{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SK57CGAN7THBWBPYNHSFCJO6AI","short_pith_number":"pith:SK57CGAN","schema_version":"1.0","canonical_sha256":"92bbf1180dfcce1b05f869e45125de0220a7d24a04a8b901aba7a84d6127a2d3","source":{"kind":"arxiv","id":"1712.04225","version":2},"attestation_state":"computed","paper":{"title":"Piecewise interlacing zeros of polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David G.L. Wang, Jiarui Zhang","submitted_at":"2017-12-12T10:56:16Z","abstract_excerpt":"We introduce the concept of piecewise interlacing zeros for studying the relation of root distribution of two polynomials. The concept is pregnant with an idea of confirming the real-rootedness of polynomials in a sequence. Roughly speaking, one constructs a collection of disjoint intervals such that one may show by induction that consecutive polynomials have interlacing zeros over each of the intervals. We confirm the real-rootedness of some polynomials satisfying a recurrence with linear polynomial coefficients. This extends Gross et al.'s work where one of the polynomial coefficients is a c"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.04225","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-12T10:56:16Z","cross_cats_sorted":[],"title_canon_sha256":"c3c51dc77da27c2a080021705c53cd0567f8b9c0d173a9483fa19d04ae66a29a","abstract_canon_sha256":"0a46154c8c247be3ad3c045d9a32deb89bf09d490edc04674368d34e253393ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:44.543887Z","signature_b64":"Qb6HehQnIM82b91InZiht9JjnVG9rAjnTgKKBCrKD7Hh+DgYFKGSsD6WvEg8DFckEnI7tQsF6IVyfa9dS/TACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92bbf1180dfcce1b05f869e45125de0220a7d24a04a8b901aba7a84d6127a2d3","last_reissued_at":"2026-05-18T00:16:44.543231Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:44.543231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Piecewise interlacing zeros of polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David G.L. Wang, Jiarui Zhang","submitted_at":"2017-12-12T10:56:16Z","abstract_excerpt":"We introduce the concept of piecewise interlacing zeros for studying the relation of root distribution of two polynomials. The concept is pregnant with an idea of confirming the real-rootedness of polynomials in a sequence. Roughly speaking, one constructs a collection of disjoint intervals such that one may show by induction that consecutive polynomials have interlacing zeros over each of the intervals. We confirm the real-rootedness of some polynomials satisfying a recurrence with linear polynomial coefficients. This extends Gross et al.'s work where one of the polynomial coefficients is a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04225","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1712.04225","created_at":"2026-05-18T00:16:44.543330+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.04225v2","created_at":"2026-05-18T00:16:44.543330+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04225","created_at":"2026-05-18T00:16:44.543330+00:00"},{"alias_kind":"pith_short_12","alias_value":"SK57CGAN7THB","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SK57CGAN7THBWBPY","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SK57CGAN","created_at":"2026-05-18T12:31:43.269735+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SK57CGAN7THBWBPYNHSFCJO6AI","json":"https://pith.science/pith/SK57CGAN7THBWBPYNHSFCJO6AI.json","graph_json":"https://pith.science/api/pith-number/SK57CGAN7THBWBPYNHSFCJO6AI/graph.json","events_json":"https://pith.science/api/pith-number/SK57CGAN7THBWBPYNHSFCJO6AI/events.json","paper":"https://pith.science/paper/SK57CGAN"},"agent_actions":{"view_html":"https://pith.science/pith/SK57CGAN7THBWBPYNHSFCJO6AI","download_json":"https://pith.science/pith/SK57CGAN7THBWBPYNHSFCJO6AI.json","view_paper":"https://pith.science/paper/SK57CGAN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.04225&json=true","fetch_graph":"https://pith.science/api/pith-number/SK57CGAN7THBWBPYNHSFCJO6AI/graph.json","fetch_events":"https://pith.science/api/pith-number/SK57CGAN7THBWBPYNHSFCJO6AI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SK57CGAN7THBWBPYNHSFCJO6AI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SK57CGAN7THBWBPYNHSFCJO6AI/action/storage_attestation","attest_author":"https://pith.science/pith/SK57CGAN7THBWBPYNHSFCJO6AI/action/author_attestation","sign_citation":"https://pith.science/pith/SK57CGAN7THBWBPYNHSFCJO6AI/action/citation_signature","submit_replication":"https://pith.science/pith/SK57CGAN7THBWBPYNHSFCJO6AI/action/replication_record"}},"created_at":"2026-05-18T00:16:44.543330+00:00","updated_at":"2026-05-18T00:16:44.543330+00:00"}