C9.2 — Monte-Carlo & finite-range checks for weighted Collatz (1,1) parity probabilities

[Copilot]

Replaces the non-functional stub in scripts/collatz_c9_2_sampling.py with a complete weighted Monte-Carlo pipeline that measures the decorrelation of Collatz parity orbits under the contact-form weight w(n) = 1/log(n).

Core sampling (collatz_c9_2_sampling.py)

• Samples odd n ≥ 33 uniformly from a configurable window [start, end]
• Applies w(n) = 1/log(n) to each draw
• "11 event": n odd and T(n) = (3n+1)//2 odd — equivalent to n ≡ 3 (mod 4); p11 is the weighted mean of this indicator
• Records the full Collatz parity orbit b_0…b_{depth-1} per draw, with correct 1-cycle continuation (1→4→2→1 → parity 1,0,0,…)
• ACF anchored at orbit position 2 (positions 0 and 1 are degenerate: always 1 and 0 for odd starts)
• Convergence checkpoints every M/100 draws
• Outputs reproducible CSV (raw draws) + JSON summary

python scripts/collatz_c9_2_sampling.py \
    --start 33 --end 1000000 --M 1000000 --depth 20 --seed 42 \
    --output scripts/out
# p11 (weighted) = 0.498429  |  deviation = -0.001571

Plot generation (collatz_c9_2_plots.py)

• Convergence: running p11 vs. sample count with 0.5 reference
• ACF: Cor(b₂, b₂₊lag) bars with ±1.96/√M CI band
• Marginals: P(b_k = 1) per orbit position
• Multi-window overlay: comparison across experiments

Documentation (C9_2_README.md)

Covers mathematical background (half-step map, "11 event", weight definition), reproduction steps, and interpretation of each plot including limitations (finite-window bias, numerical evidence only).

Committed outputs (scripts/out/)

JSON summaries and PNG plots for M=10⁵ and M=10⁶ windows. Large CSVs excluded via .gitignore.
Results: p11 ≈ 0.498, ACF decays into the 95% CI band by lag ~8 — consistent with the decorrelation hypothesis.