{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:E3MMXVTZ6ZAAQSGRMQJ56ZDCOL","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":"c2d51f93b5041dbabc9da0051f915009d4567b47630ee104f20c0fd85c9f99cc","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-06T01:46:24Z","title_canon_sha256":"06f5acc5e7ce115fd15f0787904ffea32a00db71c0c42ecb40acdae1cde2c347"},"schema_version":"1.0","source":{"id":"1304.1841","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1841","created_at":"2026-05-18T03:28:45Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1841v1","created_at":"2026-05-18T03:28:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1841","created_at":"2026-05-18T03:28:45Z"},{"alias_kind":"pith_short_12","alias_value":"E3MMXVTZ6ZAA","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E3MMXVTZ6ZAAQSGR","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E3MMXVTZ","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:e7eac9d9329df7298883dd41abd3d16aecaa8f8bc51acf25bfd57c35eb173036","target":"graph","created_at":"2026-05-18T03:28:45Z","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":"It is known (see \\cite[Br\\\"and\\'en, Lemma 2.7]{B10}) that a necessary condition for $T:=\\sum Q_k(x) D^k$ to be hyperbolicity preserving is that $Q_k(x)$ and $Q_{k-1}(x)$ have interlacing zeros. We characterize all quadratic linear operators, as a consequence we find several classes of $P_n$-multiplier sequence.","authors_text":"R. Bates, R. Yoshida","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-06T01:46:24Z","title":"Quadratic Hyperbolicity Preservers & Multiplier Sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1841","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":"sha256:62e952b4fb59094be7ad8466d2c36942c9ff19f223297ef646ddf92a9dd4eeec","target":"record","created_at":"2026-05-18T03:28:45Z","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":"c2d51f93b5041dbabc9da0051f915009d4567b47630ee104f20c0fd85c9f99cc","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-06T01:46:24Z","title_canon_sha256":"06f5acc5e7ce115fd15f0787904ffea32a00db71c0c42ecb40acdae1cde2c347"},"schema_version":"1.0","source":{"id":"1304.1841","kind":"arxiv","version":1}},"canonical_sha256":"26d8cbd679f6400848d16413df646272c41e89518b894e9219dee59f96c9804a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26d8cbd679f6400848d16413df646272c41e89518b894e9219dee59f96c9804a","first_computed_at":"2026-05-18T03:28:45.000264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:45.000264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BRyh9AQDQLyFdIVtPbMw+7pnN7RwFCLsqd2dl+CqDafXLSwuTkCLNHQ7M5P4hAS60CDvR/cfenRis2ECSJMGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:45.001185Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1841","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62e952b4fb59094be7ad8466d2c36942c9ff19f223297ef646ddf92a9dd4eeec","sha256:e7eac9d9329df7298883dd41abd3d16aecaa8f8bc51acf25bfd57c35eb173036"],"state_sha256":"1a2baca06c42a9363604e262a9d36472c0d8d2f11c20a9d2d4b7573b73c23796"}