Struct ImtProofData 

pub struct ImtProofData {
    pub root: Fp,
    pub nf_bounds: [Fp; 3],
    pub leaf_pos: u32,
    pub path: [Fp; 29],
}

Circuit-compatible IMT non-membership proof for punctured-range leaves (K=2).

Instead of storing a single (low, width) gap, each leaf commits to three sorted nullifier boundaries [nf_lo, nf_mid, nf_hi] via Poseidon3(...). The leaf covers the punctured interval (nf_lo, nf_hi) \ {nf_mid}.

Circuit witnesses

Each field maps directly to a witness in the delegation circuit’s condition 13 (IMT non-membership):

• root: public input, constrained equal to nf_imt_root in the q_per_note gate.
• nf_bounds: three field elements [nf_lo, nf_mid, nf_hi], witnessed and hashed in-circuit via Poseidon3 (two permutations) to produce the leaf commitment.
• leaf_pos: position bits that determine swap ordering at each Merkle level via 29 q_imt_swap gates.
• path: 29-level authentication path (25 PIR siblings + 4 empty-hash padding for circuit depth).

Circuit constraints (condition 13)

1. Leaf hash: leaf = Poseidon3(nf_lo, nf_mid, nf_hi) — two Poseidon permutations (width-3 sponge, ConstantLength<3>).
2. Merkle path: 29 × swap + Poseidon → computed_root.
3. Strict interval: nf_lo < value < nf_hi via two 250-bit range checks on value - nf_lo - 1 and nf_hi - value - 1.
4. Non-equality: value ≠ nf_mid by witnessing inverse(value - nf_mid).
5. Root pin: computed_root = nf_imt_root (not gated on is_note_real).

Soundness invariants

The interval check relies on nf_hi - nf_lo ≤ 2^250, which is guaranteed by sentinel nullifiers at k × 2^249 spacing (each K=2 leaf spans two intervals: 2 × 2^249 = 2^250). Without this bound, a field-wrapping span would defeat the range check.

The ordering nf_lo < nf_mid < nf_hi is enforced by tree construction (sorted nullifier input) and locked by the Merkle commitment — a forger cannot alter nf_bounds without breaking the Merkle path.

Fields

root: Fp

The Merkle root of the IMT.

nf_bounds: [Fp; 3]

Three sorted nullifier boundaries: [nf_lo, nf_mid, nf_hi].

leaf_pos: u32

Position of the leaf in the tree.

path: [Fp; 29]

Sibling hashes along the 29-level Merkle authentication path.

Implementations

impl ImtProofData

pub fn verify(&self, value: Fp) -> bool

Verify this proof out-of-circuit.

Checks that value lies strictly inside the punctured interval (nf_lo, nf_hi) \ {nf_mid} and that the Merkle path recomputes to root.

Trait Implementations

impl Clone for ImtProofData

fn clone(&self) -> ImtProofData

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for ImtProofData

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.