{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:B25IV4BCWZHGKKTLJMIWJP77CP","short_pith_number":"pith:B25IV4BC","canonical_record":{"source":{"id":"2312.00707","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-12-01T16:42:01Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"5bf3188fc072697756fa583512108c1f646f6a95f7d9bfcb336f8d9fc070abd6","abstract_canon_sha256":"6f8488bc27331a4291028072735f2bbbf44a0931782d6eaa26aca8e89cb572e2"},"schema_version":"1.0"},"canonical_sha256":"0eba8af022b64e652a6b4b1164bfff13c53135be23ec4c5628bd3c5c1e6b1165","source":{"kind":"arxiv","id":"2312.00707","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.00707","created_at":"2026-07-05T07:19:13Z"},{"alias_kind":"arxiv_version","alias_value":"2312.00707v1","created_at":"2026-07-05T07:19:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.00707","created_at":"2026-07-05T07:19:13Z"},{"alias_kind":"pith_short_12","alias_value":"B25IV4BCWZHG","created_at":"2026-07-05T07:19:13Z"},{"alias_kind":"pith_short_16","alias_value":"B25IV4BCWZHGKKTL","created_at":"2026-07-05T07:19:13Z"},{"alias_kind":"pith_short_8","alias_value":"B25IV4BC","created_at":"2026-07-05T07:19:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:B25IV4BCWZHGKKTLJMIWJP77CP","target":"record","payload":{"canonical_record":{"source":{"id":"2312.00707","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-12-01T16:42:01Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"5bf3188fc072697756fa583512108c1f646f6a95f7d9bfcb336f8d9fc070abd6","abstract_canon_sha256":"6f8488bc27331a4291028072735f2bbbf44a0931782d6eaa26aca8e89cb572e2"},"schema_version":"1.0"},"canonical_sha256":"0eba8af022b64e652a6b4b1164bfff13c53135be23ec4c5628bd3c5c1e6b1165","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:19:13.311646Z","signature_b64":"9/uTRQpdinLX4zczsRyH5sFyzxVyl6YDdY2xYxxekFLHYaXhiuh3knDal9NaQ/p5O1gWhKCTuOjGAovK+5zJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0eba8af022b64e652a6b4b1164bfff13c53135be23ec4c5628bd3c5c1e6b1165","last_reissued_at":"2026-07-05T07:19:13.311222Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:19:13.311222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.00707","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":"2026-07-05T07:19:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JCF+cEQGrGtoDmAzUrXjkJQnGZl7SHUFwnyoDVHOQc1KNVpxApEQBMvF1NhXEQzhVRiU2fC0W01MMTBFcuOpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:32:03.409575Z"},"content_sha256":"9944dfb0d8f4e8744d9b75be569aefdbd5ebe60acf50b287fe0e9207607d54ba","schema_version":"1.0","event_id":"sha256:9944dfb0d8f4e8744d9b75be569aefdbd5ebe60acf50b287fe0e9207607d54ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:B25IV4BCWZHGKKTLJMIWJP77CP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Periodicity of Singular Vectors and the Holomorphic Block-Circulant SVD on the Unit Circumference","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Giovanni Barbarino","submitted_at":"2023-12-01T16:42:01Z","abstract_excerpt":"We investigate the singular value decomposition of a rectangular matrix that is analytic on the complex unit circumference, which occurs, e.g., with the matrix of transfer functions representing a broadband multiple-input multiple-output channel. Our analysis is based on the Puiseux series expansion of the eigenvalue decomposition of analytic para-Hermitian matrices on the complex unit circumference. We study the case in which the rectangular matrix does not admit a full analytic singular value factorization, either due to partly multiplexed systems or to sign ambiguity. We show how to find an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.00707","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.00707/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:19:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TUTs15Nmzj2WjuPJw8Uzkot/BwB5wAW0skZjnW47a5Va4ietXc5/l99NNf8M3YmpnZIYw3Rsj6S65D+2OgJmAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:32:03.410485Z"},"content_sha256":"80b6159802548eb11d37edce0a6e46b27cddd6a1506a324140f34d5edbcbc7f2","schema_version":"1.0","event_id":"sha256:80b6159802548eb11d37edce0a6e46b27cddd6a1506a324140f34d5edbcbc7f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B25IV4BCWZHGKKTLJMIWJP77CP/bundle.json","state_url":"https://pith.science