False dynamic conditional store overwrites slot zero

[NullWitnessZK]

Minimal reproducer

Save as main.zok:

def main(private field i, private field x, private bool c) -> field:
    field[2] values = [1, 2]
    cond_store(values, i, x, c)
    return values[0]

Use this input:

i = 1
x = 0
c = false

The stage comparison at CirC 271f911 is:

Stage	return = 1	return = 0
Raw source IR	accepted	rejected
After LinearScan	rejected	accepted
Final R1CS relation	rejected	accepted

Expected

A false conditional store is a no-op. The array remains [1, 2], so the function returns 1.

Actual

The rewritten relation stores 0 into slot zero and returns 0.

Why it happens

The dynamic-index lowering initializes its fold with an unconditional Update(0, ...), then guards only candidate indices 1..N. If c is false, all guarded arms fall through to that slot-zero update.

Impact: an unsound verifier relation for a custom witness, plus disagreement with the bundled witness computation. The stock CLI does not directly produce a false proof here: its source-correct precompute conflicts with the malformed constraints.

Proposed fix

fix/linear-scan-conditional-store at 62bbb92 starts the fold with the untouched tuple and guards every candidate update—including index zero—with index == candidate && condition.

Self-contained regression:

cargo test false_dynamic_conditional_store_preserves_array