{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BC3WI272Q55HV5MSSQMPLBKHDC","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":"1ff0afa817baa176c0d74c03ee85fb0455bf120179c152860f1dd93222faa5f9","cross_cats_sorted":["cs.LG","cs.SY","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2026-05-26T07:24:14Z","title_canon_sha256":"2e794264a850abc1e48279a2003998dcfacb4070527875618c7471c5a4dda383"},"schema_version":"1.0","source":{"id":"2605.26640","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26640","created_at":"2026-05-27T01:06:03Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26640v1","created_at":"2026-05-27T01:06:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26640","created_at":"2026-05-27T01:06:03Z"},{"alias_kind":"pith_short_12","alias_value":"BC3WI272Q55H","created_at":"2026-05-27T01:06:03Z"},{"alias_kind":"pith_short_16","alias_value":"BC3WI272Q55HV5MS","created_at":"2026-05-27T01:06:03Z"},{"alias_kind":"pith_short_8","alias_value":"BC3WI272","created_at":"2026-05-27T01:06:03Z"}],"graph_snapshots":[{"event_id":"sha256:b3a5ba6e81da4ecdf73d9dfeeedcc3680107a63ca714dee3f7045430c747f995","target":"graph","created_at":"2026-05-27T01:06:03Z","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/2605.26640/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the sample complexity of policy gradient for log-growth control -- the problem of learning, from observed state transitions, a feedback gain that optimally stabilizes a scalar linear system driven through a multiplicative-noise actuation channel. The objective $J(K) = \\mathbb{E}[\\log|1+BK|]$ is the top Lyapunov exponent of the closed loop. This problem carries a structural difficulty we call the cusp obstruction: the optimal gain $K^*$ always places the noise singularity $b_{\\rm sing}(K) = -1/K$ in the interior of the support. At this singular optimum the policy gradient exists only a","authors_text":"Cailian Chen, Liwei Zhang, Qiuhua Pan, Xinping Guan, Yukai Shen","cross_cats":["cs.LG","cs.SY","math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2026-05-26T07:24:14Z","title":"Sample Complexity of Policy Gradient for Log-Growth Control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26640","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:f02ffc817cc288d155ab241ff7cda9ddb1b92becd7a8c01af7d62e7d7b1519f7","target":"record","created_at":"2026-05-27T01:06:03Z","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":"1ff0afa817baa176c0d74c03ee85fb0455bf120179c152860f1dd93222faa5f9","cross_cats_sorted":["cs.LG","cs.SY","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2026-05-26T07:24:14Z","title_canon_sha256":"2e794264a850abc1e48279a2003998dcfacb4070527875618c7471c5a4dda383"},"schema_version":"1.0","source":{"id":"2605.26640","kind":"arxiv","version":1}},"canonical_sha256":"08b7646bfa877a7af5929418f58547189bf71622ca051908a3ecf5dcf5d511dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08b7646bfa877a7af5929418f58547189bf71622ca051908a3ecf5dcf5d511dc","first_computed_at":"2026-05-27T01:06:03.563057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T01:06:03.563057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1RaS8Pcp0mgU9H4CgPzr6T2ay8m46psh7Nkq3gMgTHoi5em/uPVnLHKpBUzMj3Vsbs4E7EqjxYkFLNH26wCmAA==","signature_status":"signed_v1","signed_at":"2026-05-27T01:06:03.563851Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.26640","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f02ffc817cc288d155ab241ff7cda9ddb1b92becd7a8c01af7d62e7d7b1519f7","sha256:b3a5ba6e81da4ecdf73d9dfeeedcc3680107a63ca714dee3f7045430c747f995"],"state_sha256":"ec1fa91a9554946b1f53481a2f47c0e34cdb565038703f2c5c60a58a107077dd"}