{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NJBXEOEAAWJYN4HIXHGT7QQYJS","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":"dcd70935b1364ff361a6be79d1272d43724509ce521ce46b34bf1db5e72c61b2","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-01T20:42:04Z","title_canon_sha256":"4612bf6ab9e8ea69992e3bf627897086430004920dc1ccc8feab80b3f7058a9a"},"schema_version":"1.0","source":{"id":"2606.04031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04031","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04031v1","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04031","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"NJBXEOEAAWJY","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"pith_short_16","alias_value":"NJBXEOEAAWJYN4HI","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"pith_short_8","alias_value":"NJBXEOEA","created_at":"2026-06-04T00:06:44Z"}],"graph_snapshots":[{"event_id":"sha256:a3ce869c6895813dcc7595ab2364f4df3841c822a4bba469b6792e0d012ff5a4","target":"graph","created_at":"2026-06-04T00:06:44Z","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/2606.04031/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Coupled gradient descent--where the update of one parameter block depends on another--underlies bilevel optimization, two-time-scale stochastic approximation, and adversarial training. When the coupled Jacobian is block-triangular, asymptotic stability is governed by the spectral radii of the diagonal blocks, yet transient amplification before convergence can be arbitrarily large due to non-normality. We develop a sharp pseudospectral theory for such block-triangular Jacobians, proving that the Kreiss constant satisfies $K(J) \\leq 2/(1-\\gamma) + \\|C\\|/(4(1-\\gamma))$ when the diagonal blocks ar","authors_text":"Ahanaf Hasan Ariq","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-01T20:42:04Z","title":"Pseudospectral Bounds for Transient Amplification in Coupled Gradient Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04031","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":"sha256:1879776761ac1fa89a3b1abf2f643eb2fd23ad2f1ed479ba6cc83cffd193e033","target":"record","created_at":"2026-06-04T00:06:44Z","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":"dcd70935b1364ff361a6be79d1272d43724509ce521ce46b34bf1db5e72c61b2","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-01T20:42:04Z","title_canon_sha256":"4612bf6ab9e8ea69992e3bf627897086430004920dc1ccc8feab80b3f7058a9a"},"schema_version":"1.0","source":{"id":"2606.04031","kind":"arxiv","version":1}},"canonical_sha256":"6a43723880059386f0e8b9cd3fc2184ca47a9b4772a38a79f9aaf7a8c268cc7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a43723880059386f0e8b9cd3fc2184ca47a9b4772a38a79f9aaf7a8c268cc7f","first_computed_at":"2026-06-04T00:06:44.882245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T00:06:44.882245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5EaldR+/sJ5KWCt7whbe2+fUswd9M/OYQFjPlmzkXM3g43n8tPwqQdUkxh2XjxxOyKkYEGYFQ8Aq92CGa7W4Cw==","signature_status":"signed_v1","signed_at":"2026-06-04T00:06:44.882626Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.04031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1879776761ac1fa89a3b1abf2f643eb2fd23ad2f1ed479ba6cc83cffd193e033","sha256:a3ce869c6895813dcc7595ab2364f4df3841c822a4bba469b6792e0d012ff5a4"],"state_sha256":"0032615fc9803e24cb9ee27b8be643293d27bea412b4d0ba6e6d5608ee93f1d4"}