The Deterministic Horizon — Interactive Explorer

Decoherence parameters

Model preset paper Table 3/5

ε₀ · baseline per-step error

paper MLE 0.020 · 95% CI [0.017, 0.023]

γ · attention decay rate

shared across models · paper 0.15

L_eff · effective decoherence length

O(10²) steps — not the raw context window O(10⁵)

α · success threshold

depth where P(correct)=α defines d*

tool accuracy (C3)

empirical C3 mean ≈ 0.92

Deterministic Horizon

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P(correct) at d*

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Tool advantage past d*

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Neural CoT P(d)=exp(−dε₀−γd(d+1)/2L_eff) Tool-integrated (C3) Horizon d*

If my next subproblem is state-tracking steps deep →