{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SK57CGAN7THBWBPYNHSFCJO6AI","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":"0a46154c8c247be3ad3c045d9a32deb89bf09d490edc04674368d34e253393ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-12T10:56:16Z","title_canon_sha256":"c3c51dc77da27c2a080021705c53cd0567f8b9c0d173a9483fa19d04ae66a29a"},"schema_version":"1.0","source":{"id":"1712.04225","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04225","created_at":"2026-05-18T00:16:44Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04225v2","created_at":"2026-05-18T00:16:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04225","created_at":"2026-05-18T00:16:44Z"},{"alias_kind":"pith_short_12","alias_value":"SK57CGAN7THB","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SK57CGAN7THBWBPY","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SK57CGAN","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:46e2b67d7b9273bebb2b501964f5f19421206748a5c1cfff272745153fc5c865","target":"graph","created_at":"2026-05-18T00:16:44Z","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":"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","authors_text":"David G.L. Wang, Jiarui Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-12T10:56:16Z","title":"Piecewise interlacing zeros of polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04225","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":"sha256:0b6ecaeb087d89e5f550a4ca42a3134f8ba155e86a3631cd4655dc43c26881aa","target":"record","created_at":"2026-05-18T00:16:44Z","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":"0a46154c8c247be3ad3c045d9a32deb89bf09d490edc04674368d34e253393ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-12T10:56:16Z","title_canon_sha256":"c3c51dc77da27c2a080021705c53cd0567f8b9c0d173a9483fa19d04ae66a29a"},"schema_version":"1.0","source":{"id":"1712.04225","kind":"arxiv","version":2}},"canonical_sha256":"92bbf1180dfcce1b05f869e45125de0220a7d24a04a8b901aba7a84d6127a2d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92bbf1180dfcce1b05f869e45125de0220a7d24a04a8b901aba7a84d6127a2d3","first_computed_at":"2026-05-18T00:16:44.543231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:44.543231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qb6HehQnIM82b91InZiht9JjnVG9rAjnTgKKBCrKD7Hh+DgYFKGSsD6WvEg8DFckEnI7tQsF6IVyfa9dS/TACA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:44.543887Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04225","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b6ecaeb087d89e5f550a4ca42a3134f8ba155e86a3631cd4655dc43c26881aa","sha256:46e2b67d7b9273bebb2b501964f5f19421206748a5c1cfff272745153fc5c865"],"state_sha256":"1c21a1ac690a94d29bcd19b0cdeec8308a4c08cc4d52ee7aa0d6344cf6da2891"}