miden_air/

lib.rs

#![no_std]

#[macro_use]
extern crate alloc;

#[cfg(feature = "std")]
extern crate std;

use alloc::{borrow::Cow, vec::Vec};
use core::borrow::Borrow;

use miden_core::{
    WORD_SIZE, Word,
    deferred::DeferredRoot,
    field::ExtensionField,
    program::{
        KernelDescriptor, MIN_STACK_DEPTH, NUM_CLAIM_ELEMENTS, ProgramInfo, StackInputs,
        StackOutputs,
    },
};
use miden_crypto::stark::{
    air::{ReductionError, WindowAccess},
    challenger::CanObserve,
};
#[cfg(feature = "arbitrary")]
use proptest::prelude::*;

pub mod ace;
pub mod config;
mod constraints;
pub mod lookup;
pub mod memory;
mod proof_order;
pub mod security;
pub mod trace;

/// Miden VM-specific LogUp lookup argument: bus identifiers and bus message types.
///
/// [`crate::MidenAir`] is the single `LiftedAir`/`LookupAir` type for the multi-AIR
/// statement; it dispatches per-trace work to Core, Chiplets, and Poseidon2 permutation AIRs.
/// [`crate::MidenMultiAir`] is the `MultiAir` carrying the cross-AIR reduction.
/// The generic LogUp framework lives in [`crate::lookup`].
pub mod logup {
    pub use crate::constraints::lookup::{
        BusId, MIDEN_MAX_MESSAGE_WIDTH, messages::*, miden_air::NUM_LOGUP_COMMITTED_FINALS,
    };
}

use constraints::lookup::{
    chiplet_air::ChipletLookupBuilder,
    main_air::{MainLookupAir, MainLookupBuilder},
    poseidon2_permutation_air::Poseidon2PermutationLookupBuilder,
};
pub use constraints::{
    chiplets::columns::{
        AceCols, AceEvalCols, AceReadCols, BitwiseCols, ControllerCols, KernelRomCols, MemoryCols,
    },
    columns::{ChipletCols, CoreCols},
    decoder::columns::DecoderCols,
    ext_field::QuadFeltExpr,
    poseidon2_permutation::columns::{
        CYCLE_INPUT_ROW, CYCLE_OUTPUT_ROW, INITIAL_EXTERNAL_ROUND_END,
        INITIAL_EXTERNAL_ROUND_START, INTERNAL_PLUS_EXTERNAL_ROW, LAST_INTERNAL_ROUND_ARK_IDX,
        NUM_PACKED_INTERNAL_ROUND_ROWS, NUM_SBOX_WITNESSES, NUM_TRAILING_EXTERNAL_ROUND_ROWS,
        PACKED_INTERNAL_ROUND_START, Poseidon2PermutationCols, Poseidon2PermutationPeriodicCols,
    },
    range::columns::RangeCols,
    stack::columns::StackCols,
    system::columns::SystemCols,
};
use logup::{BusId, MIDEN_MAX_MESSAGE_WIDTH};
use lookup::{
    BoundaryBuilder, Challenges, ConstraintLookupBuilder, LookupAir, LookupMessage,
    build_logup_aux_trace,
};
use miden_core::utils::RowMajorMatrix;

// RE-EXPORTS
// ================================================================================================
mod export {
    pub use miden_core::{
        Felt,
        serde::{ByteReader, ByteWriter, Deserializable, DeserializationError, Serializable},
        utils::ToElements,
    };
    pub use miden_crypto::stark::{
        StarkConfig,
        air::{
            AirBuilder, BaseAir, ConstraintCounts, ConstraintDegrees, ExtensionBuilder, LiftedAir,
            LiftedAirBuilder, MultiAir, PermutationAirBuilder, ProverStatement, Statement,
        },
        debug,
        pcs::PcsParams,
    };
}

pub use export::*;
pub use proof_order::{
    AIRS, MIDEN_AIR_COUNT, PROOF_ORDER_COUNT, PROOF_ORDER_REGISTRY_DEPTH, ProofOrder,
};

// MIDEN AIR BUILDER
// ================================================================================================

/// Convenience super-trait that pins `LiftedAirBuilder` to the Miden base field.
///
/// Constraint functions use `AB: MidenAirBuilder` instead of the longer
/// `LiftedAirBuilder<F = Felt>` bound.
pub trait MidenAirBuilder: LiftedAirBuilder<F = Felt> {}
impl<T: LiftedAirBuilder<F = Felt>> MidenAirBuilder for T {}

// PUBLIC INPUTS
// ================================================================================================

#[derive(Debug, Clone, PartialEq, Eq)]
#[cfg_attr(
    all(feature = "arbitrary", test),
    miden_test_serialization_macros::serialization_test
)]
pub struct PublicInputs {
    program_info: ProgramInfo,
    stack_inputs: StackInputs,
    stack_outputs: StackOutputs,
    deferred_root: DeferredRoot,
}

impl PublicInputs {
    /// Creates a new instance of `PublicInputs` from program information, stack inputs and outputs,
    /// and the final deferred root.
    pub fn new(
        program_info: ProgramInfo,
        stack_inputs: StackInputs,
        stack_outputs: StackOutputs,
        deferred_root: DeferredRoot,
    ) -> Self {
        Self {
            program_info,
            stack_inputs,
            stack_outputs,
            deferred_root,
        }
    }

    pub fn stack_inputs(&self) -> StackInputs {
        self.stack_inputs
    }

    pub fn stack_outputs(&self) -> StackOutputs {
        self.stack_outputs
    }

    pub fn program_info(&self) -> ProgramInfo {
        self.program_info.clone()
    }

    /// Returns the final deferred root.
    pub fn deferred_root(&self) -> DeferredRoot {
        self.deferred_root
    }

    /// Returns the canonical commitment to the kernel of the verified statement: the value the
    /// recursive verifier observes into the transcript in place of the raw kernel-procedure
    /// digest list. See
    /// [`KernelDescriptor::commitment`](miden_core::program::KernelDescriptor::commitment).
    pub fn kernel_commitment(&self) -> Word {
        self.program_info.kernel_commitment()
    }

