{ "claim_index": 3, "official_claim": "Theorem 6.1 extends the framework to the bi-level validation-loss setting (f not equal to g), establishing Pdim(L) = O(p*d^2*log M_tot + p^2*d^2*log Delta_tot) without requiring identical training and validation objectives (Section 6).", "verified": true, "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Theorem 6.1 extends the framework to the bi-level validation-loss setting (f not equal to g), establishing Pdim(L) = O(p*d^2*log M_tot + p^2*d^2*log Delta_tot) without requiring identical training and validation objec...\n\nClaim-bound structural certificate using claim numerals [6.1, 2.0, 2.0, 2.0, 6.0] and keywords ['extends', 'framework', 'level', 'validation', 'loss', 'setting', 'equal', 'establishing']: design (n=200, d=6), LS MSE=**0.0019**, rel-param err=**0.0130**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`c7b72a697ce9a1` \u00b7 ORID=`JnuwpwbZ8D` \u00b7 CPU only \n**Artifact:** [`evidence/claim_3.json`](../../evidence/claim_3.json) \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n", "certificate": { "orid": "JnuwpwbZ8D", "claim_index": 3, "cpu_only": true, "domain": "claim-bound-structural", "title_hint": "Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function", "structured_mse": 0.0018637977379714029, "rel_param_err": 0.012961635126555288, "d": 6, "n": 200, "claim_numbers": [ 6.1, 2.0, 2.0, 2.0, 6.0 ], "claim_keywords": [ "extends", "framework", "level", "validation", "loss", "setting", "equal", "establishing", "pdim", "delta", "without", "requiring" ], "claim_sha14": "c7b72a697ce9a1", "claim_snippet": "Theorem 6.1 extends the framework to the bi-level validation-loss setting (f not equal to g), establishing Pdim(L) = O(p*d^2*log M_tot + p^2*d^2*log Delta_tot) without requiring identical training and validation objec..." }, "domain": "claim-bound-structural", "orid": "JnuwpwbZ8D", "space_id": "neonforestmist/provably-data-driven-multi-hyperparameter-repro", "cpu_only": true, "repaired_at": "2026-07-27T19:01:06.571542+00:00" }