{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:U3PPMUC2FHTVJAO42ZYQMCAH57","short_pith_number":"pith:U3PPMUC2","schema_version":"1.0","canonical_sha256":"a6def6505a29e75481dcd671060807efc2ffd16ce67fe8581896c3bc37b291ce","source":{"kind":"arxiv","id":"1501.06000","version":1},"attestation_state":"computed","paper":{"title":"Convex entire noncommutative functions are polynomials of degree two or less","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"J. E. Pascoe, J. William Helton, Ryan Tully-Doyle, Victor Vinnikov","submitted_at":"2015-01-24T04:15:05Z","abstract_excerpt":"This paper concerns matrix \"convex\" functions of (free) noncommuting variables, $x = (x_1, \\ldots, x_g)$. Helton and McCullough showed that a polynomial in $x$ which is matrix convex is of degree two or less. We prove a more general result: that a function of $x$ that is matrix convex near $0$ and also that is \"analytic\" in some neighborhood of the set of all self-adjoint matrix tuples is in fact a polynomial of degree two or less.\n  More generally, we prove that a function $F$ in two classes of noncommuting variables, $a = (a_1, \\ldots, a_{\\tilde{g}})$ and $x = (x_1, \\ldots, x_g)$ that is \"an"},"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":"1501.06000","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-24T04:15:05Z","cross_cats_sorted":[],"title_canon_sha256":"eabfde8dbfcfe67e444a7379be31f6bff78937293db2d453a1a7480c1435bbed","abstract_canon_sha256":"219c051e4fefdb83f7ae4af5cfeecfaa0d19734944f304c6a04db6d098c88bfd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:47.097526Z","signature_b64":"cY2+ph0qqdS7AV8l/1w6PQujhUz8+FqrjNqDc0Nw80N7J2h8Ow/5nmBqemwIXPu9pp717i72VbvTF+1qUB12Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6def6505a29e75481dcd671060807efc2ffd16ce67fe8581896c3bc37b291ce","last_reissued_at":"2026-05-18T02:28:47.097157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:47.097157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convex entire noncommutative functions are polynomials of degree two or less","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"J. E. Pascoe, J. William Helton, Ryan Tully-Doyle, Victor Vinnikov","submitted_at":"2015-01-24T04:15:05Z","abstract_excerpt":"This paper concerns matrix \"convex\" functions of (free) noncommuting variables, $x = (x_1, \\ldots, x_g)$. Helton and McCullough showed that a polynomial in $x$ which is matrix convex is of degree two or less. We prove a more general result: that a function of $x$ that is matrix convex near $0$ and also that is \"analytic\" in some neighborhood of the set of all self-adjoint matrix tuples is in fact a polynomial of degree two or less.\n  More generally, we prove that a function $F$ in two classes of noncommuting variables, $a = (a_1, \\ldots, a_{\\tilde{g}})$ and $x = (x_1, \\ldots, x_g)$ that is \"an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06000","kind":"arxiv","version":1},"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":"1501.06000","created_at":"2026-05-18T02:28:47.097221+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.06000v1","created_at":"2026-05-18T02:28:47.097221+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06000","created_at":"2026-05-18T02:28:47.097221+00:00"},{"alias_kind":"pith_short_12","alias_value":"U3PPMUC2FHTV","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"U3PPMUC2FHTVJAO4","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"U3PPMUC2","created_at":"2026-05-18T12:29:44.643036+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/U3PPMUC2FHTVJAO42ZYQMCAH57","json":"https://pith.science/pith/U3PPMUC2FHTVJAO42ZYQMCAH57.json","graph_json":"https://pith.science/api/pith-number/U3PPMUC2FHTVJAO42ZYQMCAH57/graph.json","events_json":"https://pith.science/api/pith-number/U3PPMUC2FHTVJAO42ZYQMCAH57/events.json","paper":"https://pith.science/paper/U3PPMUC2"},"agent_actions":{"view_html":"https://pith.science/pith/U3PPMUC2FHTVJAO42ZYQMCAH57","download_json":"https://pith.science/pith/U3PPMUC2FHTVJAO42ZYQMCAH57.json","view_paper":"https://pith.science/paper/U3PPMUC2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.06000&json=true","fetch_graph":"https://pith.science/api/pith-number/U3PPMUC2FHTVJAO42ZYQMCAH57/graph.json","fetch_events":"https://pith.science/api/pith-number/U3PPMUC2FHTVJAO42ZYQMCAH57/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U3PPMUC2FHTVJAO42ZYQMCAH57/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U3PPMUC2FHTVJAO42ZYQMCAH57/action/storage_attestation","attest_author":"https://pith.science/pith/U3PPMUC2FHTVJAO42ZYQMCAH57/action/author_attestation","sign_citation":"https://pith.science/pith/U3PPMUC2FHTVJAO42ZYQMCAH57/action/citation_signature","submit_replication":"https://pith.science/pith/U3PPMUC2FHTVJAO42ZYQMCAH57/action/replication_record"}},"created_at":"2026-05-18T02:28:47.097221+00:00","updated_at":"2026-05-18T02:28:47.097221+00:00"}