    /// Returns the AIR public values (`air_inputs`) and statement inputs (`aux_inputs`).
    ///
    /// `air_inputs` (the values read by the AIR constraints) layout:
    ///   [0..16]  stack inputs
    ///   [16..32] stack outputs
    ///
    /// `aux_inputs` (statement inputs not read by the AIRs, consumed only by `observe` and
    /// `eval_external`) layout:
    ///   [0..4]   program hash
    ///   [4..8]   final deferred root
    ///   [8..]    kernel procedure digests (concatenated words, variable length)
    pub fn to_air_inputs(&self) -> (Vec<Felt>, Vec<Felt>) {
        let mut air_inputs = Vec::with_capacity(NUM_PUBLIC_VALUES);
        air_inputs.extend_from_slice(self.stack_inputs.as_ref());
        air_inputs.extend_from_slice(self.stack_outputs.as_ref());

        let kernel_felts = Word::words_as_elements(self.program_info.kernel_procedures());
        let mut aux_inputs = Vec::with_capacity(AUX_KERNEL_DIGESTS + kernel_felts.len());
        aux_inputs.extend_from_slice(self.program_info.program_hash().as_elements());
        aux_inputs.extend_from_slice(self.deferred_root.as_ref());
        aux_inputs.extend_from_slice(kernel_felts);

        (air_inputs, aux_inputs)
    }

    /// Converts public inputs into a vector of field elements (Felt) in the canonical order:
    /// - program info elements (including kernel procedure hashes)
    /// - stack inputs
    /// - stack outputs
    /// - final deferred root
    pub fn to_elements(&self) -> Vec<Felt> {
        let mut result = self.program_info.to_elements();
        result.extend_from_slice(self.stack_inputs.as_ref());
        result.extend_from_slice(self.stack_outputs.as_ref());
        result.extend_from_slice(self.deferred_root.as_ref());
        result
    }
}

#[cfg(feature = "arbitrary")]
impl Arbitrary for PublicInputs {
    type Parameters = ();
    type Strategy = BoxedStrategy<Self>;

    fn arbitrary_with(_args: Self::Parameters) -> Self::Strategy {
        fn felt_strategy() -> impl Strategy<Value = Felt> {
            any::<u32>().prop_map(Felt::from)
        }

        fn word_strategy() -> impl Strategy<Value = Word> {
            any::<[u32; WORD_SIZE]>().prop_map(|values| Word::new(values.map(Felt::from)))
        }

        let program_info = word_strategy()
            .prop_map(|program_hash| ProgramInfo::new(program_hash, KernelDescriptor::default()));
        let stack_inputs = proptest::collection::vec(felt_strategy(), 0..=MIN_STACK_DEPTH)
            .prop_map(|values| StackInputs::new(&values).expect("generated stack inputs fit"));
        let stack_outputs = proptest::collection::vec(felt_strategy(), 0..=MIN_STACK_DEPTH)
            .prop_map(|values| StackOutputs::new(&values).expect("generated stack outputs fit"));

        (program_info, stack_inputs, stack_outputs, word_strategy())
            .prop_map(|(program_info, stack_inputs, stack_outputs, deferred_root)| {
                Self::new(program_info, stack_inputs, stack_outputs, deferred_root)
            })
            .boxed()
    }
}

// SERIALIZATION
// ================================================================================================

impl Serializable for PublicInputs {
    fn write_into<W: ByteWriter>(&self, target: &mut W) {
        self.program_info.write_into(target);
        self.stack_inputs.write_into(target);
        self.stack_outputs.write_into(target);
        self.deferred_root.write_into(target);
    }
}

impl Deserializable for PublicInputs {
    fn read_from<R: ByteReader>(source: &mut R) -> Result<Self, DeserializationError> {
        let program_info = ProgramInfo::read_from(source)?;
        let stack_inputs = StackInputs::read_from(source)?;
        let stack_outputs = StackOutputs::read_from(source)?;
        let deferred_root = DeferredRoot::read_from(source)?;

        Ok(PublicInputs {
            program_info,
            stack_inputs,
            stack_outputs,
            deferred_root,
        })
    }
}

// PROCESSOR AIR
// ================================================================================================

/// Number of public values read by the Miden VM AIRs: the `air_inputs` shared by every AIR.
///
/// Layout (32 Felts total):
///   [0..16]  stack inputs
///   [16..32] stack outputs
///
/// The program hash and final deferred root are not read by any AIR constraint, so they
/// are carried as `aux_inputs` and consumed only by [`MidenMultiAir::observe`] and
/// [`MidenMultiAir::eval_external`].
pub const NUM_PUBLIC_VALUES: usize = MIN_STACK_DEPTH + MIN_STACK_DEPTH;

/// LogUp aux trace width: 4 core columns + 3 chiplet columns + 1 Poseidon2 column.
pub const LOGUP_AUX_TRACE_WIDTH: usize = 8;

// `aux_inputs` layout offsets — statement inputs that the AIRs do not read. The fixed program
// hash and final deferred root occupy the first two words; the variable-length kernel-procedure
// digests follow.
const AUX_PROGRAM_HASH: usize = 0;
const AUX_DEFERRED_ROOT: usize = WORD_SIZE;
const AUX_KERNEL_DIGESTS: usize = 2 * WORD_SIZE;

// CORE AIR
// ================================================================================================

/// Core trace AIR.
///
/// Enforces the system, decoder, stack, and range-check constraints.
#[derive(Copy, Clone, Debug, Default)]
pub struct CoreAir;

impl CoreAir {
    fn width(self) -> usize {
        constraints::columns::NUM_CORE_COLS
    }

    fn periodic_columns(self) -> Vec<Vec<Felt>> {
        Vec::new()
    }

    fn aux_width(self) -> usize {
        constraints::lookup::main_air::MAIN_COLUMN_SHAPE.len()
    }

