{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:USOETTIV2CRT7R7D5S6DWTZLVM","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":"1c568a35b56287f1f6999c100485a7a05af5b6874fc315598ffb8a37a73cbe0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-09T20:33:01Z","title_canon_sha256":"0bc26ade4cc634feb5f32f370d05033ac8c22a80967e6e493e4174b7f060e453"},"schema_version":"1.0","source":{"id":"2606.11431","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.11431","created_at":"2026-06-11T01:09:48Z"},{"alias_kind":"arxiv_version","alias_value":"2606.11431v1","created_at":"2026-06-11T01:09:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11431","created_at":"2026-06-11T01:09:48Z"},{"alias_kind":"pith_short_12","alias_value":"USOETTIV2CRT","created_at":"2026-06-11T01:09:48Z"},{"alias_kind":"pith_short_16","alias_value":"USOETTIV2CRT7R7D","created_at":"2026-06-11T01:09:48Z"},{"alias_kind":"pith_short_8","alias_value":"USOETTIV","created_at":"2026-06-11T01:09:48Z"}],"graph_snapshots":[{"event_id":"sha256:4e2427b42eb73aacf1ba4499d74e907105eb7d7de2ab1d453a8d27e3014db2d6","target":"graph","created_at":"2026-06-11T01:09:48Z","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/2606.11431/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mirror Descent (MD) extends Gradient Descent (GD) beyond Euclidean geometry and has recently reappeared as a lens for KL-regularized policy optimization in reinforcement learning and LLM post-training. This raises a basic robustness question, crucial to reproducibility and reliability: how sensitive are MD dynamics to their inputs? We focus on initialization, often itself a pretrained or previously aligned model. Quadratic-regularized MD, including GD and Mahalanobis geometries, is well-known to be stable for convex smooth objectives. We show a sharp contrast: once the regularizer is non-quadr","authors_text":"Matan Schliserman, Ofir Schlisselberg, Shira Vansover-Hager, Tomer Koren","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-09T20:33:01Z","title":"Mirror Descent Beyond Euclidean Stability: An Exponential Separation in Initialization Sensitivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11431","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:f52a54c4db01f581e4206493ea4f71dda47de2eda36472ac1350de66726bbd6f","target":"record","created_at":"2026-06-11T01:09:48Z","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":"1c568a35b56287f1f6999c100485a7a05af5b6874fc315598ffb8a37a73cbe0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-09T20:33:01Z","title_canon_sha256":"0bc26ade4cc634feb5f32f370d05033ac8c22a80967e6e493e4174b7f060e453"},"schema_version":"1.0","source":{"id":"2606.11431","kind":"arxiv","version":1}},"canonical_sha256":"a49c49cd15d0a33fc7e3ecbc3b4f2bab3d11e32310b065e1000b69630a7df9e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a49c49cd15d0a33fc7e3ecbc3b4f2bab3d11e32310b065e1000b69630a7df9e1","first_computed_at":"2026-06-11T01:09:48.270920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:09:48.270920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u+KU272VWbbsn71aViy+sFD5hocO6UMVteqF9U2xO1qFwgSFU64aD8I7TkUZVCmMlIVulVivqSrXpkCQJh0hAA==","signature_status":"signed_v1","signed_at":"2026-06-11T01:09:48.271921Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.11431","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f52a54c4db01f581e4206493ea4f71dda47de2eda36472ac1350de66726bbd6f","sha256:4e2427b42eb73aacf1ba4499d74e907105eb7d7de2ab1d453a8d27e3014db2d6"],"state_sha256":"25ffb34ffd5f1d45ee0900c728fbb7253f72a12f9bf4d3886c9f754e4447ab43"}