Hybrid Gate Pipeline

Input: Function Problem

Choose polynomial coefficients or a direct function expression.

Polynomial Function expression

Polynomial coefficients Example: -2, 0, 1 means f(x) = -2 + x^2

Left bound Right bound

Backend continuity gate

Samples Max jump

Max abs value

Bisection parameters

Tolerance Max iterations

Each stage mirrors the backend checks and certificate flow.

1. Backend continuity gate

Idle

Samples the interval and rejects NaN/Inf, large jumps, and blowups.

2. Certificate export

Idle

Emits a proof-style summary of checks and sampling budget.

3. Root finding

Idle

Runs bisection only if the certificate is accepted.

Notes are appended as the pipeline runs.