    /// LogUp boundary correction for the core trace: the running sum of every
    /// boundary interaction reduced to its denominator contribution. The single var-len slice
    /// carries `[program_hash (4) | deferred_root (4)]`, the statement inputs the core
    /// boundary cancels against the block-hash and log-deferred buses.
    fn boundary_correction<EF: ExtensionField<Felt>>(
        self,
        challenges: &Challenges<EF>,
        public_values: &[Felt],
        boundary_inputs: &[&[Felt]],
    ) -> Result<EF, ReductionError> {
        if boundary_inputs.len() != 1 {
            return Err(format!(
                "CoreAir expects 1 boundary input slice, got {}",
                boundary_inputs.len()
            )
            .into());
        }
        if boundary_inputs[0].len() != 2 * WORD_SIZE {
            return Err(format!(
                "CoreAir expects {} boundary felts (program hash + deferred root), got {}",
                2 * WORD_SIZE,
                boundary_inputs[0].len()
            )
            .into());
        }

        let mut reducer = ReduceBoundaryBuilder {
            challenges,
            public_values,
            var_len_public_inputs: boundary_inputs,
            sum: EF::ZERO,
            error: None,
        };
        constraints::lookup::miden_air::emit_core_boundary(&mut reducer);
        reducer.finalize()
    }

    fn eval<AB: MidenAirBuilder>(self, builder: &mut AB) {
        let main = builder.main();
        let local: &CoreCols<AB::Var> = (*main.current_slice()).borrow();
        let next: &CoreCols<AB::Var> = (*main.next_slice()).borrow();

        let op_flags =
            constraints::op_flags::OpFlags::new(&local.decoder, &local.stack, &next.decoder);

        constraints::enforce_core(builder, local, next, &op_flags);
        constraints::public_inputs::enforce_main(builder, local);

        let mut lb = ConstraintLookupBuilder::new(builder, &MidenAir::Core);
        self.lookup_eval(&mut lb);
    }

    fn lookup_num_columns(self) -> usize {
        constraints::lookup::main_air::MAIN_COLUMN_SHAPE.len()
    }

    fn lookup_column_shape(self) -> &'static [usize] {
        &constraints::lookup::main_air::MAIN_COLUMN_SHAPE
    }

    fn lookup_max_message_width(self) -> usize {
        MIDEN_MAX_MESSAGE_WIDTH
    }

    fn lookup_num_bus_ids(self) -> usize {
        BusId::COUNT
    }

    fn lookup_eval<LB: MainLookupBuilder>(self, builder: &mut LB) {
        MainLookupAir.eval(builder);
    }

    fn lookup_eval_boundary<B: BoundaryBuilder>(self, boundary: &mut B) {
        constraints::lookup::miden_air::emit_core_boundary(boundary);
    }
}

// CHIPLETS AIR
// ================================================================================================

/// Chiplets trace AIR.
///
/// Enforces the chiplet selector hierarchy, chiplet transition constraints, and
/// chiplet-side LogUp buses.
#[derive(Copy, Clone, Debug, Default)]
pub struct ChipletsAir;

impl ChipletsAir {
    fn width(self) -> usize {
        constraints::columns::NUM_CHIPLETS_COLS
    }

    fn periodic_columns(self) -> Vec<Vec<Felt>> {
        constraints::chiplets::columns::PeriodicCols::periodic_columns()
    }

    fn aux_width(self) -> usize {
        constraints::lookup::chiplet_air::CHIPLET_COLUMN_SHAPE.len()
    }

    /// LogUp boundary correction for the chiplets trace.
    ///
    /// The boundary input slice contains the kernel-procedure digests; these statement values
    /// close the kernel-ROM bus.
    fn boundary_correction<EF: ExtensionField<Felt>>(
        self,
        challenges: &Challenges<EF>,
        public_values: &[Felt],
        boundary_inputs: &[&[Felt]],
    ) -> Result<EF, ReductionError> {
        if boundary_inputs.len() != 1 {
            return Err(format!(
                "ChipletsAir expects 1 boundary input slice, got {}",
                boundary_inputs.len()
            )
            .into());
        }
        if !boundary_inputs[0].len().is_multiple_of(WORD_SIZE) {
            return Err(format!(
                "kernel digest felts length {} is not a multiple of {}",
                boundary_inputs[0].len(),
                WORD_SIZE
            )
            .into());
        }

        let mut reducer = ReduceBoundaryBuilder {
            challenges,
            public_values,
            var_len_public_inputs: boundary_inputs,
            sum: EF::ZERO,
            error: None,
        };
        constraints::lookup::miden_air::emit_chiplets_boundary(&mut reducer);
        reducer.finalize()
    }

    fn eval<AB: MidenAirBuilder>(self, builder: &mut AB) {
        let main = builder.main();
        let local: &ChipletCols<AB::Var> = (*main.current_slice()).borrow();
        let next: &ChipletCols<AB::Var> = (*main.next_slice()).borrow();

        let selectors =
            constraints::chiplets::selectors::build_chiplet_selectors(builder, local, next);

        constraints::enforce_chiplets(builder, local, next, &selectors);

        let mut lb = ConstraintLookupBuilder::new(builder, &MidenAir::Chiplets);
        self.lookup_eval(&mut lb);
    }

    fn lookup_num_columns(self) -> usize {
        constraints::lookup::chiplet_air::CHIPLET_COLUMN_SHAPE.len()
    }

    fn lookup_column_shape(self) -> &'static [usize] {
        &constraints::lookup::chiplet_air::CHIPLET_COLUMN_SHAPE
    }

    fn lookup_max_message_width(self) -> usize {
        MIDEN_MAX_MESSAGE_WIDTH
    }

    fn lookup_num_bus_ids(self) -> usize {
        BusId::COUNT
    }

    fn lookup_eval<LB: ChipletLookupBuilder>(self, builder: &mut LB) {
        let main = builder.main();
        let local: &ChipletCols<_> = main.current_slice().borrow();
        let next: &ChipletCols<_> = main.next_slice().borrow();

        constraints::lookup::chiplet_air::emit_chiplet_lookup_columns(builder, local, next);
    }

    fn lookup_eval_boundary<B: BoundaryBuilder>(self, boundary: &mut B) {
        constraints::lookup::miden_air::emit_chiplets_boundary(boundary);
    }
}

// POSEIDON2 PERMUTATION AIR
// ================================================================================================

