C9.1 — Prove residue‑class decorrelation lemma for consecutive (1,1) events (mod 2^M)

[TOTOGT]

Goal
Prove (or reduce to a verifiable conditional) the residue‑class decorrelation lemma:

There exists δ<1 (or δ(n)→0) and M0 such that for all odd n ≥ 33 and all M ≥ M0,
| Pr( v2(3T(n)+1)=1 | v2(3n+1)=1, n mod 2^M ) − p11 | ≤ δ,

uniformly over residue classes compatible with the discrete contact form.

Deliverables

• A clear statement with explicit constants or a conditional reduction (e.g., assuming X).
• A proof sketch and full proof (or a reduction to a single micro‑lemma).
• If proof is conditional, state the exact hypothesis and constants.

Checklist

• Formalize the probability measure and normalization (contact‑form weight w(n)).
• Identify residue constraints for v2(3n+1)=1.
• Propagate constraints through one macro‑step T(n) and analyze +1 carry effects.
• Bound overlap/conditional probabilities uniformly in residue classes.
• Produce a final lemma statement with explicit δ and M0 (or conditional hypothesis).

Notes
This is the core micro‑lemma that closes Collatz D9. Link any partial numeric evidence or scripts here.