{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:UDAPKSKMVL3LBHWMCC6IG4Q7LS","short_pith_number":"pith:UDAPKSKM","schema_version":"1.0","canonical_sha256":"a0c0f5494caaf6b09ecc10bc83721f5c854387c8e5079bedf65fc2438ccc965a","source":{"kind":"arxiv","id":"1208.2288","version":1},"attestation_state":"computed","paper":{"title":"Norm-constrained determinantal representations of polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Hugo J. Woerdeman","submitted_at":"2012-08-10T21:01:43Z","abstract_excerpt":"For every multivariable polynomial $p$, with $p(0)=1$, we construct a determinantal representation $$p=\\det (I - K Z),$$ where $Z$ is a diagonal matrix with coordinate variables on the diagonal and $K$ is a complex square matrix. Such a representation is equivalent to the existence of $K$ whose principal minors satisfy certain linear relations. When norm constraints on $K$ are imposed, we give connections to the multivariable von Neumann inequality, Agler denominators, and stability. We show that if a multivariable polynomial $q$, $q(0)=0,$ satisfies the von Neumann inequality, then $1-q$ admi"},"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":"1208.2288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-10T21:01:43Z","cross_cats_sorted":[],"title_canon_sha256":"3375659c72a2c54ce561a41a2619ed73e7cf06bfb529fbb5bb14d13f296ddda5","abstract_canon_sha256":"2a47a6f598c23e765cbea5ca01012928851753f1d9a28d05242c6cdc4a0e9b57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:58.298392Z","signature_b64":"tlksQBEMkWzmnER7JbJbj1sdWt7e/UaIX7AFk3xPQXP1t1e8GEdQVzsPOY5nfuIXWpXKoFk+GXePNYOuijVNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0c0f5494caaf6b09ecc10bc83721f5c854387c8e5079bedf65fc2438ccc965a","last_reissued_at":"2026-05-18T03:48:58.297609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:58.297609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Norm-constrained determinantal representations of polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Hugo J. Woerdeman","submitted_at":"2012-08-10T21:01:43Z","abstract_excerpt":"For every multivariable polynomial $p$, with $p(0)=1$, we construct a determinantal representation $$p=\\det (I - K Z),$$ where $Z$ is a diagonal matrix with coordinate variables on the diagonal and $K$ is a complex square matrix. Such a representation is equivalent to the existence of $K$ whose principal minors satisfy certain linear relations. When norm constraints on $K$ are imposed, we give connections to the multivariable von Neumann inequality, Agler denominators, and stability. We show that if a multivariable polynomial $q$, $q(0)=0,$ satisfies the von Neumann inequality, then $1-q$ admi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2288","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":"1208.2288","created_at":"2026-05-18T03:48:58.297735+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.2288v1","created_at":"2026-05-18T03:48:58.297735+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2288","created_at":"2026-05-18T03:48:58.297735+00:00"},{"alias_kind":"pith_short_12","alias_value":"UDAPKSKMVL3L","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"UDAPKSKMVL3LBHWM","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"UDAPKSKM","created_at":"2026-05-18T12:27:23.164592+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/UDAPKSKMVL3LBHWMCC6IG4Q7LS","json":"https://pith.science/pith/UDAPKSKMVL3LBHWMCC6IG4Q7LS.json","graph_json":"https://pith.science/api/pith-number/UDAPKSKMVL3LBHWMCC6IG4Q7LS/graph.json","events_json":"https://pith.science/api/pith-number/UDAPKSKMVL3LBHWMCC6IG4Q7LS/events.json","paper":"https://pith.science/paper/UDAPKSKM"},"agent_actions":{"view_html":"https://pith.science/pith/UDAPKSKMVL3LBHWMCC6IG4Q7LS","download_json":"https://pith.science/pith/UDAPKSKMVL3LBHWMCC6IG4Q7LS.json","view_paper":"https://pith.science/paper/UDAPKSKM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.2288&json=true","fetch_graph":"https://pith.science/api/pith-number/UDAPKSKMVL3LBHWMCC6IG4Q7LS/graph.json","fetch_events":"https://pith.science/api/pith-number/UDAPKSKMVL3LBHWMCC6IG4Q7LS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UDAPKSKMVL3LBHWMCC6IG4Q7LS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UDAPKSKMVL3LBHWMCC6IG4Q7LS/action/storage_attestation","attest_author":"https://pith.science/pith/UDAPKSKMVL3LBHWMCC6IG4Q7LS/action/author_attestation","sign_citation":"https://pith.science/pith/UDAPKSKMVL3LBHWMCC6IG4Q7LS/action/citation_signature","submit_replication":"https://pith.science/pith/UDAPKSKMVL3LBHWMCC6IG4Q7LS/action/replication_record"}},"created_at":"2026-05-18T03:48:58.297735+00:00","updated_at":"2026-05-18T03:48:58.297735+00:00"}