Verify the formula against a seeded simulation

Verify the formula against a seeded simulation

Simulate the encode, noise, and majority-decode cycle for a fixed number of shots at each p on the same grid, using a recorded seed. Compare each simulated rate against the analytic value with a binomial interval. Deliverable: A simulator and a table with p, analytic_rate, simulated_rate, shots, and whether the analytic value falls inside the interval.