{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AXPO2FQQMTOTLEYR22VIZUJWO3","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":"2a23669c7bebe4cd39316293dacd7f92205e59e74986bae5bb7f9cd10bf1ee98","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-04T16:06:15Z","title_canon_sha256":"25c3f0c0adee1db30cfbe9d2df199828440a464862127d499846e6171226c623"},"schema_version":"1.0","source":{"id":"1403.0824","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0824","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0824v2","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0824","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"pith_short_12","alias_value":"AXPO2FQQMTOT","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AXPO2FQQMTOTLEYR","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AXPO2FQQ","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:56e6d50101b922380f6cf996e02b6588f5322f8803a111940b10690a9c2c3131","target":"graph","created_at":"2026-05-18T01:24:04Z","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":"A theorem of J. Bochi and N. Gourmelon states that an invertible linear cocycle admits a dominated splitting if and only if the singular values of its iterates become separated at a uniform exponential rate. It is not difficult to show that for cocycles of non-invertible linear maps over an invertible dynamical system -- which we refer to as semi-invertible cocycles -- this criterion fails to imply the existence of a dominated splitting. In this article we show that a simple modification of Bochi and Gourmelon's singular value criterion is equivalent to the existence of a dominated splitting i","authors_text":"Ian D. Morris","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-04T16:06:15Z","title":"Dominated splittings for semi-invertible operator cocycles on Hilbert space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0824","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":"sha256:93e670d6317a2ee304b49648736c89f38110331d6264e291101c34579ad41f66","target":"record","created_at":"2026-05-18T01:24:04Z","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":"2a23669c7bebe4cd39316293dacd7f92205e59e74986bae5bb7f9cd10bf1ee98","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-04T16:06:15Z","title_canon_sha256":"25c3f0c0adee1db30cfbe9d2df199828440a464862127d499846e6171226c623"},"schema_version":"1.0","source":{"id":"1403.0824","kind":"arxiv","version":2}},"canonical_sha256":"05deed161064dd359311d6aa8cd13676f2389347c011f77f613a1ccc60a6c9da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05deed161064dd359311d6aa8cd13676f2389347c011f77f613a1ccc60a6c9da","first_computed_at":"2026-05-18T01:24:04.394001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:04.394001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ow+uB1HQZm5vWnK0KY89QHN5J92PArmPVkI9ZiWc/pwsoc0q4F94z6+Xbu7ph2kgMyO9QUYW2Vpd6QDAezhcCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:04.394625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0824","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93e670d6317a2ee304b49648736c89f38110331d6264e291101c34579ad41f66","sha256:56e6d50101b922380f6cf996e02b6588f5322f8803a111940b10690a9c2c3131"],"state_sha256":"a75f899cf949d1209610fc9cf80851f20fb4c9201967ef48902e4dd53cd9662f"}