{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TCMVQURWR75MBB4N4YNU3GDYWW","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":"ff18176a15ad341aa70395e7bf2bc22a6537b705ad7ca27cb4dfa391307c7a97","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-13T14:45:07Z","title_canon_sha256":"cf7bc9bbe3e5ae0226cea5f2c4dc9e6a9af6c5197cfc8dd655bbefe43a512df4"},"schema_version":"1.0","source":{"id":"2607.11626","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.11626","created_at":"2026-07-14T02:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"2607.11626v1","created_at":"2026-07-14T02:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.11626","created_at":"2026-07-14T02:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"TCMVQURWR75M","created_at":"2026-07-14T02:22:15Z"},{"alias_kind":"pith_short_16","alias_value":"TCMVQURWR75MBB4N","created_at":"2026-07-14T02:22:15Z"},{"alias_kind":"pith_short_8","alias_value":"TCMVQURW","created_at":"2026-07-14T02:22:15Z"}],"graph_snapshots":[{"event_id":"sha256:47650e6e4dbec1a2c38bc3ae1426bd0873adb2208cd49e2fe32376665470bff8","target":"graph","created_at":"2026-07-14T02:22:15Z","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/2607.11626/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the policy convergence of unregularized policy mirror descent (PMD) with arbitrary constant step sizes for finite discounted Markov decision processes. We focus on decomposable mirror maps of the form $h(p)=\\sum_a \\psi(p(a))$, where $\\psi$ satisfies standard Legendre-type assumptions. Under these conditions, we prove that the policy sequence generated by PMD converges in the policy domain to a limiting optimal policy, even when the optimal policy set is not a singleton. This result covers a broad class of commonly used mirror maps, including the squared Euclidean mirror map underlying","authors_text":"Ke Wei, Wenye Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-13T14:45:07Z","title":"On the Policy Convergence of Policy Mirror Descent Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11626","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":"sha256:49d051397d2dec424615b2ce5ac86c8b10335b605b91d03cf5c62d04d81f88de","target":"record","created_at":"2026-07-14T02:22:15Z","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":"ff18176a15ad341aa70395e7bf2bc22a6537b705ad7ca27cb4dfa391307c7a97","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-13T14:45:07Z","title_canon_sha256":"cf7bc9bbe3e5ae0226cea5f2c4dc9e6a9af6c5197cfc8dd655bbefe43a512df4"},"schema_version":"1.0","source":{"id":"2607.11626","kind":"arxiv","version":1}},"canonical_sha256":"98995852368ffac0878de61b4d9878b5a8288139812a8b3432f0d29f614505c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98995852368ffac0878de61b4d9878b5a8288139812a8b3432f0d29f614505c9","first_computed_at":"2026-07-14T02:22:15.591859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T02:22:15.591859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"795Rc//qnKcNjsumY7N/KDtjOXkVHaETDKsfN1N3OBsN4jpXYHZrrrPXbX9NFkZMxgFtSlVHG5nKCBUkLRObCA==","signature_status":"signed_v1","signed_at":"2026-07-14T02:22:15.592994Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.11626","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49d051397d2dec424615b2ce5ac86c8b10335b605b91d03cf5c62d04d81f88de","sha256:47650e6e4dbec1a2c38bc3ae1426bd0873adb2208cd49e2fe32376665470bff8"],"state_sha256":"af7d30ffa58891eb0cfe8d71aec2ecf531000ec73621dc38dd9af99841a8486f"}