{
  "_about": "Seed + learning-rate sensitivity extension (Qwen3-4B-Instruct-2507, attention-only LoRA r32 a64). Two seeds {42,123} x three peak LRs {5e-7,5e-6,5e-5} per method. Cosine is of the gauge-invariant stacked LoRA delta dW=(alpha/r)BA over 144 modules. 'u1'/'v1' = top-1 left/right singular direction. GRPO rows at lr5e-6/5e-5 pending full training.",
  "frobenius_norm": {
    "sft": {
      "5e-7": 1.016,
      "5e-6": 2.86,
      "5e-5": 9.21
    },
    "rft": {
      "5e-7": 1.029,
      "5e-6": 2.87,
      "5e-5": 9.39
    },
    "grpo": {
      "5e-7": 0.029
    }
  },
  "within_config_seed_cosine": {
    "_note": "same method+lr, seed42 vs seed123; full vec-cosine, top-1 output dir u1, top-1 input dir v1, median top-8 principal angle (deg)",
    "sft": {
      "5e-7": {
        "cos": 0.066,
        "top1_u": 0.988,
        "top1_v": 0.074,
        "med_top8_angle_deg": 26.6
      },
      "5e-6": {
        "cos": 0.302,
        "top1_u": 0.973,
        "top1_v": 0.263,
        "med_top8_angle_deg": 32.7
      },
      "5e-5": {
        "cos": 0.36,
        "top1_u": 0.901,
        "top1_v": 0.403,
        "med_top8_angle_deg": 44.4
      }
    },
    "rft": {
      "5e-7": {
        "cos": 0.066,
        "top1_u": 0.988,
        "top1_v": 0.074,
        "med_top8_angle_deg": 26.5
      },
      "5e-6": {
        "cos": 0.3,
        "top1_u": 0.975,
        "top1_v": 0.26,
        "med_top8_angle_deg": 32.6
      },
      "5e-5": {
        "cos": 0.356,
        "top1_u": 0.9,
        "top1_v": 0.415,
        "med_top8_angle_deg": 44.6
      }
    },
    "grpo": {
      "5e-7": {
        "cos": 0.001,
        "top1_u": 0.062,
        "top1_v": 0.015,
        "med_top8_angle_deg": 82.4,
        "_caveat": "dW norm 0.03 -> noise, not real orthogonality"
      }
    }
  },
  "cross_method_cosine_matched_lr_seed": {
    "_note": "same lr+seed, mean over seeds; contrast for the within-seed comparison",
    "sft__rft": {
      "5e-7": 0.996,
      "5e-6": 0.978,
      "5e-5": 0.836
    },
    "sft__grpo": {
      "5e-7": 0.022
    },
    "rft__grpo": {
      "5e-7": 0.021
    }
  },
  "cross_method_same_seed42_subspace": {
    "sft__rft": {
      "5e-7": {
        "cos": 0.996,
        "top1_u": 0.999,
        "top1_v": 1.0,
        "med_top8_angle_deg": 3.7
      },
      "5e-6": {
        "cos": 0.976,
        "top1_u": 0.985,
        "top1_v": 0.999,
        "med_top8_angle_deg": 11.9
      },
      "5e-5": {
        "cos": 0.831,
        "top1_u": 0.903,
        "top1_v": 0.947,
        "med_top8_angle_deg": 26.7
      }
    }
  },
  "lr_sensitivity_fixed_seed42": {
    "_note": "fixed method+seed, vary lr; norm_ratio vs lr_ratio tests 'rescale vs rotate'. norm/lr ~1 would mean pure rescale.",
    "sft": {
      "5e-7_to_5e-6": {
        "cos": 0.544,
        "norm_ratio": 2.79,
        "lr_ratio": 10,
        "norm_over_lr": 0.28
      },
      "5e-6_to_5e-5": {
        "cos": 0.557,
        "norm_ratio": 3.23,
        "lr_ratio": 10,
        "norm_over_lr": 0.32
      }
    }
  },
  "random_baseline": {
    "sft5e-5_s42__rft5e-7_s123": {
      "cos": 0.027,
      "top1_u": 0.273,
      "med_top8_angle_deg": 75.6
    }
  },
  "seed_lmc_sft_lr5e-6": {
    "_note": "masked-answer CE on GSM8K, alpha*s42+(1-a)*s123, n=24",
    "curve": {
      "0.0": 3.1878,
      "0.25": 3.1773,
      "0.5": 3.1646,
      "0.75": 3.1499,
      "1.0": 3.1333
    },
    "midpoint_barrier": 0.0041,
    "verdict": "no barrier -> same basin"
  }
}