{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OHZP3H4JYIDDWTU7HWXYOTVCY5","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":"60ead6b35be8f4e8a56f77d59437226bd9b07dc5213658880e7a3660f2b14848","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-07-14T12:41:16Z","title_canon_sha256":"cd47cfea7e6218efb9496403ade8e1b6a2f39434e6289e09f463957494be9622"},"schema_version":"1.0","source":{"id":"1907.07089","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.07089","created_at":"2026-05-17T23:40:28Z"},{"alias_kind":"arxiv_version","alias_value":"1907.07089v1","created_at":"2026-05-17T23:40:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.07089","created_at":"2026-05-17T23:40:28Z"},{"alias_kind":"pith_short_12","alias_value":"OHZP3H4JYIDD","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OHZP3H4JYIDDWTU7","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OHZP3H4J","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:817e30ac4b66d6606889de69d5b3c3a92b7a65804bea74d114022cf47f16f78c","target":"graph","created_at":"2026-05-17T23:40:28Z","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":"Multiplicative and additive $D$-stability, diagonal stability, Schur $D$-stability, $H$-stability are classical concepts which arise in studying linear dynamical systems. We unify these types of stability, as well as many others, in one concept of $({\\mathfrak D}, {\\mathcal G}, \\circ)$-stability, which depends on a stability region ${\\mathfrak D} \\subset {\\mathbb C}$, a matrix class ${\\mathcal G}$ and a binary matrix operation $\\circ$. This approach allows us to unite several well-known matrix problems and to consider common methods of their analysis. In order to collect these methods, we make","authors_text":"Olga Kushel","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-07-14T12:41:16Z","title":"Unifying matrix stability concepts with a view to applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07089","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":"sha256:892d8d852170c29b684f38af1167dcdc5b40a3e726e5f6a0c73d7658fcd463f3","target":"record","created_at":"2026-05-17T23:40:28Z","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":"60ead6b35be8f4e8a56f77d59437226bd9b07dc5213658880e7a3660f2b14848","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-07-14T12:41:16Z","title_canon_sha256":"cd47cfea7e6218efb9496403ade8e1b6a2f39434e6289e09f463957494be9622"},"schema_version":"1.0","source":{"id":"1907.07089","kind":"arxiv","version":1}},"canonical_sha256":"71f2fd9f89c2063b4e9f3daf874ea2c751639355d174fb680b3a713c03842dad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71f2fd9f89c2063b4e9f3daf874ea2c751639355d174fb680b3a713c03842dad","first_computed_at":"2026-05-17T23:40:28.139892Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:28.139892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k2byeWcgEOM291v3Ev/O5RCCJB5D9fnQd0pVu1k5PIL0GkrNWes+THBBz4FFs88t9XdjHKTiNA/vcNYdXyzhAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:28.140564Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.07089","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:892d8d852170c29b684f38af1167dcdc5b40a3e726e5f6a0c73d7658fcd463f3","sha256:817e30ac4b66d6606889de69d5b3c3a92b7a65804bea74d114022cf47f16f78c"],"state_sha256":"f9dfe3c526b02ea951620046dbf3cd1338329c4ba794602b7e7d818469383eb6"}