/pith/B25IV4BCWZHGKKTLJMIWJP77CP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B25IV4BCWZHGKKTLJMIWJP77CP/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":"2026-08-03T17:32:03Z","links":{"resolver":"https://pith.science/pith/B25IV4BCWZHGKKTLJMIWJP77CP","bundle":"https://pith.science/pith/B25IV4BCWZHGKKTLJMIWJP77CP/bundle.json","state":"https://pith.science/pith/B25IV4BCWZHGKKTLJMIWJP77CP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B25IV4BCWZHGKKTLJMIWJP77CP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:B25IV4BCWZHGKKTLJMIWJP77CP","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":"6f8488bc27331a4291028072735f2bbbf44a0931782d6eaa26aca8e89cb572e2","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-12-01T16:42:01Z","title_canon_sha256":"5bf3188fc072697756fa583512108c1f646f6a95f7d9bfcb336f8d9fc070abd6"},"schema_version":"1.0","source":{"id":"2312.00707","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.00707","created_at":"2026-07-05T07:19:13Z"},{"alias_kind":"arxiv_version","alias_value":"2312.00707v1","created_at":"2026-07-05T07:19:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.00707","created_at":"2026-07-05T07:19:13Z"},{"alias_kind":"pith_short_12","alias_value":"B25IV4BCWZHG","created_at":"2026-07-05T07:19:13Z"},{"alias_kind":"pith_short_16","alias_value":"B25IV4BCWZHGKKTL","created_at":"2026-07-05T07:19:13Z"},{"alias_kind":"pith_short_8","alias_value":"B25IV4BC","created_at":"2026-07-05T07:19:13Z"}],"graph_snapshots":[{"event_id":"sha256:80b6159802548eb11d37edce0a6e46b27cddd6a1506a324140f34d5edbcbc7f2","target":"graph","created_at":"2026-07-05T07:19:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2312.00707/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the singular value decomposition of a rectangular matrix that is analytic on the complex unit circumference, which occurs, e.g., with the matrix of transfer functions representing a broadband multiple-input multiple-output channel. Our analysis is based on the Puiseux series expansion of the eigenvalue decomposition of analytic para-Hermitian matrices on the complex unit circumference. We study the case in which the rectangular matrix does not admit a full analytic singular value factorization, either due to partly multiplexed systems or to sign ambiguity. We show how to find an","authors_text":"Giovanni Barbarino","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-12-01T16:42:01Z","title":"On the Periodicity of Singular Vectors and the Holomorphic Block-Circulant SVD on the Unit Circumference"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.00707","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":"sha256:9944dfb0d8f4e8744d9b75be569aefdbd5ebe60acf50b287fe0e9207607d54ba","target":"record","created_at":"2026-07-05T07:19:13Z","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":"6f8488bc27331a4291028072735f2bbbf44a0931782d6eaa26aca8e89cb572e2","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-12-01T16:42:01Z","title_canon_sha256":"5bf3188fc072697756fa583512108c1f646f6a95f7d9bfcb336f8d9fc070abd6"},"schema_version":"1.0","source":{"id":"2312.00707","kind":"arxiv","version":1}},"canonical_sha256":"0eba8af022b64e652a6b4b1164bfff13c53135be23ec4c5628bd3c5c1e6b1165","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0eba8af022b64e652a6b4b1164bfff13c53135be23ec4c5628bd3c5c1e6b1165","first_computed_at":"2026-07-05T07:19:13.311222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:19:13.311222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9/uTRQpdinLX4zczsRyH5sFyzxVyl6YDdY2xYxxekFLHYaXhiuh3knDal9NaQ/p5O1gWhKCTuOjGAovK+5zJBw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:19:13.311646Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.00707","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9944dfb0d8f4e8744d9b75be569aefdbd5ebe60acf50b287fe0e9207607d54ba","sha256:80b6159802548eb11d37edce0a6e46b27cddd6a1506a324140f34d5edbcbc7f2"],"state_sha256":"5f7437922c724c3eb8741af872476e2b1a02fa54f1405ca47d5efdd5382a151b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WzDCgYEzEVzTrqiMt+24cizQMQLRl/WlN9nZls/XsWz4qPP10KLa2F0GU4RrlLSbqFsWvp2kl/ud7+i6SLg1Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T17:32:03.417851Z","bundle_sha256":"ce88684922b22a86e7b2efd492a41820c25975ed4de18d88ac69d4f8426ace99"}}