk. This region has been extensively studied over decades. Recently, Akiyama and Peth\\H{o} considered the subsets $\\mathcal{E}_d^{(s)}$ of the Schur-Cohn region that correspond to polynomials of degree $d$ with exactly $s$ pairs of nonreal roots. They were especially interested in the $d$-dimensional Lebesgue measures $v_d^{(s)}:=\\lambda_d(\\","authors_text":"J\\\"org Thuswaldner, Peter Kirschenhofer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-22T12:51:22Z","title":"Distribution results on polynomials with bounded roots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06947","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":"sha256:8f2b51498cb7de5b6bc1a3a39086e02919ffbe1e4de237a5377561281f538a0c","target":"record","created_at":"2026-05-18T00:46:02Z","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":"ec295312cf9a69da80bff22deb64008b929721b40e9a7b0180e5f639e245a744","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-22T12:51:22Z","title_canon_sha256":"420b3b98bc58e5f56720965224b9b579f389426cf044bd3bf409f8f7994904c4"},"schema_version":"1.0","source":{"id":"1609.06947","kind":"arxiv","version":2}},"canonical_sha256":"6fc7ff96b4687a7f321bf7022f764f11b514a18e6ab4e2552478ad98cb603b95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fc7ff96b4687a7f321bf7022f764f11b514a18e6ab4e2552478ad98cb603b95","first_computed_at":"2026-05-18T00:46:02.488669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:02.488669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BrxlSe1wkasdpadzVpuDkTPjubpDmCAjncqMvAy3X3pFX2LfNLvXcXhiGRuE7Oh13NJ0QZE0tiDfzgFKj371Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:02.489065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06947","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f2b51498cb7de5b6bc1a3a39086e02919ffbe1e4de237a5377561281f538a0c","sha256:c3c5e09d4945121080a5afebc4b2e9be82bec6f48832c678ae68465aa4644cc6"],"state_sha256":"01fc4c240ba16a8795e956591dc26a17416ea44599759c712e1745bf194fec83"}