{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4VXCWHS4SGLEHSGHTOS4N5GHQA","short_pith_number":"pith:4VXCWHS4","canonical_record":{"source":{"id":"1706.08236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-26T05:30:31Z","cross_cats_sorted":["math.CV","math.FA"],"title_canon_sha256":"6c8a32c60b34593f53f2e92cf4e18d461bf3c01dfff347ce76f55edba1e0b2fa","abstract_canon_sha256":"dc098f8c6ac15a92ae5b634fe562d2e157e5c94543812016b1fd2599f91f058c"},"schema_version":"1.0"},"canonical_sha256":"e56e2b1e5c919643c8c79ba5c6f4c78014b480cd98cbb5ad028e617db998351c","source":{"kind":"arxiv","id":"1706.08236","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08236","created_at":"2026-05-18T00:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08236v1","created_at":"2026-05-18T00:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08236","created_at":"2026-05-18T00:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"4VXCWHS4SGLE","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4VXCWHS4SGLEHSGH","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4VXCWHS4","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4VXCWHS4SGLEHSGHTOS4N5GHQA","target":"record","payload":{"canonical_record":{"source":{"id":"1706.08236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-26T05:30:31Z","cross_cats_sorted":["math.CV","math.FA"],"title_canon_sha256":"6c8a32c60b34593f53f2e92cf4e18d461bf3c01dfff347ce76f55edba1e0b2fa","abstract_canon_sha256":"dc098f8c6ac15a92ae5b634fe562d2e157e5c94543812016b1fd2599f91f058c"},"schema_version":"1.0"},"canonical_sha256":"e56e2b1e5c919643c8c79ba5c6f4c78014b480cd98cbb5ad028e617db998351c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:43.110645Z","signature_b64":"WR5nEXc8WtNpbZcOsHTbJcWMeUMWEPrALQsjDeAORvST/UHOOFElWq46q0HeGxKOpm0nVUrhsHP+5C5xsyXtDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e56e2b1e5c919643c8c79ba5c6f4c78014b480cd98cbb5ad028e617db998351c","last_reissued_at":"2026-05-18T00:41:43.110201Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:43.110201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.08236","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mBfOH1InOZLqI7Luna4F9gATpDju/X/Kv7MDBmguPHUCOEzOnZDJ/5PhGhFQfq6B9myNl8Sqtsr/MBS8ffZBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:02:45.625942Z"},"content_sha256":"3bd60ccb099bd1132a8f698befd02fbb38f666feea78a3926c59ca1909942d1f","schema_version":"1.0","event_id":"sha256:3bd60ccb099bd1132a8f698befd02fbb38f666feea78a3926c59ca1909942d1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4VXCWHS4SGLEHSGHTOS4N5GHQA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The noncommutative L\\\"owner theorem for matrix monotone functions over operator systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.FA"],"primary_cat":"math.OA","authors_text":"J. E. Pascoe","submitted_at":"2017-06-26T05:30:31Z","abstract_excerpt":"Given a function $f: (a,b) \\rightarrow \\mathbb{R},$ L\\\"owner's theorem states $f$ is monotone when extended to self-adjoint matrices via the functional calculus, if and only if $f$ extends to a self-map of the complex upper half plane. In recent years, several generalizations of L\\\"owner's theorem have been proven in several variables. We use the relaxed Agler, McCarthy and Young theorem on locally matrix monotone functions in several commuting variables to generalize results in the noncommutative case. Specifically, we show that a real free function defined over an operator system must analyt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08236","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QPD075ghmesT9MmJD5d6DlRLeHkA1VxxC/mFjpNR1yDS2LWmxTu3Xd+o22BOLOb3pxK16Km9RM5oZCzwFbWMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:02:45.626296Z"},"content_sha256":"d74f2a81e3055149e72b081eda7ac7b8c4aa79c7289d9ff9700cc019d297d695","schema_version":"1.0","event_id":"sha256:d74f2a81e3055149e72b081eda7ac7b8c4aa79c7289d9ff9700cc019d297d695"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4VXCWHS4SGLEHSGHTOS4N5GHQA/bundle.json","state_url":"https://pith.science/pith/4VXCWHS4SGLEHSGHTOS4N5GHQA