{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:J7BZFESBUBGN23OBJA3X2OOU6U","short_pith_number":"pith:J7BZFESB","canonical_record":{"source":{"id":"1505.05437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-20T16:05:13Z","cross_cats_sorted":[],"title_canon_sha256":"7b74222e1620e626200ca675411842e6c7ac5d354ce506776f08f0c1850c2de9","abstract_canon_sha256":"ca532ee280004d9338069981b9357485e7587604022abf17b999fa893a3d0a31"},"schema_version":"1.0"},"canonical_sha256":"4fc3929241a04cdd6dc148377d39d4f51fce8a07e708ead125d40dee5b20cc2c","source":{"kind":"arxiv","id":"1505.05437","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05437","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05437v1","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05437","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"pith_short_12","alias_value":"J7BZFESBUBGN","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"J7BZFESBUBGN23OB","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"J7BZFESB","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:J7BZFESBUBGN23OBJA3X2OOU6U","target":"record","payload":{"canonical_record":{"source":{"id":"1505.05437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-20T16:05:13Z","cross_cats_sorted":[],"title_canon_sha256":"7b74222e1620e626200ca675411842e6c7ac5d354ce506776f08f0c1850c2de9","abstract_canon_sha256":"ca532ee280004d9338069981b9357485e7587604022abf17b999fa893a3d0a31"},"schema_version":"1.0"},"canonical_sha256":"4fc3929241a04cdd6dc148377d39d4f51fce8a07e708ead125d40dee5b20cc2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:56.351177Z","signature_b64":"oWL7bWfXG3FQFfbRILnMng9VjVHkWIAawrr8jxxrZAEM30Vr2TkLznim+AqGCCmTc/N7tEHjUe0ZysOwBK96Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fc3929241a04cdd6dc148377d39d4f51fce8a07e708ead125d40dee5b20cc2c","last_reissued_at":"2026-05-18T02:03:56.350527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:56.350527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.05437","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":"2026-05-18T02:03:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h1sl0BeoW+P3J2JygMf5+QdpVoiJzPcdtsC0GfdpFFxe/bHQ+KZAAI43XgZdKT5dW1zyFkX0veDwL5+qMHC+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:00:59.522432Z"},"content_sha256":"3f96274555eb90184c93648a9ffbbf9099473a0b084218c5297b22e673fcb2f2","schema_version":"1.0","event_id":"sha256:3f96274555eb90184c93648a9ffbbf9099473a0b084218c5297b22e673fcb2f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:J7BZFESBUBGN23OBJA3X2OOU6U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational inner functions on a square-matrix polyball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Hugo J. Woerdeman, Victor Vinnikov","submitted_at":"2015-05-20T16:05:13Z","abstract_excerpt":"We establish the existence of a finite-dimensional unitary realization for every matrix-valued rational inner function from the Schur--Agler class on a unit square-matrix polyball. In the scalar-valued case, we characterize the denominators of these functions. We also show that every polynomial with no zeros in the closed domain is such a denominator. One of our tools is the Kor\\'{a}nyi--Vagi theorem generalizing Rudin's description of rational inner functions to the case of bounded symmetric domains; we provide a short elementary proof of this theorem suitable in our setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05437","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":"2026-05-18T02:03:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EHyJ4iEV8It+7N+I3wKMbC99uWfr/8Pd564Q41Qn5u+Lv3dyBARIRbJdjHt/8Pjcrqu+UTaz3DhZiJkzYfbeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:00:59.522772Z"},"content_sha256":"96a537bc5f618f2ca1aa3c87dcfd16d1b3fa3c7ab93f1702c67f5b4bca89c7a2","schema_version":"1.0","event_id":"sha256:96a537bc5f618f2ca1aa3c87dcfd16d1b3fa3c7ab93f1702c67f5b4bca89c7a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J7BZFESBUBGN23OBJA3X2OOU6U/bundle.json","state_url":"https://pith.science/pith/J7BZFESBUBGN23OBJA3X2OOU6U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J7BZFESBUBGN23OBJA3X2OOU6U/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":"2026-06-02T17:00:59Z","links":{"resolver":"https://pith.science/pith/J7BZFESBUBGN23OBJA3X2OOU6U","bundle":"https://pith.science/pith/J7BZFESBUBGN23OBJA3X2OOU6U/bundle.json","state":"https://pith.science/pith/J7BZFESBUBGN23OBJA3X2OOU6U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J7BZFESBUBGN23OBJA3X2OOU6U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:J7BZFESBUBGN23OBJA3X2OOU6U","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":"ca532ee280004d9338069981b9357485e7587604022abf17b999fa893a3d0a31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-20T16:05:13Z","title_canon_sha256":"7b74222e1620e626200ca675411842e6c7ac5d354ce506776f08f0c1850c2de9"},"schema_version":"1.0","source":{"id":"1505.05437","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05437","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05437v1","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05437","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"pith_short_12","alias_value":"J7BZFESBUBGN","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"J7BZFESBUBGN23OB","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"J7BZFESB","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:96a537bc5f618f2ca1aa3c87dcfd16d1b3fa3c7ab93f1702c67f5b4bca89c7a2","target":"graph","created_at":"2026-05-18T02:03:56Z","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":"We establish the existence of a finite-dimensional unitary realization for every matrix-valued rational inner function from the Schur--Agler class on a unit square-matrix polyball. In the scalar-valued case, we characterize the denominators of these functions. We also show that every polynomial with no zeros in the closed domain is such a denominator. One of our tools is the Kor\\'{a}nyi--Vagi theorem generalizing Rudin's description of rational inner functions to the case of bounded symmetric domains; we provide a short elementary proof of this theorem suitable in our setting.","authors_text":"Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Hugo J. Woerdeman, Victor Vinnikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-20T16:05:13Z","title":"Rational inner functions on a square-matrix polyball"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05437","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":"sha256:3f96274555eb90184c93648a9ffbbf9099473a0b084218c5297b22e673fcb2f2","target":"record","created_at":"2026-05-18T02:03:56Z","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":"ca532ee280004d9338069981b9357485e7587604022abf17b999fa893a3d0a31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-20T16:05:13Z","title_canon_sha256":"7b74222e1620e626200ca675411842e6c7ac5d354ce506776f08f0c1850c2de9"},"schema_version":"1.0","source":{"id":"1505.05437","kind":"arxiv","version":1}},"canonical_sha256":"4fc3929241a04cdd6dc148377d39d4f51fce8a07e708ead125d40dee5b20cc2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fc3929241a04cdd6dc148377d39d4f51fce8a07e708ead125d40dee5b20cc2c","first_computed_at":"2026-05-18T02:03:56.350527Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:56.350527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oWL7bWfXG3FQFfbRILnMng9VjVHkWIAawrr8jxxrZAEM30Vr2TkLznim+AqGCCmTc/N7tEHjUe0ZysOwBK96Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:56.351177Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.05437","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f96274555eb90184c93648a9ffbbf9099473a0b084218c5297b22e673fcb2f2","sha256:96a537bc5f618f2ca1aa3c87dcfd16d1b3fa3c7ab93f1702c67f5b4bca89c7a2"],"state_sha256":"db5546ce4f1e4bfa9db1e2b85ad1979a3126f9d04d77168351017467176fea1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GD4J9Xw0TW5UWkqj7r3QYZgq0XP4H9x97KRcEgQjUtFUJy4BzO4gjuWaln6N9z9ae0F0282CpThi2rPyo56MBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:00:59.524559Z","bundle_sha256":"add59b9051b07bab79449aed82ff0baae7df3522747758a73c966768e5742e84"}}