{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SCPXQNZDIYK4OUPKFWSRB6ZCEH","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":"0b8e60ffff7be021e08fdb30197104a6468b9a4cb8e5e3ba99edcadb6c9b4963","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-17T23:20:50Z","title_canon_sha256":"c94c17483410ed45c17de441485cdaea5d93ec8d10e9e4577231d5c1dcaf5785"},"schema_version":"1.0","source":{"id":"2605.17692","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17692","created_at":"2026-05-20T00:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17692v1","created_at":"2026-05-20T00:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17692","created_at":"2026-05-20T00:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"SCPXQNZDIYK4","created_at":"2026-05-20T00:04:53Z"},{"alias_kind":"pith_short_16","alias_value":"SCPXQNZDIYK4OUPK","created_at":"2026-05-20T00:04:53Z"},{"alias_kind":"pith_short_8","alias_value":"SCPXQNZD","created_at":"2026-05-20T00:04:53Z"}],"graph_snapshots":[{"event_id":"sha256:9263f7e1461119fa39f0bc3fdacec83ea87243ea1f4b9a7524ac65cce3e0f569","target":"graph","created_at":"2026-05-20T00:04:53Z","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":[{"findings_count":0,"name":"cited_work_retraction","ran_at":"2026-05-19T21:51:57.526512Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"shingle_duplication","ran_at":"2026-05-19T21:49:43.948874Z","status":"skipped","version":"0.1.0"},{"findings_count":0,"name":"citation_quote_validity","ran_at":"2026-05-19T21:49:43.747761Z","status":"skipped","version":"0.1.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.520955Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T21:21:57.430894Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.17692/integrity.json","findings":[],"snapshot_sha256":"43f472827ed5c93d4e3d2263b9da1ef5c859337d9d7c4552a7b6b597c1d6de73","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the training problem of a deep linear neural network under the squared loss admits an exact convex reformulation in a lifted space over a generalized completely positive cone. The reformulation has the same optimal value as the original nonconvex problem and is linear in the lifted variables, with all nonconvexity encoded in the cone constraint. Its ambient lifted dimension depends only on the input and output dimensions, independent of the network depth and the number of data points, and the bottleneck width enters only through scalar constraints. The construction proceeds by red","authors_text":"Alp Yurtsever, Karthik Prakhya","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-17T23:20:50Z","title":"Exact Convex Reformulations of Linear Neural Networks via Completely Positive Lifting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17692","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":"sha256:6398de7eb28dbcb3a787c8967e819781768a7fcdd22ec1ca9ed3ee34d25899a1","target":"record","created_at":"2026-05-20T00:04:53Z","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":"0b8e60ffff7be021e08fdb30197104a6468b9a4cb8e5e3ba99edcadb6c9b4963","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-17T23:20:50Z","title_canon_sha256":"c94c17483410ed45c17de441485cdaea5d93ec8d10e9e4577231d5c1dcaf5785"},"schema_version":"1.0","source":{"id":"2605.17692","kind":"arxiv","version":1}},"canonical_sha256":"909f7837234615c751ea2da510fb2221cdbe0f79fc9c8effbf228216e28c56c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"909f7837234615c751ea2da510fb2221cdbe0f79fc9c8effbf228216e28c56c5","first_computed_at":"2026-05-20T00:04:53.066795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:04:53.066795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EQyQcZ36Qp8PekKxrtfNWqoSbcgluA0H3DHWSusfXUrP/vvO+kCdBuMbttg+277J5RNOxHvlIPbFcR7aMmA3Ag==","signature_status":"signed_v1","signed_at":"2026-05-20T00:04:53.067666Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17692","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6398de7eb28dbcb3a787c8967e819781768a7fcdd22ec1ca9ed3ee34d25899a1","sha256:9263f7e1461119fa39f0bc3fdacec83ea87243ea1f4b9a7524ac65cce3e0f569"],"state_sha256":"7b5f87caa690767767eaf8b4622e9ad2151e9ca40ede7246374ebbb397df1b7b"}