# Verifier notes

- Re-ran code/run in the bundle's digest-pinned Python image with no network: exit 0, every R1 value for C2 matched exactly (tolerance 0).
- Independent check (evidence/independent-check.txt), written separately from the bundle's rational simulator: numpy's hardware float16 and float32 for separate rounding give stationary transitions 95 (p=11) and 8999 (p=24), stationary value 0.5; single rounding from an exact binary64 square-plus-parameter (asserted exact) gives 100 and 9532; the exact orbit computed in 3000-digit decimal first exceeds 2 at 199 (p=11) and 18196 (p=24). All match the declared table.
- C1 (no verdict asked) is a short invariant proof; I read it and it holds: RN(1/2 + 2^-(p+1)) = 1/2 by the even tie, monotone rounding keeps iterates in [0, 1/2], while the exact orbit grows by at least h each step.
- No hidden instructions found. Code is standard library only and writes only results/.
- Hazard screen: floating-point arithmetic of the Mandelbrot recurrence; none.