{
 "analysis": "A3 basin-approach dynamics",
 "date": "2026-08-08",
 "plan": "history/plans/2026-08-08_analysis_phase.md A3",
 "method": {
  "data": "VAL scalars val/cos_to_target and val/erank from hub tensorboard event files (multi-file runs merged by step, later file wins on duplicates)",
  "model": "y(t) = y_inf - (y_inf - y0) * exp(-(t - t_first)/tau), scipy curve_fit; fit_full = all points (first val at step 1000); fit_late_ge2000 = steps >= 2000 (past warmup)",
  "model_free": "t50/t90/t95 = first step crossing y0 + frac*(final5mean - y0), linear interp; robust to the fit instability below",
  "note": "single exponential systematically under-models every curve: observed t90/t50 = 5.27-7.66 across all 8 trunks vs 3.32 for a pure exponential. The approach is two-timescale (fast half-depth lock by ~2-3.4k steps, heavy consolidation tail). Late-phase fits reach R2 >= .95 for 11/16 curves; a2_dense-s0 is unfittable (R2 .5452 full / .4374 late) despite a smooth monotone curve - model misfit, not noise. Cross-run comparisons therefore use the model-free crossings."
 },
 "runs": {
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     "final_value": 0.8393,
     "fit_full": {
      "y_inf": 0.8353,
      "y0": 0.7164,
      "tau_steps": 5998.0,
      "r2": 0.9404,
      "t_offset": 1000.0,
      "n_points": 62
     },
     "fit_late_ge2000": {
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      "y0": 0.7562,
      "tau_steps": 9037.0,
      "r2": 0.9672,
      "t_offset": 2000.0,
      "n_points": 61
     },
     "crossings_model_free": {
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      "t90_steps": 18940.0,
      "t95_steps": 27690.0,
      "t90_over_t50": 5.853
     },
     "fit_quality": "late_ok"
    },
    "val/erank": {
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     "step_range": [
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      62000.0
     ],
     "y_at_step1000": 52.78,
     "final_value": 98.59,
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      "y0": 61.8,
      "tau_steps": 6249.0,
      "r2": 0.9305,
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      "n_points": 62
     },
     "fit_late_ge2000": {
      "y_inf": 98.18,
      "y0": 73.88,
      "tau_steps": 9795.0,
      "r2": 0.959,
      "t_offset": 2000.0,
      "n_points": 61
     },
     "crossings_model_free": {
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      "t90_steps": 19620.0,
      "t95_steps": 31030.0,
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     },
     "fit_quality": "late_ok"
    }
   }
  },
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   }
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     "fit_quality": "poor_single_exp"
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   "seed": "-",
   "source_repo": "AbstractPhil/captionbert-8192-v2",
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     "fit_late_ge2000": {
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     "crossings_model_free": {
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     "y_at_step1000": 51.52,
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     "fit_quality": "late_ok"
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  },
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   "seed": "-",
   "source_repo": "AbstractPhil/captionbert-8192-v2-B",
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      "tau_steps": 3759.0,
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     "fit_late_ge2000": {
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     },
     "crossings_model_free": {
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    "val/erank": {
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     "y_at_step1000": 50.99,
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      "r2": 0.9149,
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      "n_points": 62
     },
     "fit_late_ge2000": {
      "y_inf": 102.6,
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      "r2": 0.9653,
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      "n_points": 61
     },
     "crossings_model_free": {
      "t50_steps": 2234.0,
      "t90_steps": 17120.0,
      "t95_steps": 24550.0,
      "t90_over_t50": 7.666
     },
     "fit_quality": "late_ok"
    }
   }
  }
 },
 "verdict": {
  "same_attractor": "yes - endpoint band cos .8390-.8420, erank 98.56-99.21 (E1 six) with captionbert trunks landing the high-erank corner 102.9/103.2",
  "same_path_shape": "yes - all 8 trunks share the two-timescale approach (t90/t50 5.27-7.66, all far above the 3.32 of a single exponential); no trunk takes a qualitatively different route",
  "anchored_vs_dense": "REVERSED vs small-bed expectation: dense reaches 90% basin depth FASTER. t90(cos) a2_dense 14785/14770 (seeds s0/s1) vs a1_anchored 18936/17870 and a3_random 17717/18811. Same ordering on erank (a2 18186/16990 vs a1 19616/18580, a3 19224/19763). The small-bed anchored sample-efficiency advantage (.9055 vs .7790 @2ep) is a CAPABILITY-gauge fact; on the TRAINING gauge at full scale, routing costs ~3-4k steps of basin depth. Consistent with A2: routed function accrues LATE - the router is still organizing while dense is already settling",
  "learned_vs_frozen_anchors": "indistinguishable paths: a1 seed-mean t90(cos) 18403 vs a3 18264 (0.8% apart); anchor learnability does not change basin approach",
  "seed_consistency": "high, arm-dominated: t90(cos) seed spread a2 0.1%, a1 5.8%, a3 6.0%; every arm's two seeds are closer to each other than to any other arm",
  "captionbert_trunks": "fastest approach of all 8 (t90 cos 11952/13894) and higher erank asymptote (final 102.9/103.2) - the 5-teacher consensus bed both accelerates the approach and lands a wider basin corner",
  "tau_table_late_fit_cos": {
   "a1_anchored-s0": 9037,
   "a1_anchored-s1": 8341,
   "a2_dense-s0": "unreliable (R2 .44)",
   "a2_dense-s1": 8243,
   "a3_random-s0": 7833,
   "a3_random-s1": 7860,
   "captionbert-v2": 6332,
   "captionbert-v2-B": 7982
  },
  "tau_table_late_fit_erank": {
   "a1_anchored-s0": 9795,
   "a1_anchored-s1": 8896,
   "a2_dense-s0": "unreliable (R2 .54)",
   "a2_dense-s1": 10030,
   "a3_random-s0": 9206,
   "a3_random-s1": 8970,
   "captionbert-v2": 7132,
   "captionbert-v2-B": 8482
  }
 }
}