{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:K4XWASKOG4FZR3YTR7NBLZXKKZ","short_pith_number":"pith:K4XWASKO","schema_version":"1.0","canonical_sha256":"572f60494e370b98ef138fda15e6ea565073582ba96fae45b6263fa58cd2d301","source":{"kind":"arxiv","id":"0809.4874","version":1},"attestation_state":"computed","paper":{"title":"Noncommutative ball maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Igor Klep, J. William Helton, Nick Slinglend, Scott McCullough","submitted_at":"2008-09-28T22:18:30Z","abstract_excerpt":"In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting variables and evaluate these functions on sets of matrices of all dimensions; we call such situations dimension-free. These types of functions have recently been used in the study of dimension-free linear system engineering problems.\n  In this paper we characterize NC analytic maps that send dimension-free matrix balls to dimension-free matrix balls and carry the b"},"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":"0809.4874","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-09-28T22:18:30Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"0f137e0e56a18e5078042413a9e18ecf5d5540b568ae184f486f85cbeae92118","abstract_canon_sha256":"b7deb69b10f2330e1e9fb49f74809c0feac7d864dad252f392d30fad0289d5cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:06.465412Z","signature_b64":"FsdwYI+paDNGLQwvE30ns+1UhK4c8FI4Zti8KjW4OYi8g+PnVdmdBkCcHkwDYwrjygyk64iPmTu+N5tHVbelAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"572f60494e370b98ef138fda15e6ea565073582ba96fae45b6263fa58cd2d301","last_reissued_at":"2026-05-18T04:24:06.464816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:06.464816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Noncommutative ball maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Igor Klep, J. William Helton, Nick Slinglend, Scott McCullough","submitted_at":"2008-09-28T22:18:30Z","abstract_excerpt":"In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting variables and evaluate these functions on sets of matrices of all dimensions; we call such situations dimension-free. These types of functions have recently been used in the study of dimension-free linear system engineering problems.\n  In this paper we characterize NC analytic maps that send dimension-free matrix balls to dimension-free matrix balls and carry the b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4874","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":"0809.4874","created_at":"2026-05-18T04:24:06.464906+00:00"},{"alias_kind":"arxiv_version","alias_value":"0809.4874v1","created_at":"2026-05-18T04:24:06.464906+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.4874","created_at":"2026-05-18T04:24:06.464906+00:00"},{"alias_kind":"pith_short_12","alias_value":"K4XWASKOG4FZ","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"K4XWASKOG4FZR3YT","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"K4XWASKO","created_at":"2026-05-18T12:25:57.157939+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/K4XWASKOG4FZR3YTR7NBLZXKKZ","json":"https://pith.science/pith/K4XWASKOG4FZR3YTR7NBLZXKKZ.json","graph_json":"https://pith.science/api/pith-number/K4XWASKOG4FZR3YTR7NBLZXKKZ/graph.json","events_json":"https://pith.science/api/pith-number/K4XWASKOG4FZR3YTR7NBLZXKKZ/events.json","paper":"https://pith.science/paper/K4XWASKO"},"agent_actions":{"view_html":"https://pith.science/pith/K4XWASKOG4FZR3YTR7NBLZXKKZ","download_json":"https://pith.science/pith/K4XWASKOG4FZR3YTR7NBLZXKKZ.json","view_paper":"https://pith.science/paper/K4XWASKO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0809.4874&json=true","fetch_graph":"https://pith.science/api/pith-number/K4XWASKOG4FZR3YTR7NBLZXKKZ/graph.json","fetch_events":"https://pith.science/api/pith-number/K4XWASKOG4FZR3YTR7NBLZXKKZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K4XWASKOG4FZR3YTR7NBLZXKKZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K4XWASKOG4FZR3YTR7NBLZXKKZ/action/storage_attestation","attest_author":"https://pith.science/pith/K4XWASKOG4FZR3YTR7NBLZXKKZ/action/author_attestation","sign_citation":"https://pith.science/pith/K4XWASKOG4FZR3YTR7NBLZXKKZ/action/citation_signature","submit_replication":"https://pith.science/pith/K4XWASKOG4FZR3YTR7NBLZXKKZ/action/replication_record"}},"created_at":"2026-05-18T04:24:06.464906+00:00","updated_at":"2026-05-18T04:24:06.464906+00:00"}