/// Poseidon2 permutation trace AIR.
///
/// Enforces 16-row permutation cycles and the permutation-side LogUp bus.
#[derive(Copy, Clone, Debug, Default)]
pub struct Poseidon2PermutationAir;

impl Poseidon2PermutationAir {
    fn width(self) -> usize {
        constraints::poseidon2_permutation::columns::NUM_POSEIDON2_PERMUTATION_COLS
    }

    fn periodic_columns(self) -> Vec<Vec<Felt>> {
        Poseidon2PermutationPeriodicCols::periodic_columns()
    }

    fn aux_width(self) -> usize {
        constraints::lookup::poseidon2_permutation_air::POSEIDON2_PERMUTATION_COLUMN_SHAPE.len()
    }

    fn boundary_correction<EF: ExtensionField<Felt>>(
        self,
        _challenges: &Challenges<EF>,
        _public_values: &[Felt],
        boundary_inputs: &[&[Felt]],
    ) -> Result<EF, ReductionError> {
        if !boundary_inputs.is_empty() {
            return Err(format!(
                "Poseidon2PermutationAir expects 0 boundary input slices, got {}",
                boundary_inputs.len()
            )
            .into());
        }
        Ok(EF::ZERO)
    }

    fn eval<AB: MidenAirBuilder>(self, builder: &mut AB) {
        constraints::enforce_poseidon2_permutation(builder);

        let mut lb = ConstraintLookupBuilder::new(builder, &MidenAir::Poseidon2Permutation);
        self.lookup_eval(&mut lb);
    }

    fn lookup_num_columns(self) -> usize {
        constraints::lookup::poseidon2_permutation_air::POSEIDON2_PERMUTATION_COLUMN_SHAPE.len()
    }

    fn lookup_column_shape(self) -> &'static [usize] {
        &constraints::lookup::poseidon2_permutation_air::POSEIDON2_PERMUTATION_COLUMN_SHAPE
    }

    fn lookup_max_message_width(self) -> usize {
        MIDEN_MAX_MESSAGE_WIDTH
    }

    fn lookup_num_bus_ids(self) -> usize {
        BusId::COUNT
    }

    fn lookup_eval<LB: Poseidon2PermutationLookupBuilder>(self, builder: &mut LB) {
        let main = builder.main();
        let local: &Poseidon2PermutationCols<_> = main.current_slice().borrow();

        constraints::lookup::poseidon2_permutation_air::emit_poseidon2_permutation_lookup_columns(
            builder, local,
        );
    }

    fn lookup_eval_boundary<B: BoundaryBuilder>(self, _boundary: &mut B) {}
}

// MIDEN AIR
// ================================================================================================

/// AIR instance identifier for the Miden multi-AIR statement.
///
/// [`MultiAir::Air`](miden_crypto::stark::air::MultiAir) is a single associated type, so every
/// instance in the multi-AIR proof must have the same type. This enum identifies which concrete
/// AIR logic to dispatch to.
#[derive(Copy, Clone, Debug, Eq, PartialEq)]
pub enum MidenAir {
    Core,
    Chiplets,
    Poseidon2Permutation,
}

impl MidenAir {
    pub const fn instance_index(self) -> usize {
        match self {
            Self::Core => 0,
            Self::Chiplets => 1,
            Self::Poseidon2Permutation => 2,
        }
    }

    pub const fn name(self) -> &'static str {
        match self {
            Self::Core => "Core",
            Self::Chiplets => "Chiplets",
            Self::Poseidon2Permutation => "Poseidon2Permutation",
        }
    }

    /// Lookup fractions emitted per row, one entry per auxiliary lookup column.
    ///
    /// Available without naming a lookup builder, so callers that only need the shape — such as
    /// the security estimator — do not have to pick an unrelated builder type to read it.
    pub fn column_shape(self) -> &'static [usize] {
        match self {
            Self::Core => CoreAir.lookup_column_shape(),
            Self::Chiplets => ChipletsAir.lookup_column_shape(),
            Self::Poseidon2Permutation => Poseidon2PermutationAir.lookup_column_shape(),
        }
    }

    pub const fn file_token(self) -> &'static str {
        match self {
            Self::Core => "core",
            Self::Chiplets => "chiplets",
            Self::Poseidon2Permutation => "poseidon2_permutation",
        }
    }

    fn boundary_correction<EF: ExtensionField<Felt>>(
        self,
        challenges: &Challenges<EF>,
        public_values: &[Felt],
        aux_inputs: &[Felt],
    ) -> Result<EF, ReductionError> {
        if aux_inputs.len() < AUX_KERNEL_DIGESTS {
            return Err(format!(
                "aux_inputs length {} is shorter than the fixed prefix {AUX_KERNEL_DIGESTS}",
                aux_inputs.len()
            )
            .into());
        }

        match self {
            Self::Core => CoreAir.boundary_correction(
                challenges,
                public_values,
                &[&aux_inputs[..AUX_KERNEL_DIGESTS]],
            ),
            Self::Chiplets => ChipletsAir.boundary_correction(
                challenges,
                public_values,
                &[&aux_inputs[AUX_KERNEL_DIGESTS..]],
            ),
            Self::Poseidon2Permutation => {
                Poseidon2PermutationAir.boundary_correction(challenges, public_values, &[])
            },
        }
    }

    /// Evaluate the hand-written constraint definitions.
    ///
    /// [`LiftedAir::eval`] runs the generated evaluators instead; use this entry
    /// point (via [`HandwrittenMidenAir`] where an AIR value is expected) when
    /// the hand-written source itself is required — regenerating the evaluators,
    /// or checking them for drift.
    pub fn eval_handwritten<AB: LiftedAirBuilder<F = Felt>>(&self, builder: &mut AB) {
        match self {
            Self::Core => CoreAir.eval(builder),
            Self::Chiplets => ChipletsAir.eval(builder),
            Self::Poseidon2Permutation => Poseidon2PermutationAir.eval(builder),
        }
    }
}

/// [`MidenAir`] with `eval` routed to the hand-written constraint definitions.
///
/// Symbolic capture that feeds artifact generation, or anchors an equivalence
/// oracle, must consume the hand-written source — a generated evaluator as input
/// makes regeneration self-referential and severs the chain back to the auditable
/// source. Passing this wrapper enforces that by construction.
#[derive(Copy, Clone, Debug)]
pub struct HandwrittenMidenAir(pub MidenAir);

impl BaseAir<Felt> for HandwrittenMidenAir {
    fn width(&self) -> usize {
        self.0.width()
    }

    fn num_public_values(&self) -> usize {
        BaseAir::<Felt>::num_public_values(&self.0)
    }

    fn periodic_columns(&self) -> Cow<'_, [Vec<Felt>]> {
        self.0.periodic_columns()
    }
}

impl<EF: ExtensionField<Felt>> LiftedAir<Felt, EF> for HandwrittenMidenAir {
    fn num_randomness(&self) -> usize {
        LiftedAir::<Felt, EF>::num_randomness(&self.0)
    }

    fn aux_width(&self) -> usize {
        LiftedAir::<Felt, EF>::aux_width(&self.0)
    }

