{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:A3P2JDCVGJTWFMNY4HIKANUUVT","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":"c14bc0e944bf05b6675032e9879fc513313ed70ee4645cc73d8612b6b936361f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-25T02:35:42Z","title_canon_sha256":"d770e39a4656dc76b8f2de85eea2260641df541f734dcde0f39af90838003f92"},"schema_version":"1.0","source":{"id":"1501.06107","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06107","created_at":"2026-05-18T02:28:42Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06107v1","created_at":"2026-05-18T02:28:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06107","created_at":"2026-05-18T02:28:42Z"},{"alias_kind":"pith_short_12","alias_value":"A3P2JDCVGJTW","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A3P2JDCVGJTWFMNY","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A3P2JDCV","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:488268508736ddf8de39bc9b585cd29791fd3a0a47e7f974c877500598e2eaa8","target":"graph","created_at":"2026-05-18T02:28:42Z","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":"This paper is concerned with the distribution in the complex plane of the roots of a polynomial sequence $\\{W_n(x)\\}_{n\\ge0}$ given by a recursion $W_n(x)=aW_{n-1}(x)+(bx+c)W_{n-2}(x)$, with $W_0(x)=1$ and $W_1(x)=t(x-r)$, where $a>0$, $b>0$, and $c,t,r\\in\\mathbb{R}$. Our results include proof of the distinct-real-rootedness of every such polynomial $W_n(x)$, derivation of the best bound for the zero-set $\\{x\\mid W_n(x)=0\\ \\text{for some $n\\ge1$}\\}$, and determination of three precise limit points of this zero-set. Also, we give several applications from combinatorics and topological graph the","authors_text":"D.G.L. Wang, J.L. Gross, T. Mansour, T.W. Tucker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-25T02:35:42Z","title":"Root geometry of polynomial sequences I: Type $(0,1)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06107","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":"sha256:90887091d353893785702889c033e51e0495dd725f779713a59b9d6ae3cb177c","target":"record","created_at":"2026-05-18T02:28:42Z","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":"c14bc0e944bf05b6675032e9879fc513313ed70ee4645cc73d8612b6b936361f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-25T02:35:42Z","title_canon_sha256":"d770e39a4656dc76b8f2de85eea2260641df541f734dcde0f39af90838003f92"},"schema_version":"1.0","source":{"id":"1501.06107","kind":"arxiv","version":1}},"canonical_sha256":"06dfa48c55326762b1b8e1d0a03694acd89d14c5013d1d5b1e9a8f5297411fb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06dfa48c55326762b1b8e1d0a03694acd89d14c5013d1d5b1e9a8f5297411fb4","first_computed_at":"2026-05-18T02:28:42.330093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:42.330093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RGZ7yznuHhcRCTYBT1RT1bZIkNT5FvSKGJBLMlOp+iTwpoY0FpLjfkUbAQHbb1UsnKp8BLdFL9dDhsuZ+RVSAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:42.330569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06107","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90887091d353893785702889c033e51e0495dd725f779713a59b9d6ae3cb177c","sha256:488268508736ddf8de39bc9b585cd29791fd3a0a47e7f974c877500598e2eaa8"],"state_sha256":"9a0c454166f327fff8342978a03b7459e309ae92fb463da1e859b3869b481812"}