{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2BGDBW72MN6U4YA62ZIEUWG7K7","short_pith_number":"pith:2BGDBW72","schema_version":"1.0","canonical_sha256":"d04c30dbfa637d4e601ed6504a58df57f16a9b57410f4b3773a1a24c6912e1d3","source":{"kind":"arxiv","id":"1405.5076","version":5},"attestation_state":"computed","paper":{"title":"L\\\"owner's Theorem in several variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Mikl\\'os P\\'alfia","submitted_at":"2014-05-20T13:27:58Z","abstract_excerpt":"In this paper we establish a multivariable non-commutative generalization of L\\\"owner's classical theorem from 1934 characterizing operator monotone functions as real functions admitting analytic continuation mapping the upper complex half-plane into itself. The non-commutative several variable theorem proved here characterizes several variable operator monotone functions, not assumed to be free analytic or even continuous, as free functions that admit free analytic continuation mapping the upper operator poly-halfspace into the upper operator halfspace over an arbitrary Hilbert space. We esta"},"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":"1405.5076","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-20T13:27:58Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"024a635763fd47282cdf86ff3387a6f6b08d570d266ea2fb9c77d6057204cebc","abstract_canon_sha256":"458e4e0a6cac31bb9d7972537b2c9837531d8f394e3d1c2f54dfc1bb603d0618"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:36.586711Z","signature_b64":"Lpw53qXK7cCrKXDdOPV+C6lfG7TabRh6Oar/3e9OZiqV5xssLQ4JVqDgOi7v30QgrH9iGK0U5MDTOtci5mfrBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d04c30dbfa637d4e601ed6504a58df57f16a9b57410f4b3773a1a24c6912e1d3","last_reissued_at":"2026-05-18T01:12:36.586190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:36.586190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"L\\\"owner's Theorem in several variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Mikl\\'os P\\'alfia","submitted_at":"2014-05-20T13:27:58Z","abstract_excerpt":"In this paper we establish a multivariable non-commutative generalization of L\\\"owner's classical theorem from 1934 characterizing operator monotone functions as real functions admitting analytic continuation mapping the upper complex half-plane into itself. The non-commutative several variable theorem proved here characterizes several variable operator monotone functions, not assumed to be free analytic or even continuous, as free functions that admit free analytic continuation mapping the upper operator poly-halfspace into the upper operator halfspace over an arbitrary Hilbert space. We esta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5076","kind":"arxiv","version":5},"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":"1405.5076","created_at":"2026-05-18T01:12:36.586271+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.5076v5","created_at":"2026-05-18T01:12:36.586271+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5076","created_at":"2026-05-18T01:12:36.586271+00:00"},{"alias_kind":"pith_short_12","alias_value":"2BGDBW72MN6U","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"2BGDBW72MN6U4YA6","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"2BGDBW72","created_at":"2026-05-18T12:28:09.283467+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1906.09014","citing_title":"Cauchy-Riemann equations for free noncommutative functions","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2BGDBW72MN6U4YA62ZIEUWG7K7","json":"https://pith.science/pith/2BGDBW72MN6U4YA62ZIEUWG7K7.json","graph_json":"https://pith.science/api/pith-number/2BGDBW72MN6U4YA62ZIEUWG7K7/graph.json","events_json":"https://pith.science/api/pith-number/2BGDBW72MN6U4YA62ZIEUWG7K7/events.json","paper":"https://pith.science/paper/2BGDBW72"},"agent_actions":{"view_html":"https://pith.science/pith/2BGDBW72MN6U4YA62ZIEUWG7K7","download_json":"https://pith.science/pith/2BGDBW72MN6U4YA62ZIEUWG7K7.json","view_paper":"https://pith.science/paper/2BGDBW72","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.5076&json=true","fetch_graph":"https://pith.science/api/pith-number/2BGDBW72MN6U4YA62ZIEUWG7K7/graph.json","fetch_events":"https://pith.science/api/pith-number/2BGDBW72MN6U4YA62ZIEUWG7K7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2BGDBW72MN6U4YA62ZIEUWG7K7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2BGDBW72MN6U4YA62ZIEUWG7K7/action/storage_attestation","attest_author":"https://pith.science/pith/2BGDBW72MN6U4YA62ZIEUWG7K7/action/author_attestation","sign_citation":"https://pith.science/pith/2BGDBW72MN6U4YA62ZIEUWG7K7/action/citation_signature","submit_replication":"https://pith.science/pith/2BGDBW72MN6U4YA62ZIEUWG7K7/action/replication_record"}},"created_at":"2026-05-18T01:12:36.586271+00:00","updated_at":"2026-05-18T01:12:36.586271+00:00"}