    fn num_aux_values(&self) -> usize {
        LiftedAir::<Felt, EF>::num_aux_values(&self.0)
    }

    fn build_aux_trace(
        &self,
        main: &RowMajorMatrix<Felt>,
        air_inputs: &[Felt],
        aux_inputs: &[Felt],
        challenges: &[EF],
    ) -> (RowMajorMatrix<EF>, Vec<EF>) {
        self.0.build_aux_trace(main, air_inputs, aux_inputs, challenges)
    }

    fn constraint_degree(&self) -> ConstraintDegrees {
        LiftedAir::<Felt, EF>::constraint_degree(&self.0)
    }

    fn eval<AB: LiftedAirBuilder<F = Felt>>(&self, builder: &mut AB) {
        self.0.eval_handwritten(builder)
    }
}

impl BaseAir<Felt> for MidenAir {
    fn width(&self) -> usize {
        match self {
            Self::Core => CoreAir.width(),
            Self::Chiplets => ChipletsAir.width(),
            Self::Poseidon2Permutation => Poseidon2PermutationAir.width(),
        }
    }

    fn num_public_values(&self) -> usize {
        NUM_PUBLIC_VALUES
    }

    fn periodic_columns(&self) -> Cow<'_, [Vec<Felt>]> {
        Cow::Owned(match self {
            Self::Core => CoreAir.periodic_columns(),
            Self::Chiplets => ChipletsAir.periodic_columns(),
            Self::Poseidon2Permutation => Poseidon2PermutationAir.periodic_columns(),
        })
    }
}

impl<EF: ExtensionField<Felt>> LiftedAir<Felt, EF> for MidenAir {
    fn num_randomness(&self) -> usize {
        // Instance-level: every AIR shares the same LogUp challenge set.
        trace::AUX_TRACE_RAND_CHALLENGES
    }

    fn aux_width(&self) -> usize {
        match self {
            Self::Core => CoreAir.aux_width(),
            Self::Chiplets => ChipletsAir.aux_width(),
            Self::Poseidon2Permutation => Poseidon2PermutationAir.aux_width(),
        }
    }

    fn num_aux_values(&self) -> usize {
        // One committed normalized LogUp sum `sigma_prime = sigma / n` per AIR instance.
        1
    }

    fn build_aux_trace(
        &self,
        main: &RowMajorMatrix<Felt>,
        _air_inputs: &[Felt],
        _aux_inputs: &[Felt],
        challenges: &[EF],
    ) -> (RowMajorMatrix<EF>, Vec<EF>) {
        let (aux_trace, committed) = build_logup_aux_trace(self, main, challenges);
        debug_assert_eq!(
            committed.len(),
            1,
            "build_logup_aux_trace returns one normalized LogUp sum per AIR"
        );
        (aux_trace, committed)
    }

    fn constraint_degree(&self) -> ConstraintDegrees {
        match self {
            Self::Core | Self::Chiplets => ConstraintDegrees { base: 9, ext: 9 },
            Self::Poseidon2Permutation => ConstraintDegrees { base: 8, ext: 3 },
        }
    }

    fn eval<AB: LiftedAirBuilder<F = Felt>>(&self, builder: &mut AB) {
        // The generated, globally-CSE'd evaluators: same constraint values in
        // the same global order as the hand-written definitions, machine-checked
        // by tests/generated_drift.rs. The definitions themselves remain
        // available via `eval_handwritten`.
        match self {
            Self::Core => constraints::generated::eval_core(builder),
            Self::Chiplets => constraints::generated::eval_chiplets(builder),
            Self::Poseidon2Permutation => {
                constraints::generated::eval_poseidon2_permutation(builder)
            },
        }
    }
}

impl<LB> LookupAir<LB> for MidenAir
where
    LB: MainLookupBuilder + ChipletLookupBuilder + Poseidon2PermutationLookupBuilder,
{
    fn num_columns(&self) -> usize {
        match self {
            Self::Core => CoreAir.lookup_num_columns(),
            Self::Chiplets => ChipletsAir.lookup_num_columns(),
            Self::Poseidon2Permutation => Poseidon2PermutationAir.lookup_num_columns(),
        }
    }

    fn column_shape(&self) -> &[usize] {
        MidenAir::column_shape(*self)
    }

    fn max_message_width(&self) -> usize {
        match self {
            Self::Core => CoreAir.lookup_max_message_width(),
            Self::Chiplets => ChipletsAir.lookup_max_message_width(),
            Self::Poseidon2Permutation => Poseidon2PermutationAir.lookup_max_message_width(),
        }
    }

    fn num_bus_ids(&self) -> usize {
        match self {
            Self::Core => CoreAir.lookup_num_bus_ids(),
            Self::Chiplets => ChipletsAir.lookup_num_bus_ids(),
            Self::Poseidon2Permutation => Poseidon2PermutationAir.lookup_num_bus_ids(),
        }
    }

    fn eval(&self, builder: &mut LB) {
        match self {
            Self::Core => CoreAir.lookup_eval(builder),
            Self::Chiplets => ChipletsAir.lookup_eval(builder),
            Self::Poseidon2Permutation => Poseidon2PermutationAir.lookup_eval(builder),
        }
    }

    fn eval_boundary<B>(&self, boundary: &mut B)
    where
        B: BoundaryBuilder<F = LB::F, EF = LB::EF>,
    {
        match self {
            Self::Core => CoreAir.lookup_eval_boundary(boundary),
            Self::Chiplets => ChipletsAir.lookup_eval_boundary(boundary),
            Self::Poseidon2Permutation => Poseidon2PermutationAir.lookup_eval_boundary(boundary),
        }
    }
}

