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Then for each real $\\xi$, the function $e^{\\xi\\nu_0(t)}+e^{\\xi\\nu_1(t)}+\\,\\cdots\\,+e^{\\xi\\nu_n(t)}$ is exponentially convex on the interval $-\\infty<t<\\infty$."},"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":"1604.07909","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-04-27T02:36:15Z","cross_cats_sorted":[],"title_canon_sha256":"5893c3b00c0dff6fdad1c5bb6d33151db58329fd5bf0310c18b16db1cf9f70fb","abstract_canon_sha256":"3e5efa4edcab54551cb5763f94ed2d1cbd28207acbdfe0af85e7fa765b1e0171"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:57.162800Z","signature_b64":"1/Pxqw3c9Fju7/Lz+pInuYfRS4cW2VgG8DzKOwjt/rPcX76vIF+1dTZ13eUwpPVoaD5gR5JXgJiEn6IP/YRbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e14b36dd96011c18b41b46a3ab0372a6e983e4c8709c655ad1cd588b9fa822be","last_reissued_at":"2026-05-18T01:15:57.162165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:57.162165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the roots of a hyperbolic polynomial pencil","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Victor Katsnelson","submitted_at":"2016-04-27T02:36:15Z","abstract_excerpt":"Let $\\nu_0(t),\\nu_1(t),\\,\\ldots\\,,\\nu_n(t)$ be the roots of the equation $R(z)=t$, where $R(z)$ is a rational function of the form \\[R(z)=z+\\sum\\limits_{k=1}^n\\frac{\\alpha_k}{z-\\mu_k},\\] $\\mu_k$ are pairwise different real numbers, $\\alpha_k>0,\\,1\\leq{}k\\leq{}n$. Then for each real $\\xi$, the function $e^{\\xi\\nu_0(t)}+e^{\\xi\\nu_1(t)}+\\,\\cdots\\,+e^{\\xi\\nu_n(t)}$ is exponentially convex on the interval $-\\infty<t<\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07909","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":"1604.07909","created_at":"2026-05-18T01:15:57.162257+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.07909v2","created_at":"2026-05-18T01:15:57.162257+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07909","created_at":"2026-05-18T01:15:57.162257+00:00"},{"alias_kind":"pith_short_12","alias_value":"4FFTNXMWAEOB","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4FFTNXMWAEOBRNA3","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4FFTNXMW","created_at":"2026-05-18T12:29:58.707656+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/4FFTNXMWAEOBRNA3I2R2WA3SU3","json":"https://pith.science/pith/4FFTNXMWAEOBRNA3I2R2WA3SU3.json","graph_json":"https://pith.science/api/pith-number/4FFTNXMWAEOBRNA3I2R2WA3SU3/graph.json","events_json":"https://pith.science/api/pith-number/4FFTNXMWAEOBRNA3I2R2WA3SU3/events.json","paper":"https://pith.science/paper/4FFTNXMW"},"agent_actions":{"view_html":"https://pith.science/pith/4FFTNXMWAEOBRNA3I2R2WA3SU3","download_json":"https://pith.science/pith/4FFTNXMWAEOBRNA3I2R2WA3SU3.json","view_paper":"https://pith.science/paper/4FFTNXMW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.07909&json=true","fetch_graph":"https://pith.science/api/pith-number/4FFTNXMWAEOBRNA3I2R2WA3SU3/graph.json","fetch_events":"https://pith.science/api/pith-number/4FFTNXMWAEOBRNA3I2R2WA3SU3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4FFTNXMWAEOBRNA3I2R2WA3SU3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4FFTNXMWAEOBRNA3I2R2WA3SU3/action/storage_attestation","attest_author":"https://pith.science/pith/4FFTNXMWAEOBRNA3I2R2WA3SU3/action/author_attestation","sign_citation":"https://pith.science/pith/4FFTNXMWAEOBRNA3I2R2WA3SU3/action/citation_signature","submit_replication":"https://pith.science/pith/4FFTNXMWAEOBRNA3I2R2WA3SU3/action/replication_record"}},"created_at":"2026-05-18T01:15:57.162257+00:00","updated_at":"2026-05-18T01:15:57.162257+00:00"}