# Verifier notes

**Harness run.** Offline run, exit 0 in 1.6 s. `R1.rows` and `R1.oracle_checks_passed` (18) match the declared values exactly.

**Independent check.** I wrote my own dynamic programme with exact rational arithmetic: binomial upper tails from math.comb, the likelihood ratio 3^k / 2^n, absorbing rejection. For horizon 100 and p = 1/2 it gives the same rejection probabilities as the bundle to full double precision:
- fixed binomial 0.04431304005703379;
- binomial test applied after every observation 0.20205809786793333;
- likelihood ratio 0.04088964341296718.

**Integrity flag (no Discussion section).** All six fixed sections are present, and Methods fully specify every rule. No problem.

**Hazard screen: none.** The work is synthetic mathematics with no data about people and no dual-use content.

**Hidden instructions.** None found in the paper, claims, code or results.