{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JDWNFNBLVDM5APYWYS27DDDNFK","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":"d102fdc2afe329a19f5db292308a2592d137a35fa82f2ca7bb6219bc9a5a521c","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-09T03:48:27Z","title_canon_sha256":"1b91c15589be9dbb3cd268fa34ae5f375c8df3f92a1dcd63a177ebaa00e80b6d"},"schema_version":"1.0","source":{"id":"2606.10383","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.10383","created_at":"2026-06-10T01:10:15Z"},{"alias_kind":"arxiv_version","alias_value":"2606.10383v1","created_at":"2026-06-10T01:10:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10383","created_at":"2026-06-10T01:10:15Z"},{"alias_kind":"pith_short_12","alias_value":"JDWNFNBLVDM5","created_at":"2026-06-10T01:10:15Z"},{"alias_kind":"pith_short_16","alias_value":"JDWNFNBLVDM5APYW","created_at":"2026-06-10T01:10:15Z"},{"alias_kind":"pith_short_8","alias_value":"JDWNFNBL","created_at":"2026-06-10T01:10:15Z"}],"graph_snapshots":[{"event_id":"sha256:0f25043605e6b122c5011168229039bca5a461aeadb56364f7ac887294e07ef1","target":"graph","created_at":"2026-06-10T01:10:15Z","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/2606.10383/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study non-separable objectives in which the loss depend on dataset-level quantities. We introduce an SGD-style framework that employs two batch-gradient constructs: the ideal per-batch gradient `$G$' and a cached surrogate `$H$' for cases where full-data terms are expensive.\n  Notably, in the sample-wise separable case, our method reduces to standard mini-batch SGD. Our main contribution is a unified local convergence theory: under mild smoothness and Jacobian-boundedness assumptions,\n  we prove local linear convergence under local strong convexity and local $O(1/k)$ sublinear convergence u","authors_text":"Ruofan Wu, Yingzhou Li","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-09T03:48:27Z","title":"A stochastic gradient algorithm for non-separable optimization with convergence guarantee"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10383","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":"sha256:8890678ee1a7262bd42b43bc9162cc4a5b0716285db78c3aa7ef7c9cb761ba26","target":"record","created_at":"2026-06-10T01:10:15Z","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":"d102fdc2afe329a19f5db292308a2592d137a35fa82f2ca7bb6219bc9a5a521c","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-09T03:48:27Z","title_canon_sha256":"1b91c15589be9dbb3cd268fa34ae5f375c8df3f92a1dcd63a177ebaa00e80b6d"},"schema_version":"1.0","source":{"id":"2606.10383","kind":"arxiv","version":1}},"canonical_sha256":"48ecd2b42ba8d9d03f16c4b5f18c6d2aa2eedb61e3d9c47df9fc2c910d8aedd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48ecd2b42ba8d9d03f16c4b5f18c6d2aa2eedb61e3d9c47df9fc2c910d8aedd9","first_computed_at":"2026-06-10T01:10:15.140845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:10:15.140845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Arwb1f0LImZrOKcrXG1GUTQzANtITGU7Eskv+TKt+MmmJ9woaMJd6k/5DTPHO5e/waF4mXCN7FLswgwVNNUGBQ==","signature_status":"signed_v1","signed_at":"2026-06-10T01:10:15.141666Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.10383","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8890678ee1a7262bd42b43bc9162cc4a5b0716285db78c3aa7ef7c9cb761ba26","sha256:0f25043605e6b122c5011168229039bca5a461aeadb56364f7ac887294e07ef1"],"state_sha256":"3176291154603c61bbe81daa0ea8b1d9df6cd05c6bd1326215e1d5bea9b1ba2a"}