Struct Proof 

pub struct Proof<F> {

    pub commitments: (ZipPlusCommitment, ZipPlusCommitment, ZipPlusCommitment),
    pub zip: Vec<u8>,
    pub ideal_check: Proof<F>,
    pub cpr_proof: Proof<F>,
    pub combined_sumcheck: MultiDegreeSumcheckProof<F>,
    pub multipoint_eval: Proof<F>,
    pub witness_lifted_evals: Vec<Vec<DynamicPolynomial<F>>>,
    pub lookup_proof: Option<BatchedLookupProof<F>>,
    pub booleanity_proof: Option<BooleanityProof<F>>,
    pub affine_booleanity_proof: Option<BooleanityProof<F>>,
    pub ideal_checks_fq: Vec<Proof<F>>,
    pub cpr_proofs_fq: Vec<Proof<F>>,
    pub combined_sumchecks_fq: Vec<MultiDegreeSumcheckProof<F>>,
    pub multipoint_evals_fq: Vec<Proof<F>>,
    pub witness_lifted_evals_pp: Option<Vec<DynamicPolynomial<F>>>,
}

Full proof produced by the Zinc+ PIOP for UCS.

Lifted-eval families

Witness lifted evals are sent per family: for each of the $n + 2$ families (Q[X] / $q_0$, the declared $q_1, \dots, q_n$, and the PCS-only $q’’$), the prover sends a vector of DynamicPolynomial<F> carrying the per-family coefficient lift of each witness column. The verifier reads each family’s lifts under that family’s field cfg, no per-coefficient cfg.project projection is needed.

Fields

commitments: (ZipPlusCommitment, ZipPlusCommitment, ZipPlusCommitment)

Zip+ commitments to the witness columns.

zip: Vec<u8>

Serialized PCS proof data (Zip+ proving transcripts).

ideal_check: Proof<F>

Randomized ideal check proof (Q[X] family).

cpr_proof: Proof<F>

Combined polynomial resolver proof (up_evals + down_evals).

combined_sumcheck: MultiDegreeSumcheckProof<F>

Multi-degree sumcheck proof (CPR group + lookup groups).

multipoint_eval: Proof<F>

Multi-point evaluation sumcheck proof (combines up_evals and down_evals at r* into a single evaluation point r_0).

witness_lifted_evals: Vec<Vec<DynamicPolynomial<F>>>

Witness-only polynomial MLE evaluations at $r_0$, per constraint family.

Indexing follows the standard family convention used throughout the protocol:

• witness_lifted_evals[0] — Q[X] family under $q_0$, $\bar u_j^{(0)}(X) = \sum_b \mathrm{eq}(b, r_0^{(0)}) \cdot u_j(b) \in F_{q_0}[X]$.
• witness_lifted_evals[i] for $i \in 1..=n$ — the $i$-th declared prime family from zinc_uair::UairSignature::primes, lifted into $F_{q_i}[X]$ at $r_0$ projected mod $q_i$.

Length is n + 1 where n = primes().len(). Each inner Vec orders columns as [wit_bin..., wit_arb..., wit_int...].

The verifier recomputes per-family public lifted-evals from public data, interleaves them with these, evaluates at projecting_elements[family_idx] for the per-family MP-eval consistency check.

lookup_proof: Option<BatchedLookupProof<F>>

Lookup argument proof. None when the UAIR has no lookup specs.

booleanity_proof: Option<BooleanityProof<F>>

Binary-polynomial booleanity argument proof. None when the UAIR has no witness binary-poly columns (the argument is omitted from the multi-degree sumcheck in that case).

affine_booleanity_proof: Option<BooleanityProof<F>>

Affine-virtual booleanity argument proof. None when the UAIR has no affine virtual specs.

ideal_checks_fq: Vec<Proof<F>>

Per-prime $F_{q_i}[X]$ ideal-check proofs, one per declared prime in zinc_uair::UairSignature::primes, in the same order. Empty for UAIRs with $Q[X]$-only constraints.

cpr_proofs_fq: Vec<Proof<F>>

Per-prime CPR proofs, one per declared prime, produced by the lockstep sumcheck in step 5. Empty for UAIRs with $Q[X]$ only constraints.

combined_sumchecks_fq: Vec<MultiDegreeSumcheckProof<F>>

Per-prime multi-degree sumcheck proofs, one per declared prime, produced by the lockstep sumcheck driver in step 5. Empty for UAIRs with $Q[X]$ only constraints.

multipoint_evals_fq: Vec<Proof<F>>

Per-prime multipoint-eval proofs, one per declared prime, produced by the lockstep multipoint-eval in step 6. Empty for UAIRs with $Q[X]$ only constraints.

witness_lifted_evals_pp: Option<Vec<DynamicPolynomial<F>>>

Witness-only lifted MLE evaluations under the PCS-only prime $q’‘$, sampled fresh at step 7 start. Length equals the number of witness columns. The verifier uses these directly for the PCS evaluation check at $r^\star = r_0 \bmod q’‘$ — no per-coefficient $\phi_{q’’}$ projection needed.

Kept separate from witness_lifted_evals because $q’‘$ plays a distinct role (PCS-only; no MP-eval / constraint check happens under $q’’$).

If no $F_q[X]$ constraints are present, this will be None to indicate $q’’ := q_0$ and this is identical to witness_lifted_evals.

Trait Implementations

impl<F: Clone> Clone for Proof<F>

fn clone(&self) -> Proof<F>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F: Debug> Debug for Proof<F>

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

Formats the value using the given formatter.

impl<F> GenTranscribable for Proof<F>

where F: ConstTranscribable,

fn read_transcription_bytes_exact(bytes: &[u8]) -> Self

Creates a new instance from a byte buffer. The buffer must be exactly the expected length.

fn write_transcription_bytes_exact(&self, buf: &mut [u8])

Transcribes the current instance into a byte buffer. The buffer must be exactly the expected length.

impl<F: PartialEq> PartialEq for Proof<F>

fn eq(&self, other: &Proof<F>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<F> Transcribable for Proof<F>

where F: ConstTranscribable,

fn get_num_bytes(&self) -> usize

Returns the number of bytes required to represent this type. The buffer passed to write_transcription_bytes should be exactly the length returned by this function.

const LENGTH_NUM_BYTES: usize = u32::NUM_BYTES

Number of bytes required to represent length of this type, could be zero if known in advance.

fn read_num_bytes(bytes: &[u8]) -> usize

Read number of bytes required to represent this type. The buffer must be exactly LENGTH_NUM_BYTES long. The buffer passed to read_transcription_bytes should be exactly the length returned by this function.

fn read_transcription_bytes_subset(bytes: &[u8]) -> (Self, &[u8])

Reads an instance of this type from the beginning of the byte slice, and returns the instance along with the remaining byte slice.

fn write_transcription_bytes_subset<'a>( &self, buf: &'a mut [u8], ) -> &'a mut [u8]

Writes this instance, prefixed by length, into the beginning of the byte buffer, and returns the remaining byte buffer.

impl<F: Eq> Eq for Proof<F>

impl<F> StructuralPartialEq for Proof<F>