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4VXCWHS4SGLEHSGHTOS4N5GHQA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T16:02:45Z","links":{"resolver":"https://pith.science/pith/4VXCWHS4SGLEHSGHTOS4N5GHQA","bundle":"https://pith.science/pith/4VXCWHS4SGLEHSGHTOS4N5GHQA/bundle.json","state":"https://pith.science/pith/4VXCWHS4SGLEHSGHTOS4N5GHQA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4VXCWHS4SGLEHSGHTOS4N5GHQA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4VXCWHS4SGLEHSGHTOS4N5GHQA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"dc098f8c6ac15a92ae5b634fe562d2e157e5c94543812016b1fd2599f91f058c","cross_cats_sorted":["math.CV","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-26T05:30:31Z","title_canon_sha256":"6c8a32c60b34593f53f2e92cf4e18d461bf3c01dfff347ce76f55edba1e0b2fa"},"schema_version":"1.0","source":{"id":"1706.08236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08236","created_at":"2026-05-18T00:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08236v1","created_at":"2026-05-18T00:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08236","created_at":"2026-05-18T00:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"4VXCWHS4SGLE","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4VXCWHS4SGLEHSGH","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4VXCWHS4","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:d74f2a81e3055149e72b081eda7ac7b8c4aa79c7289d9ff9700cc019d297d695","target":"graph","created_at":"2026-05-18T00:41:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Given a function $f: (a,b) \\rightarrow \\mathbb{R},$ L\\\"owner's theorem states $f$ is monotone when extended to self-adjoint matrices via the functional calculus, if and only if $f$ extends to a self-map of the complex upper half plane. In recent years, several generalizations of L\\\"owner's theorem have been proven in several variables. We use the relaxed Agler, McCarthy and Young theorem on locally matrix monotone functions in several commuting variables to generalize results in the noncommutative case. Specifically, we show that a real free function defined over an operator system must analyt","authors_text":"J. E. Pascoe","cross_cats":["math.CV","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-26T05:30:31Z","title":"The noncommutative L\\\"owner theorem for matrix monotone functions over operator systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08236","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3bd60ccb099bd1132a8f698befd02fbb38f666feea78a3926c59ca1909942d1f","target":"record","created_at":"2026-05-18T00:41:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dc098f8c6ac15a92ae5b634fe562d2e157e5c94543812016b1fd2599f91f058c","cross_cats_sorted":["math.CV","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-26T05:30:31Z","title_canon_sha256":"6c8a32c60b34593f53f2e92cf4e18d461bf3c01dfff347ce76f55edba1e0b2fa"},"schema_version":"1.0","source":{"id":"1706.08236","kind":"arxiv","version":1}},"canonical_sha256":"e56e2b1e5c919643c8c79ba5c6f4c78014b480cd98cbb5ad028e617db998351c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e56e2b1e5c919643c8c79ba5c6f4c78014b480cd98cbb5ad028e617db998351c","first_computed_at":"2026-05-18T00:41:43.110201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:43.110201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WR5nEXc8WtNpbZcOsHTbJcWMeUMWEPrALQsjDeAORvST/UHOOFElWq46q0HeGxKOpm0nVUrhsHP+5C5xsyXtDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:43.110645Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.08236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bd60ccb099bd1132a8f698befd02fbb38f666feea78a3926c59ca1909942d1f","sha256:d74f2a81e3055149e72b081eda7ac7b8c4aa79c7289d9ff9700cc019d297d695"],"state_sha256":"605443131b77c62b85f179131606eaba2f5a54477068b90089d700b5c92b24d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0UX78A0bgC29gjNy6QU3JMIGbXeIrjUv3TAe3QON7CUPk4sIr71uFrfaXdjkSSa0lhuyODhT4/k4Hit3ygmLCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:02:45.628418Z","bundle_sha256":"d4c3c5a876eecaa28a8aa37b70dd22ce8278b3e27e6de092a227ae04a2ad5cf8"}}