C9.3: Formalize averaging measure μ and finite-window conventions for D9 analysis

[Copilot]

D9 artifacts had no canonical definition of the averaging measure μ, window function w(n), or agreed window types — scripts used inconsistent (and partially broken) windowing logic with no asymptotic specification.

Canonical specification (docs/d9_averaging_window_conventions.md)

Defines the three window types every D9 artifact must use:

Type	Window	Size	w(n)
Contiguous	[1, N]	N	n
Dyadic	[2^k, 2^(k+1))	2^k	⌊log₂n⌋
Logarithmic	[1, N], weight 1/n	H_N ≈ ln N	n

Also specifies: normalization rule for μ_W, limsup/liminf conventions, the chain d̲(A) ≤ δ(A) ≤ d̄(A), and a mandatory D9 metadata JSON schema for every artifact.

New implementation (scripts/collatz_c9_3_averaging.py)

python scripts/collatz_c9_3_averaging.py \
  --event strong_decrease --window-type dyadic --param 20 \
  --limsup-liminf --output scripts/out/d9.json
# [C9.3] window_type=dyadic  param=20  mu_W(strong_decrease)=0.25
# [C9.3] limsup≈0.25  liminf≈0.25  status=converged

Exposes mu_contiguous, mu_dyadic, mu_logarithmic, estimate_limsup_liminf, and build_d9_metadata as importable functions.

C9.2 fixes (scripts/collatz_c9_2_sampling.py)

• T(n) replaced: was (3n+1) // 2^0 (wrong); now uses correct 2-adic valuation
• sample() now actually iterates over the window (previously iterated M times on a fixed n)
• Dyadic windows validated against spec boundaries at runtime
• mu_W in output JSON is now the exhaustive event count over the full window (|{n∈W: A(n)}| / |W|), not len(sampled_results) / |W|
• Output JSON includes the canonical D9 metadata block

Cross-references

• docs/analysis_ns/README.md updated to point to the new spec (closes the open "waiting for windowing definition" status)
• .gitignore added to exclude scripts/out/ empirical outputs