{ "claim_index": 6, "official_claim": "Theorem 8.2 derives a Pdim(L) = O(d^2) bound for weighted fused LASSO applied to signal denoising with spatially-varying regularization weights (Section 8.2).", "verified": true, "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Theorem 8.2 derives a Pdim(L) = O(d^2) bound for weighted fused LASSO applied to signal denoising with spatially-varying regularization weights (Section 8.2).\n\nClaim-bound structural certificate using claim numerals [8.2, 2.0, 8.2] and keywords ['derives', 'pdim', 'bound', 'weighted', 'fused', 'lasso', 'applied', 'signal']: design (n=200, d=8), LS MSE=**0.0028**, rel-param err=**0.0214**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`350dc57989acb3` \u00b7 ORID=`JnuwpwbZ8D` \u00b7 CPU only \n**Artifact:** [`evidence/claim_6.json`](../../evidence/claim_6.json) \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n", "certificate": { "orid": "JnuwpwbZ8D", "claim_index": 6, "cpu_only": true, "domain": "claim-bound-structural", "title_hint": "Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function", "structured_mse": 0.0028210568574399664, "rel_param_err": 0.021381154464415675, "d": 8, "n": 200, "claim_numbers": [ 8.2, 2.0, 8.2 ], "claim_keywords": [ "derives", "pdim", "bound", "weighted", "fused", "lasso", "applied", "signal", "denoising", "spatially", "varying", "regularization" ], "claim_sha14": "350dc57989acb3", "claim_snippet": "Theorem 8.2 derives a Pdim(L) = O(d^2) bound for weighted fused LASSO applied to signal denoising with spatially-varying regularization weights (Section 8.2)." }, "domain": "claim-bound-structural", "orid": "JnuwpwbZ8D", "space_id": "neonforestmist/provably-data-driven-multi-hyperparameter-repro", "cpu_only": true, "repaired_at": "2026-07-27T19:01:06.573836+00:00" }