{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:V6BDXJFKHE5I2INBSJ3AZTMVY7","short_pith_number":"pith:V6BDXJFK","canonical_record":{"source":{"id":"1611.06462","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-20T02:00:55Z","cross_cats_sorted":[],"title_canon_sha256":"29214b3ce4ba4e2d82522fe0c5f15ef4a109affee4013f5bace311a65ee628c0","abstract_canon_sha256":"8fcdbb3f0e21104386b313b1552ea5d8fc78b9491692e868989280cb7dd5dbc8"},"schema_version":"1.0"},"canonical_sha256":"af823ba4aa393a8d21a192760ccd95c7c3d53672b41e5f915ebe3e44a5912458","source":{"kind":"arxiv","id":"1611.06462","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06462","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06462v1","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06462","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"pith_short_12","alias_value":"V6BDXJFKHE5I","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"V6BDXJFKHE5I2INB","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"V6BDXJFK","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:V6BDXJFKHE5I2INBSJ3AZTMVY7","target":"record","payload":{"canonical_record":{"source":{"id":"1611.06462","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-20T02:00:55Z","cross_cats_sorted":[],"title_canon_sha256":"29214b3ce4ba4e2d82522fe0c5f15ef4a109affee4013f5bace311a65ee628c0","abstract_canon_sha256":"8fcdbb3f0e21104386b313b1552ea5d8fc78b9491692e868989280cb7dd5dbc8"},"schema_version":"1.0"},"canonical_sha256":"af823ba4aa393a8d21a192760ccd95c7c3d53672b41e5f915ebe3e44a5912458","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:36.728110Z","signature_b64":"6OzfYBq9Tk5AVGO4D++QCC9A2aWqb1XnlVnTAiqphryY+V6Vz9zGcCnwyLSMr56KNarYhvgHuc/o0yNDedQvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af823ba4aa393a8d21a192760ccd95c7c3d53672b41e5f915ebe3e44a5912458","last_reissued_at":"2026-05-18T00:57:36.727614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:36.727614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.06462","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":"2026-05-18T00:57:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vLdWRs0pUS1pvd2ObwirRrmrSBsjEnaPQpEbmxXRFO8rKcGj6s3ZVRun4t5ZkQFaYht2m8AW3uERqd9w/RhXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:45:49.543258Z"},"content_sha256":"8331ad8eb93049115fb5d2b17fad7e8353fed7f10cfa78dde3ddd25d58494941","schema_version":"1.0","event_id":"sha256:8331ad8eb93049115fb5d2b17fad7e8353fed7f10cfa78dde3ddd25d58494941"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:V6BDXJFKHE5I2INBSJ3AZTMVY7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"In Sung Hwang, Ra\\'ul E. Curto, Woo Young Lee","submitted_at":"2016-11-20T02:00:55Z","abstract_excerpt":"In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. \\ We first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. \\ We propose a new notion of tensored-scalar singularity, and then answer questions on Hankel operators with matrix-valued bounded type symbols. \\ We also examine an interpolation problem related to a certain functional equation on matrix functions of bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06462","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":"2026-05-18T00:57:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RdhpRbLK2bJ+HMEvoI22jUn4e/ndv9M/Hr54Z9AZx2uMONQA5fOfWw88EJngTMvR7gwFL8Ou8Qj+ZnNeQM5qDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:45:49.543980Z"},"content_sha256":"b582beae3bb6b016e81a8a30c4cadcbc7fdb635bf099b905e4dbdece516a3b10","schema_version":"1.0","event_id":"sha256:b582beae3bb6b016e81a8a30c4cadcbc7fdb635bf099b905e4dbdece516a3b10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V6BDXJFKHE5I2INBSJ3AZTMVY7/bundle.json","state_url":"https://pith.science/pith/V6BDXJFKHE5I2INBSJ3AZTMVY7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V6BDXJFKHE5I2INBSJ3AZTMVY7/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":"2026-05-29T17:45:49Z","links":{"resolver":"https://pith.science/pith/V6BDXJFKHE5I2INBSJ3AZTMVY7","bundle":"https://pith.science/pith/V6BDXJFKHE5I2INBSJ3AZTMVY7/bundle.json","state":"https://pith.science/pith/V6BDXJFKHE5I2INBSJ3AZTMVY7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V6BDXJFKHE5I2INBSJ3AZTMVY7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:V6BDXJFKHE5I2INBSJ3AZTMVY7","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":"8fcdbb3f0e21104386b313b1552ea5d8fc78b9491692e868989280cb7dd5dbc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-20T02:00:55Z","title_canon_sha256":"29214b3ce4ba4e2d82522fe0c5f15ef4a109affee4013f5bace311a65ee628c0"},"schema_version":"1.0","source":{"id":"1611.06462","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06462","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06462v1","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06462","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"pith_short_12","alias_value":"V6BDXJFKHE5I","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"V6BDXJFKHE5I2INB","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"V6BDXJFK","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:b582beae3bb6b016e81a8a30c4cadcbc7fdb635bf099b905e4dbdece516a3b10","target":"graph","created_at":"2026-05-18T00:57:36Z","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":"In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. \\ We first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. \\ We propose a new notion of tensored-scalar singularity, and then answer questions on Hankel operators with matrix-valued bounded type symbols. \\ We also examine an interpolation problem related to a certain functional equation on matrix functions of bo","authors_text":"In Sung Hwang, Ra\\'ul E. Curto, Woo Young Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-20T02:00:55Z","title":"Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06462","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":"sha256:8331ad8eb93049115fb5d2b17fad7e8353fed7f10cfa78dde3ddd25d58494941","target":"record","created_at":"2026-05-18T00:57:36Z","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":"8fcdbb3f0e21104386b313b1552ea5d8fc78b9491692e868989280cb7dd5dbc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-20T02:00:55Z","title_canon_sha256":"29214b3ce4ba4e2d82522fe0c5f15ef4a109affee4013f5bace311a65ee628c0"},"schema_version":"1.0","source":{"id":"1611.06462","kind":"arxiv","version":1}},"canonical_sha256":"af823ba4aa393a8d21a192760ccd95c7c3d53672b41e5f915ebe3e44a5912458","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af823ba4aa393a8d21a192760ccd95c7c3d53672b41e5f915ebe3e44a5912458","first_computed_at":"2026-05-18T00:57:36.727614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:36.727614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6OzfYBq9Tk5AVGO4D++QCC9A2aWqb1XnlVnTAiqphryY+V6Vz9zGcCnwyLSMr56KNarYhvgHuc/o0yNDedQvBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:36.728110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06462","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8331ad8eb93049115fb5d2b17fad7e8353fed7f10cfa78dde3ddd25d58494941","sha256:b582beae3bb6b016e81a8a30c4cadcbc7fdb635bf099b905e4dbdece516a3b10"],"state_sha256":"76a26a833083670951a440c7521bdd89f80d2ae38480cbc0cbb4dbf1cbbc7678"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+D+lEhM6JEX6AKlIsAAmAyR8CSX8D7Nl/soJxVZjXjU3BwzDCOgX7Iv4EtIvpYbyk3YV6nasWxVN4fML9JUgCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:45:49.547743Z","bundle_sha256":"1d08e67f6a456f1fe0c4377fd6aadbaa1a7cf93815d00e51665d44048ecc8245"}}