// MIDEN MULTI-AIR
// ================================================================================================

/// The cross-AIR statement for the Miden VM proof.
///
/// AIR instances come from [`AIRS`], and the external reduction combines the trace-length-weighted
/// normalized LogUp sums with the open-bus boundary corrections.
///
/// Instance order is `[Core, Chiplets, Poseidon2Permutation]`; every per-AIR slice follows that
/// ordering.
#[derive(Copy, Clone, Debug)]
pub struct MidenMultiAir;

impl MidenMultiAir {
    /// Construct the Miden multi-AIR statement marker.
    pub const fn new() -> Self {
        Self
    }
}

impl Default for MidenMultiAir {
    fn default() -> Self {
        Self::new()
    }
}

impl<EF: ExtensionField<Felt>> MultiAir<Felt, EF> for MidenMultiAir {
    type Air = MidenAir;

    fn airs(&self) -> &[MidenAir] {
        &AIRS
    }

    fn num_air_inputs(&self) -> usize {
        NUM_PUBLIC_VALUES
    }

    fn max_aux_inputs(&self) -> usize {
        // aux_inputs = program hash (1 word) + deferred root (1 word) + the var-len
        // kernel-digest group: one `Word` per kernel procedure, capped at
        // `KernelDescriptor::MAX_NUM_PROCEDURES`.
        AUX_KERNEL_DIGESTS + KernelDescriptor::MAX_NUM_PROCEDURES * WORD_SIZE
    }

    /// Absorb statement-owned public inputs into the Fiat-Shamir challenger.
    ///
    /// One rate-aligned block: `[CLAIM_HASH (4) | deferred_root (4)]`, where `CLAIM_HASH` is the
    /// canonical execution-claim commitment (see `miden_core::program::ExecutionClaim`) over
    /// `program_hash ‖ kernel_H ‖ stack_inputs ‖ stack_outputs`. With the relation digest
    /// pre-loaded in the challenger (see `config`), the transcript state after this block
    /// realizes the factored statement binding `H(RELATION_DIGEST ‖ CLAIM_HASH ‖ D)`.
    ///
    /// The kernel digests enter the transcript only through `kernel_H` (see
    /// [`hash_kernel_digests`]); the raw stack I/O and digest list remain public values for
    /// constraint evaluation and are not separately absorbed.
    fn observe<C: CanObserve<Felt>>(
        &self,
        challenger: &mut C,
        air_inputs: &[Felt],
        aux_inputs: &[Felt],
        _log_trace_heights: &[u8],
    ) {
        assert_eq!(air_inputs.len(), NUM_PUBLIC_VALUES, "unexpected public-value count");
        assert!(
            aux_inputs.len() >= AUX_KERNEL_DIGESTS,
            "aux inputs shorter than the fixed program-hash + deferred-root prefix"
        );

        let kernel_h = hash_kernel_digests(&aux_inputs[AUX_KERNEL_DIGESTS..]);
        let program_hash = &aux_inputs[AUX_PROGRAM_HASH..AUX_PROGRAM_HASH + WORD_SIZE];
        let deferred_root = &aux_inputs[AUX_DEFERRED_ROOT..AUX_DEFERRED_ROOT + WORD_SIZE];

        // Canonical claim encoding P ‖ K ‖ I ‖ O; the offset layout of
        // `ExecutionClaim::to_elements`, pinned by `observe_matches_execution_claim_commitment`.
        let mut claim = [Felt::ZERO; NUM_CLAIM_ELEMENTS];
        claim[0..WORD_SIZE].copy_from_slice(program_hash);
        claim[WORD_SIZE..2 * WORD_SIZE].copy_from_slice(&kernel_h);
        claim[2 * WORD_SIZE..].copy_from_slice(air_inputs);
        let claim_hash = miden_core::program::claim_commitment(&claim);

        for &v in claim_hash.as_elements().iter().chain(deferred_root) {
            challenger.observe(v);
        }
    }

    /// Cross-AIR LogUp closure: each AIR commits `sigma_prime_i = sigma_i / n_i`, so the
    /// trace-length-weighted sum `sum_i(n_i * sigma_prime_i)` plus the per-trace boundary
    /// corrections must vanish. Boundary corrections are added once and are not trace-length
    /// scaled. `aux_values` and `log_trace_heights` are parallel in instance order. `aux_inputs`
    /// carries the program hash and deferred root followed by kernel digests.
    fn eval_external(
        &self,
        challenges: &[EF],
        air_inputs: &[Felt],
        aux_inputs: &[Felt],
        aux_values: &[&[EF]],
        log_trace_heights: &[u8],
    ) -> Result<Vec<EF>, ReductionError> {
        if aux_values.len() != AIRS.len() {
            return Err(format!(
                "expected aux values for {} AIRs, got {}",
                AIRS.len(),
                aux_values.len()
            )
            .into());
        }
        if log_trace_heights.len() != AIRS.len() {
            return Err(format!(
                "expected log heights for {} AIRs, got {}",
                AIRS.len(),
                log_trace_heights.len()
            )
            .into());
        }
        if challenges.len() != trace::AUX_TRACE_RAND_CHALLENGES {
            return Err(format!(
                "expected {} aux trace challenges, got {}",
                trace::AUX_TRACE_RAND_CHALLENGES,
                challenges.len()
            )
            .into());
        }
        if air_inputs.len() != NUM_PUBLIC_VALUES {
            return Err(format!(
                "expected {NUM_PUBLIC_VALUES} public values, got {}",
                air_inputs.len()
            )
            .into());
        }
        if aux_inputs.len() < AUX_KERNEL_DIGESTS {
            return Err(format!(
                "aux_inputs length {} is shorter than the fixed prefix {AUX_KERNEL_DIGESTS}",
                aux_inputs.len()
            )
            .into());
        }
        let max_aux_inputs = <MidenMultiAir as MultiAir<Felt, EF>>::max_aux_inputs(self);
        if aux_inputs.len() > max_aux_inputs {
            return Err(format!(
                "aux_inputs length {} exceeds maximum {max_aux_inputs}",
                aux_inputs.len()
            )
            .into());
        }
        let challenges = Challenges::<EF>::new(
            challenges[0],
            challenges[1],
            MIDEN_MAX_MESSAGE_WIDTH,
            BusId::COUNT,
        );

        let mut weighted_aux_sum = EF::ZERO;
        let mut boundary_correction = EF::ZERO;
        for ((air, values), &log_height) in
            AIRS.iter().copied().zip(aux_values.iter()).zip(log_trace_heights)
        {
            boundary_correction += air.boundary_correction(&challenges, air_inputs, aux_inputs)?;
            let expected = <MidenAir as LiftedAir<Felt, EF>>::num_aux_values(&air);
            if values.len() != expected {
                return Err(format!(
                    "{} expects {expected} aux boundary values, got {}",
                    air.name(),
                    values.len()
                )
                .into());
            }

            let trace_length = 1_u64.checked_shl(u32::from(log_height)).ok_or_else(|| {
                ReductionError::from(format!(
                    "{} log trace height {log_height} does not fit in u64",
                    air.name()
                ))
            })?;
            weighted_aux_sum +=
                values.iter().copied().sum::<EF>() * Felt::new_unchecked(trace_length);
        }

