{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Q6CSRSDISX7IBKTZYZTH2UYIV2","short_pith_number":"pith:Q6CSRSDI","canonical_record":{"source":{"id":"1410.0283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-10-01T16:47:26Z","cross_cats_sorted":[],"title_canon_sha256":"88e25959b56808c967cf3fc406717c2e34b9b9d966c68734a5f36a2a31553cd5","abstract_canon_sha256":"b3c5c779270f5423c082a4b90f52f7279d925837714befa23dc54f71c31d257a"},"schema_version":"1.0"},"canonical_sha256":"878528c86895fe80aa79c6667d5308aebe077b5370fab76a57652592532b0652","source":{"kind":"arxiv","id":"1410.0283","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0283","created_at":"2026-05-18T02:30:07Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0283v2","created_at":"2026-05-18T02:30:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0283","created_at":"2026-05-18T02:30:07Z"},{"alias_kind":"pith_short_12","alias_value":"Q6CSRSDISX7I","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q6CSRSDISX7IBKTZ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q6CSRSDI","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Q6CSRSDISX7IBKTZYZTH2UYIV2","target":"record","payload":{"canonical_record":{"source":{"id":"1410.0283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-10-01T16:47:26Z","cross_cats_sorted":[],"title_canon_sha256":"88e25959b56808c967cf3fc406717c2e34b9b9d966c68734a5f36a2a31553cd5","abstract_canon_sha256":"b3c5c779270f5423c082a4b90f52f7279d925837714befa23dc54f71c31d257a"},"schema_version":"1.0"},"canonical_sha256":"878528c86895fe80aa79c6667d5308aebe077b5370fab76a57652592532b0652","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:07.872262Z","signature_b64":"fJGpUKASwVU3143ri93PDLe4p53nGuxZaw7Y/BkiRPADTBihVAnQHvD+gd6xvNs6iaELF7PM2F+mHqYhbSyqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"878528c86895fe80aa79c6667d5308aebe077b5370fab76a57652592532b0652","last_reissued_at":"2026-05-18T02:30:07.871856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:07.871856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.0283","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hnJxOwygY3aKsUT5jGAssITS9iTtd7cHeb7sznoWArEHgu4tYAEOu+pXsN4ad6n/ZY6qHogxIKeeaVA2/ZBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:54:17.566233Z"},"content_sha256":"24a076f06d6c583000f6c6325088116d0b35297d2d1a2fb9c77b34b680fcc89b","schema_version":"1.0","event_id":"sha256:24a076f06d6c583000f6c6325088116d0b35297d2d1a2fb9c77b34b680fcc89b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Q6CSRSDISX7IBKTZYZTH2UYIV2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizations of rectangular (para)-unitary rational Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Daniel Alpay, Izchak Lewkowicz, Palle Jorgensen","submitted_at":"2014-10-01T16:47:26Z","abstract_excerpt":"We here present three characterizations of not necessarily causal, rational functions which are (co)-isometric on the unit circle: (i) Through the realization matrix of Schur stable systems. (ii) The Blaschke-Potapov product, which is then employed to introduce an easy-to-use description of all these functions with dimensions and McMillan degree as parameters. (iii) Through the (not necessarily reducible) Matrix Fraction Description (MFD).\n  In cases (ii) and (iii) the poles of the rational functions involved may be anywhere in the complex plane, but the unit circle (including both zero and in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0283","kind":"arxiv","version":2},"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":"2026-05-18T02:30:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yGAs2nCHD8PqFA6JxM5BPDi11tW5yWbRwSLqLugHh5DCt7c/Dyg/uaq8mSM/MvUDkCWMBMcMuXwGQpOQ7lm9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:54:17.567024Z"},"content_sha256":"e88ce245a540e77712aa3d402fc9c9d56bf8f23ec2cc655520f147b1f8333c23","schema_version":"1.0","event_id":"sha256:e88ce245a540e77712aa3d402fc9c9d56bf8f23ec2cc655520f147b1f8333c23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q6CSRSDISX7IBKTZYZTH2UYIV2/bundle.json","state_url":"https://pith.science/pith/Q6CSRSDISX7IBKTZYZTH2UYIV2