{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PWYSL3XNIZJBLIUMWWPFMYVVES","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":"7ed608758d9dbfc451a09f8885d5379036ad0254120fcdd18872c0f0c0e04c5d","cross_cats_sorted":["cs.SY","math.AP","math.FA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-07-29T10:58:03Z","title_canon_sha256":"5828a5abea40aed5bfc40c7eda8a43a521b15f03d96a5d6c553973d0e80f17eb"},"schema_version":"1.0","source":{"id":"1107.5928","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5928","created_at":"2026-05-18T04:11:31Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5928v3","created_at":"2026-05-18T04:11:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5928","created_at":"2026-05-18T04:11:31Z"},{"alias_kind":"pith_short_12","alias_value":"PWYSL3XNIZJB","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PWYSL3XNIZJBLIUM","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PWYSL3XN","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:beb14984cc23d2a5e83072c2a2eb7a52892043bab96b84c4103cc418b552240c","target":"graph","created_at":"2026-05-18T04:11:31Z","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":"An abstract $\\nu$-metric was introduced by Ball and Sasane, with a view towards extending the classical $\\nu$-metric of Vinnicombe from the case of rational transfer functions to more general nonrational transfer function classes of infinite-dimensional linear control systems. In this short note, we give an important concrete special instance of the abstract $\\nu$-metric, by verifying that all the assumptions demanded in the abstract set-up are satisfied when the ring of stable transfer functions is the Hardy algebra $H^\\infty$. This settles the open question implicit in \\cite{BalSas2}.","authors_text":"Amol Sasane","cross_cats":["cs.SY","math.AP","math.FA","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-07-29T10:58:03Z","title":"Extension of the $\\nu$-metric for stabilizable plants over $H^\\infty$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5928","kind":"arxiv","version":3},"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":"sha256:131b435a0aca1abbd3f1a3cca27143b4d59efc2ed2652a3ca33c46c7d9d2d8df","target":"record","created_at":"2026-05-18T04:11:31Z","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":"7ed608758d9dbfc451a09f8885d5379036ad0254120fcdd18872c0f0c0e04c5d","cross_cats_sorted":["cs.SY","math.AP","math.FA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-07-29T10:58:03Z","title_canon_sha256":"5828a5abea40aed5bfc40c7eda8a43a521b15f03d96a5d6c553973d0e80f17eb"},"schema_version":"1.0","source":{"id":"1107.5928","kind":"arxiv","version":3}},"canonical_sha256":"7db125eeed465215a28cb59e5662b524a818ed25a98e3fffbddfd0c6e00a91a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7db125eeed465215a28cb59e5662b524a818ed25a98e3fffbddfd0c6e00a91a7","first_computed_at":"2026-05-18T04:11:31.446376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:31.446376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lAiCcyW4s3E6IvuH83VDcmswIdHRyGBA4g+iTTqDWQMHSzq3xHRg8POTdysMwyHs/x5p200EAG9Z/GrgbGZsBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:31.447046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.5928","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:131b435a0aca1abbd3f1a3cca27143b4d59efc2ed2652a3ca33c46c7d9d2d8df","sha256:beb14984cc23d2a5e83072c2a2eb7a52892043bab96b84c4103cc418b552240c"],"state_sha256":"e6307832122e5d1ea4ef4c4899cebd45fc85ed632c6dbbfc13218ebd559d26c7"}