Logistic Fit for Shot Transitions

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• Logistic surrogate fittingmethod0.778
  Fitting a logistic function to success probability as a function of S or shot count to estimate midpoints and widths.
• The logistic surrogate is a phenomenological fit, not a mechanistic derivationclaim0.753
  Caveat about the threshold analysis
• The logistic fit for threshold behavior is a phenomenological surrogate for interpretability, not a mechanistic derivationclaim0.727
  Authors' explicit epistemic limitation on the threshold model
• logistic surrogate modelmethod0.727
  Sigmoid fit linking S to success probability.
• Logistic success surrogateconcept0.704
  Phenomenological fit P(success)=σ(αS+β) used to summarize sharpness and midpoints.
• Shot midpoints follow k50 ∝ dr/ρd; higher cohesion and lower mismatch yield fewer required examplesclaim0.695
  Core quantitative prediction of UCCT validated by E2 threshold ordering
• The ordering of few-shot thresholds k50 and transition widths aligns with k50 ∝ dr/ρd.claim0.693
  Interpretation of E2 results.
• bootstrap confidence intervalmethod0.693
  Used to report uncertainty for geometry summaries and effect sizes.