{
  "arxiv_revision": "2605.17126v1",
  "counts": {
    "balancedness_examples.csv": 3,
    "glm_favorable_transfer.csv": 8,
    "glm_grid.csv": 45,
    "infinite_B_controls.csv": 256,
    "intrinsic_fallback.csv": 600,
    "linear_safety.csv": 216,
    "literal_claim_evidence.csv": 6,
    "objective_structures.csv": 4,
    "optimization_diagnostics.csv": 373,
    "outlier_radius_sweep.csv": 6,
    "population_comparability.csv": 1200,
    "source_pins.csv": 4,
    "spectrum_collapse.csv": 6,
    "transfer_delta_scaling.csv": 10,
    "transfer_epsilon_scaling.csv": 6,
    "transfer_m_scaling.csv": 6
  },
  "gates": {
    "arbitrary_outlier_control": true,
    "balancedness_without_rho": true,
    "delta_squared_law": true,
    "epsilon_squared_law": true,
    "glm_direct": true,
    "glm_mvt_exact": true,
    "glm_transfer_direct": true,
    "infinite_B_control": true,
    "intrinsic_fallback_direct": true,
    "joint_convexity": true,
    "linear_safety_direct": true,
    "nu_destructive_control": true,
    "nuisance_blind": true,
    "objective_prediction_space": true,
    "one_over_m_law": true,
    "optimizer_objectives_decrease": true,
    "population_comparability_direct": true,
    "registered_algorithm_executed": true,
    "six_registered_claims_exact": true,
    "source_assets_exact": true
  },
  "paper_id": "D5Ijcnz1L9",
  "registered_claims": [
    "Theorem 2 establishes an in-sample MSE bound for each task j that guarantees safety, \u2130\u2c7c\u2071\u207f(\u03b8\u0302\u2c7c) \u2272 q\u00b2(d/n)\u03b6 regardless of the balancedness constant B, outlier fraction \u03b5, or heterogeneity \u03b4 (Section 5.1, Theorem 2).",
    "Theorem 2 also shows a transfer guarantee for inlier tasks when B \u2272 min(1/\u03b5, m): \u2130\u2c7c\u2071\u207f(\u03b8\u0302\u2c7c) \u2272 (Bd/mn + min(B\u03b4\u00b2, d/n) + B\u00b2\u03b5\u00b2d/n)\u03b6, achieved without knowing \u03b5, \u03b4, or the inlier set S (Section 5.1, Theorem 2).",
    "Assumption 1 (Balancedness) replaces the classical Lower Boundedness of Second Moments condition \u03c1I \u2aaf \u03a3\u2c7c with the one-sided condition \u03a3\u2c7c \u2aaf B\u00b7\u03a3_S, accommodating rank-deficient or decaying covariate spectra where prior eigenvalue-lower-bound approaches (e.g. Duan & Wang 2023, depending on 1/\u03c1\u00b2) fail (Section 4, Assumption 1).",
    "Theorem 3 extends the in-sample MSE guarantees of Theorem 2 to population risk via an empirical-to-population comparability constant \u03bd\u2c7c, retaining an intrinsic-dimension fallback for the safety guarantee (Section 5.2, Theorem 3).",
    "Theorem 4 extends the same adaptive safety/transfer MSE guarantees to generalized linear models under bounded-domain assumptions (Section 6, Theorem 4).",
    "Algorithm 1 solves a joint convex objective \u2112(\u0398)=\u03a3\u2c7c w\u2c7c(f\u2c7c(\u03b8\u2c7c)+\u03bb\u2c7c\u2016\u03b8\u2c7c-\u03b2\u2016_{\u03a3\u2c7c}) that penalizes disagreement in prediction space (via task-specific norms) rather than raw parameter space (Section 3, Algorithm 1)."
  ],
  "scope": "Direct finite Algorithm 1 experiments at the paper's native synthetic dimensions plus exact algebra; no finite run is presented as a universal proof.",
  "summary": {
    "convexity_violations": 0,
    "degenerate_balancedness_pairs": 14197,
    "delta_squared_r2": 1.0,
    "delta_squared_slope": 1.9999999999999996,
    "epsilon_squared_r2": 0.9992608122163799,
    "epsilon_squared_slope": 2.1474761241097524,
    "glm_configs": 45,
    "intrinsic_fallback_pairs": 600,
    "intrinsic_fallback_violations": 0,
    "large_delta_mse": 3.1603965096785505,
    "large_delta_over_safety_scale": 1.0611905374630106,
    "linear_safety_configs": 216,
    "linear_tasks_evaluated": 6480,
    "m_scaling_r2": 0.9983439676342425,
    "m_scaling_slope": -1.0086816250389234,
    "max_balancedness_closed_form_error": 0.0,
    "max_glm_mvt_ratio": 0.06192957643612639,
    "max_glm_safety_ratio": 1.6494871421278146,
    "max_linear_safety_ratio": 1.409812905125891,
    "max_prediction_norm_identity_error": 1.1546319456101628e-14,
    "median_glm_itl_over_mtlr": 17.234969116944626,
    "naive_nu_one_failures": 1119,
    "nullspace_checks": 3500,
    "pooling_ratio_at_radius_100000": 3672340790.1570725,
    "population_comparability_violations": 0,
    "population_pairs": 1200
  }
}