{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UBVVAGV22XX6S4CBUAIPR2RLD6","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":"a0381b14883aaa2451a7bc53f68cbce81a07cd9f710eb7d25cd0073efb6a7819","cross_cats_sorted":["math.CV","math.FA","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-12-02T14:19:29Z","title_canon_sha256":"0b9547fcf080fd151463b8783be857c372026748829568fd53a5b2222419a540"},"schema_version":"1.0","source":{"id":"1012.0427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0427","created_at":"2026-05-18T04:34:17Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0427v1","created_at":"2026-05-18T04:34:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0427","created_at":"2026-05-18T04:34:17Z"},{"alias_kind":"pith_short_12","alias_value":"UBVVAGV22XX6","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UBVVAGV22XX6S4CB","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UBVVAGV2","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:0103cb131b658c221150c61d050f80f5466f9b7ef489bebf3131cbfc9a486bab","target":"graph","created_at":"2026-05-18T04:34:17Z","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":"Let $\\calA_+$ denote the set of Laplace transforms of complex Borel measures $\\mu$ on $[0,+\\infty)$ such that $\\mu$ does not have a singular non-atomic part. In \\cite{BalSas}, an extension of the classical $\\nu$-metric of Vinnicombe was given, which allowed one to address robust stabilization problems for unstable plants over $\\calA_+$. In this article, we show that this new $\\nu$-metric gives a topology on unstable plants which coincides with the classical gap topology for unstable plants over $\\calA_+$ with a single input and a single output.","authors_text":"Amol Sasane","cross_cats":["math.CV","math.FA","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-12-02T14:19:29Z","title":"The new $\\nu$-metric induces the classical gap topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0427","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":"sha256:9172edb37286b04d130eae68983347d58891fdc61a0fcfa10ec5a8394eee646f","target":"record","created_at":"2026-05-18T04:34:17Z","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":"a0381b14883aaa2451a7bc53f68cbce81a07cd9f710eb7d25cd0073efb6a7819","cross_cats_sorted":["math.CV","math.FA","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-12-02T14:19:29Z","title_canon_sha256":"0b9547fcf080fd151463b8783be857c372026748829568fd53a5b2222419a540"},"schema_version":"1.0","source":{"id":"1012.0427","kind":"arxiv","version":1}},"canonical_sha256":"a06b501abad5efe97041a010f8ea2b1f903cd1e8d7684e1c6d5ccef6ba67671f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a06b501abad5efe97041a010f8ea2b1f903cd1e8d7684e1c6d5ccef6ba67671f","first_computed_at":"2026-05-18T04:34:17.838617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:17.838617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rQjHYt7+gBgw4RZitbXTznhKYX0P3dDt8kPKgomPUaWwGLowI3y27shHt/PILjeFKnV263zRYUqxXfc8UahFAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:17.839071Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.0427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9172edb37286b04d130eae68983347d58891fdc61a0fcfa10ec5a8394eee646f","sha256:0103cb131b658c221150c61d050f80f5466f9b7ef489bebf3131cbfc9a486bab"],"state_sha256":"47029e687894144a43691d37ca533e8d45055f5b126089bdf18644a40d9e8f01"}