Shot midpoint ordering k50(B10) < k50(B8) ≈ k50(B9) and transition widths correlate with mismatch D(P0∥PT)

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• Shot midpoint ordering k50(B10) < k50(B8) ≈ k50(B9) tracks pretraining exposure densityclaim0.896
  Interpretation that pattern density from pretraining determines few-shot requirements
• Hypothesis: Shot midpoint ordering k50(B10) < k50(B8) ≈ k50(B9) follows pretraining exposure densityhypothesis0.895
  E2 prediction that bases with higher pretraining exposure require fewer shots to cross threshold
• The ordering of few-shot thresholds k50 and transition widths aligns with k50 ∝ dr/ρd.claim0.868
  Interpretation of E2 results.
• Shot midpoints follow k50 ∝ dr/ρd; higher cohesion and lower mismatch yield fewer required examplesclaim0.852
  Core quantitative prediction of UCCT validated by E2 threshold ordering
• k50 ordering: B10 (0.28) < B8 (1.83) < B9 (2.91) follows pretraining densityfinding0.817
  Monotone ordering consistent with k50 ∝ dr/ρd.
• Transition widths ∆k increase with mismatch D(P0 ∥ PT), evidenced by wider widths from B10 to B9claim0.794
  Interpretive claim linking phase width in E2 to mismatch term in UCCT
• Hypothesis: Peak alignment location S_max and normalized trajectory area AUS_N predict shot midpoints θ50hypothesis0.776
  E3 prediction that internal geometry provides a bridge to behavioral thresholds
• B9 phase width (k90 − k10) = 3.74 ± 0.31 shotsfinding0.772
  Widest transition in E2; consistent with lower prior density requiring more shots for reliable threshold crossing