{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IHL2WBZ6B7CXLNHU2TSKTT4WLV","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":"9d478293a89273df6517cbdd8acec19469705117e50aa9d4cbc411d8e414765b","cross_cats_sorted":["math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-24T16:42:46Z","title_canon_sha256":"37965cdecd6b705bd20e38c48387cc3c32d3a09b20b333f8d9b4db17e0779a8b"},"schema_version":"1.0","source":{"id":"2607.22474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.22474","created_at":"2026-07-27T01:21:22Z"},{"alias_kind":"arxiv_version","alias_value":"2607.22474v1","created_at":"2026-07-27T01:21:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.22474","created_at":"2026-07-27T01:21:22Z"},{"alias_kind":"pith_short_12","alias_value":"IHL2WBZ6B7CX","created_at":"2026-07-27T01:21:22Z"},{"alias_kind":"pith_short_16","alias_value":"IHL2WBZ6B7CXLNHU","created_at":"2026-07-27T01:21:22Z"},{"alias_kind":"pith_short_8","alias_value":"IHL2WBZ6","created_at":"2026-07-27T01:21:22Z"}],"graph_snapshots":[{"event_id":"sha256:d7d042c19cb8556ab589814594fa23aa2df96587d70c5ae1188bbfb58df5b50b","target":"graph","created_at":"2026-07-27T01:21:22Z","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/2607.22474/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In overparameterized linear regression, many weak spectral directions act like a ridge penalty on the signal-bearing spectrum; negative ridge is the natural correction, pushing filters above one. The stable negative-ridge endpoint, however, is structurally limited: its pole must stay below the smallest nonzero empirical eigenvalue, and it anti-shrinks smaller eigenvalues more than larger ones. Early-stopped negative-shifted gradient descent escapes this constraint. Its filter is smooth at the would-be pole and mixed-sign-capable: above-ridgeless directions form a leading prefix, with lower dir","authors_text":"Peng Zhao","cross_cats":["math.ST","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-24T16:42:46Z","title":"Beyond Negative-Ridge Endpoints: Mixed-Sign Spectral Regularization via Negative-Shifted Gradient Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22474","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":"sha256:948119fc41845474724243e01aeda17ce847059d2a3350805b95ebfe85e3e52c","target":"record","created_at":"2026-07-27T01:21:22Z","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":"9d478293a89273df6517cbdd8acec19469705117e50aa9d4cbc411d8e414765b","cross_cats_sorted":["math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-24T16:42:46Z","title_canon_sha256":"37965cdecd6b705bd20e38c48387cc3c32d3a09b20b333f8d9b4db17e0779a8b"},"schema_version":"1.0","source":{"id":"2607.22474","kind":"arxiv","version":1}},"canonical_sha256":"41d7ab073e0fc575b4f4d4e4a9cf965d5dad9daa6f4d66c323a16fb99937106b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41d7ab073e0fc575b4f4d4e4a9cf965d5dad9daa6f4d66c323a16fb99937106b","first_computed_at":"2026-07-27T01:21:22.917817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-27T01:21:22.917817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bwGWhP5PwSg9H/LaVqe9hq8Rev98/JYKecDq8ZNskndOqa5vHNRls3m8HtX/pCYFi1eqgoaXD/sq0UJ2ThgjBw==","signature_status":"signed_v1","signed_at":"2026-07-27T01:21:22.918707Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.22474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:948119fc41845474724243e01aeda17ce847059d2a3350805b95ebfe85e3e52c","sha256:d7d042c19cb8556ab589814594fa23aa2df96587d70c5ae1188bbfb58df5b50b"],"state_sha256":"ea298322739e852fd7169db52d4d03651ce8a7b4510bd96321e58cb2b31ffadb"}