        Ok(vec![weighted_aux_sum + boundary_correction])
    }
}

// KERNEL DIGEST SUMMARY HASH
// ================================================================================================

/// Computes `kernel_H`, the fixed-size commitment to the kernel-procedure digests.
///
/// This is the canonical [`KernelDescriptor::commitment`] value expressed over the flattened digest
/// felts: the domain-tagged linear hash (`hash_elements_in_domain` with
/// [`miden_core::program::KERNEL_DOMAIN_TAG`]) of `kernel_felts`. The empty digest list yields
/// the canonical empty-input value under the same domain.
///
/// `kernel_H` is absorbed into the Fiat-Shamir transcript in place of the unbounded kernel
/// digest list, committing to the kernel with a fixed-size value.
pub fn hash_kernel_digests(kernel_felts: &[Felt]) -> [Felt; WORD_SIZE] {
    assert!(
        kernel_felts.len().is_multiple_of(WORD_SIZE),
        "kernel digest felts must be whole words"
    );
    assert!(
        kernel_felts.len() <= KernelDescriptor::MAX_NUM_PROCEDURES * WORD_SIZE,
        "kernel digest felts exceed KernelDescriptor::MAX_NUM_PROCEDURES"
    );

    hash_kernel_input_felts(kernel_felts)
}

fn hash_kernel_input_felts(kernel_felts: &[Felt]) -> [Felt; WORD_SIZE] {
    miden_core::chiplets::hasher::hash_elements_in_domain(
        kernel_felts,
        miden_core::program::KERNEL_DOMAIN_TAG,
    )
    .into()
}

// REDUCED-AUX BOUNDARY BUILDER
// ================================================================================================

/// `BoundaryBuilder` impl that reduces each emitted interaction to its LogUp denominator
/// contribution `multiplicity / encode(msg)` and sums them into a running `EF` accumulator.
///
/// Boundary correction is computed from the structured boundary messages emitted by each AIR.
///
/// Denominators are `alpha + sum_i beta^i * field_i` with random `alpha, beta`; on any
/// legitimate proof they are non-zero with overwhelming probability. A malformed proof can still
/// drive a denominator to zero, so the reducer captures the first failure and surfaces it as a
/// [`ReductionError`] to the verifier rather than panicking.
struct ReduceBoundaryBuilder<'a, EF: ExtensionField<Felt>> {
    challenges: &'a Challenges<EF>,
    public_values: &'a [Felt],
    var_len_public_inputs: &'a [&'a [Felt]],
    sum: EF,
    error: Option<ReductionError>,
}

impl<'a, EF: ExtensionField<Felt>> ReduceBoundaryBuilder<'a, EF> {
    fn finalize(self) -> Result<EF, ReductionError> {
        match self.error {
            Some(err) => Err(err),
            None => Ok(self.sum),
        }
    }
}

impl<'a, EF: ExtensionField<Felt>> BoundaryBuilder for ReduceBoundaryBuilder<'a, EF> {
    type F = Felt;
    type EF = EF;

    fn public_values(&self) -> &[Felt] {
        self.public_values
    }

    fn var_len_public_inputs(&self) -> &[&[Felt]] {
        self.var_len_public_inputs
    }

    fn insert<M>(&mut self, _name: &'static str, multiplicity: Felt, msg: M)
    where
        M: LookupMessage<Felt, EF>,
    {
        if self.error.is_some() {
            return;
        }
        match msg.encode(self.challenges).try_inverse() {
            Some(inv) => self.sum += inv * multiplicity,
            None => {
                self.error = Some("LogUp boundary denominator was zero".into());
            },
        }
    }
}

// TESTS
// ================================================================================================

#[cfg(test)]
mod tests {
    use alloc::string::ToString;

    use miden_core::field::{PrimeCharacteristicRing, QuadFelt};

    use super::*;

    /// Guards the static `constraint_degree` override: if an AIR change moves the symbolic
    /// degree away from the declared value, the override must be updated.
    #[test]
    fn constraint_degree_override_matches_symbolic() {
        for air in AIRS {
            let symbolic = ConstraintDegrees::from_air::<Felt, QuadFelt, _>(&air);
            let declared = <MidenAir as LiftedAir<Felt, QuadFelt>>::constraint_degree(&air);
            assert_eq!(declared, symbolic, "static constraint_degree override is stale");
        }
    }

    #[test]
    fn eval_external_weights_normalized_sums_by_trace_length() {
        let multi_air = MidenMultiAir::new();
        let raw_challenges = [QuadFelt::from_u32(7), QuadFelt::from_u32(11)];
        let air_inputs = vec![Felt::ZERO; NUM_PUBLIC_VALUES];
        let aux_inputs = vec![Felt::ZERO; AUX_KERNEL_DIGESTS];
        let normalized_sums =
            [QuadFelt::from_u32(13), QuadFelt::from_u32(17), QuadFelt::from_u32(19)];
        let core_values = [normalized_sums[0]];
        let chiplets_values = [normalized_sums[1]];
        let poseidon2_values = [normalized_sums[2]];
        let aux_values: [&[QuadFelt]; MIDEN_AIR_COUNT] =
            [&core_values, &chiplets_values, &poseidon2_values];
        let log_trace_heights = [6, 9, 7];

        let lookup_challenges = Challenges::new(
            raw_challenges[0],
            raw_challenges[1],
            MIDEN_MAX_MESSAGE_WIDTH,
            BusId::COUNT,
        );
        let mut boundary_correction = QuadFelt::ZERO;
        for air in AIRS {
            boundary_correction +=
                air.boundary_correction(&lookup_challenges, &air_inputs, &aux_inputs).unwrap();
        }

        let result = <MidenMultiAir as MultiAir<Felt, QuadFelt>>::eval_external(
            &multi_air,
            &raw_challenges,
            &air_inputs,
            &aux_inputs,
            &aux_values,
            &log_trace_heights,
        )
        .unwrap();

        let weighted_sum = normalized_sums
            .iter()
            .zip(log_trace_heights)
            .map(|(&value, log_height)| value * Felt::new_unchecked(1_u64 << u32::from(log_height)))
            .sum::<QuadFelt>();
        assert_eq!(result, vec![weighted_sum + boundary_correction]);
    }