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q6CSRSDISX7IBKTZYZTH2UYIV2/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":"2026-05-30T03:54:17Z","links":{"resolver":"https://pith.science/pith/Q6CSRSDISX7IBKTZYZTH2UYIV2","bundle":"https://pith.science/pith/Q6CSRSDISX7IBKTZYZTH2UYIV2/bundle.json","state":"https://pith.science/pith/Q6CSRSDISX7IBKTZYZTH2UYIV2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q6CSRSDISX7IBKTZYZTH2UYIV2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q6CSRSDISX7IBKTZYZTH2UYIV2","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":"b3c5c779270f5423c082a4b90f52f7279d925837714befa23dc54f71c31d257a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-10-01T16:47:26Z","title_canon_sha256":"88e25959b56808c967cf3fc406717c2e34b9b9d966c68734a5f36a2a31553cd5"},"schema_version":"1.0","source":{"id":"1410.0283","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0283","created_at":"2026-05-18T02:30:07Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0283v2","created_at":"2026-05-18T02:30:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0283","created_at":"2026-05-18T02:30:07Z"},{"alias_kind":"pith_short_12","alias_value":"Q6CSRSDISX7I","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q6CSRSDISX7IBKTZ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q6CSRSDI","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:e88ce245a540e77712aa3d402fc9c9d56bf8f23ec2cc655520f147b1f8333c23","target":"graph","created_at":"2026-05-18T02:30:07Z","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 here present three characterizations of not necessarily causal, rational functions which are (co)-isometric on the unit circle: (i) Through the realization matrix of Schur stable systems. (ii) The Blaschke-Potapov product, which is then employed to introduce an easy-to-use description of all these functions with dimensions and McMillan degree as parameters. (iii) Through the (not necessarily reducible) Matrix Fraction Description (MFD).\n  In cases (ii) and (iii) the poles of the rational functions involved may be anywhere in the complex plane, but the unit circle (including both zero and in","authors_text":"Daniel Alpay, Izchak Lewkowicz, Palle Jorgensen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-10-01T16:47:26Z","title":"Characterizations of rectangular (para)-unitary rational Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0283","kind":"arxiv","version":2},"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":"sha256:24a076f06d6c583000f6c6325088116d0b35297d2d1a2fb9c77b34b680fcc89b","target":"record","created_at":"2026-05-18T02:30:07Z","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":"b3c5c779270f5423c082a4b90f52f7279d925837714befa23dc54f71c31d257a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-10-01T16:47:26Z","title_canon_sha256":"88e25959b56808c967cf3fc406717c2e34b9b9d966c68734a5f36a2a31553cd5"},"schema_version":"1.0","source":{"id":"1410.0283","kind":"arxiv","version":2}},"canonical_sha256":"878528c86895fe80aa79c6667d5308aebe077b5370fab76a57652592532b0652","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"878528c86895fe80aa79c6667d5308aebe077b5370fab76a57652592532b0652","first_computed_at":"2026-05-18T02:30:07.871856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:07.871856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fJGpUKASwVU3143ri93PDLe4p53nGuxZaw7Y/BkiRPADTBihVAnQHvD+gd6xvNs6iaELF7PM2F+mHqYhbSyqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:07.872262Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0283","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24a076f06d6c583000f6c6325088116d0b35297d2d1a2fb9c77b34b680fcc89b","sha256:e88ce245a540e77712aa3d402fc9c9d56bf8f23ec2cc655520f147b1f8333c23"],"state_sha256":"12be356bc52633004730b2ce929cfd961d789d339b996daf4f1aec90f3cfe7a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DzRzWsAGNb3po2ybIgAxBEiDMTk1wgaXOp0AN9+R1hqQJJiAcr1g6awzmo22NGLXcGNB4/Lgo98gfwl8tXDjCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T03:54:17.570646Z","bundle_sha256":"e780ecd6a3da5e0573da40d78fdd67e9cb7467b50973abe5202a7368dfb965c4"}}