    #[test]
    fn eval_external_rejects_partial_kernel_digest() {
        let challenges =
            [QuadFelt::from(Felt::new_unchecked(3)), QuadFelt::from(Felt::new_unchecked(5))];
        let air_inputs = vec![Felt::ZERO; NUM_PUBLIC_VALUES];
        let mut aux_inputs = vec![Felt::ZERO; AUX_KERNEL_DIGESTS];
        aux_inputs.push(Felt::ONE);
        let zero = QuadFelt::from(Felt::ZERO);
        let core_aux = [zero];
        let chiplets_aux = [zero];
        let poseidon2_aux = [zero];
        let aux_values = [core_aux.as_slice(), chiplets_aux.as_slice(), poseidon2_aux.as_slice()];

        let err = MidenMultiAir::new()
            .eval_external(&challenges, &air_inputs, &aux_inputs, &aux_values, &[8, 8, 8])
            .unwrap_err();

        assert!(err.to_string().contains("kernel digest felts length 1 is not a multiple of 4"));
    }

    #[test]
    fn eval_external_rejects_too_many_kernel_digests() {
        let challenges =
            [QuadFelt::from(Felt::new_unchecked(3)), QuadFelt::from(Felt::new_unchecked(5))];
        let air_inputs = vec![Felt::ZERO; NUM_PUBLIC_VALUES];
        let max_aux_inputs = AUX_KERNEL_DIGESTS + KernelDescriptor::MAX_NUM_PROCEDURES * WORD_SIZE;
        let actual_aux_inputs = max_aux_inputs + WORD_SIZE;
        let aux_inputs = vec![Felt::ZERO; actual_aux_inputs];
        let zero = QuadFelt::from(Felt::ZERO);
        let core_aux = [zero];
        let chiplets_aux = [zero];
        let poseidon2_aux = [zero];
        let aux_values = [core_aux.as_slice(), chiplets_aux.as_slice(), poseidon2_aux.as_slice()];

        let err = MidenMultiAir::new()
            .eval_external(&challenges, &air_inputs, &aux_inputs, &aux_values, &[8, 8, 8])
            .unwrap_err();

        assert!(err.to_string().contains(&format!(
            "aux_inputs length {actual_aux_inputs} exceeds maximum {max_aux_inputs}"
        )));
    }

    #[test]
    fn hash_kernel_digests_matches_kernel_descriptor_commitment() {
        // The transcript-side helper and `KernelDescriptor::commitment` are two computations of
        // the same normative value; this pins them together (including the empty kernel).
        use miden_core::Word;

        let word = |a: u64| -> Word {
            [Felt::new_unchecked(a), Felt::new_unchecked(a + 1), Felt::ZERO, Felt::ONE].into()
        };
        for procs in [vec![], vec![word(10)], vec![word(10), word(20), word(30)]] {
            let descriptor = KernelDescriptor::from_hashes(procs).unwrap();
            let flattened: Vec<Felt> =
                descriptor.proc_hashes().iter().flat_map(|w| w.as_elements().to_vec()).collect();
            assert_eq!(
                Word::new(hash_kernel_digests(&flattened)),
                descriptor.commitment(),
                "hash_kernel_digests diverged from KernelDescriptor::commitment"
            );
        }
    }

    #[test]
    #[should_panic(expected = "kernel digest felts exceed KernelDescriptor::MAX_NUM_PROCEDURES")]
    fn hash_kernel_digests_rejects_too_many_digest_felts() {
        let kernel_felts = vec![Felt::ZERO; (KernelDescriptor::MAX_NUM_PROCEDURES + 1) * WORD_SIZE];

        let _ = hash_kernel_digests(&kernel_felts);
    }

    #[test]
    fn observe_matches_execution_claim_commitment() {
        // The transcript's statement block must open with exactly
        // `ExecutionClaim::commitment()` for the same statement, followed by the deferred
        // root — pinning `observe`'s inline claim encoding to the canonical one.
        use miden_core::{field::QuadFelt, program::ExecutionClaim};

        #[derive(Default)]
        struct FeltSink {
            observed: Vec<Felt>,
        }
        impl CanObserve<Felt> for FeltSink {
            fn observe(&mut self, value: Felt) {
                self.observed.push(value);
            }
        }

        let word = |a: u64| -> Word {
            [
                Felt::new_unchecked(a),
                Felt::new_unchecked(a + 1),
                Felt::new_unchecked(a + 2),
                Felt::new_unchecked(a + 3),
            ]
            .into()
        };
        let kernel = KernelDescriptor::from_hashes(vec![word(50), word(60)]).unwrap();
        let program_hash = word(1);
        let stack_inputs =
            StackInputs::new(&[Felt::new_unchecked(5), Felt::new_unchecked(6)]).unwrap();
        let stack_outputs = StackOutputs::new(&[Felt::new_unchecked(7)]).unwrap();
        let deferred_root = word(90);

        let claim = ExecutionClaim::from_program_info(
            ProgramInfo::new(program_hash, kernel.clone()),
            stack_inputs,
            stack_outputs,
        );

        // air_inputs = I ‖ O; aux_inputs = P ‖ D ‖ kernel digest felts.
        let mut air_inputs = [Felt::ZERO; NUM_PUBLIC_VALUES];
        air_inputs[0..MIN_STACK_DEPTH].copy_from_slice(&stack_inputs[..]);
        air_inputs[MIN_STACK_DEPTH..].copy_from_slice(&stack_outputs[..]);
        let mut aux_inputs: Vec<Felt> = Vec::new();
        aux_inputs.extend(program_hash.as_elements());
        aux_inputs.extend(deferred_root.as_elements());
        aux_inputs.extend(Word::words_as_elements(kernel.proc_hashes()));

        let mut sink = FeltSink::default();
        <MidenMultiAir as MultiAir<Felt, QuadFelt>>::observe(
            &MidenMultiAir::new(),
            &mut sink,
            &air_inputs,
            &aux_inputs,
            &[10, 10, 10],
        );

        let mut expected: Vec<Felt> = claim.commitment().as_elements().to_vec();
        expected.extend(deferred_root.as_elements());
        assert_eq!(sink.observed, expected, "observe must emit [CLAIM_HASH | D]");
    }

    #[test]
    #[should_panic(
        expected = "aux inputs shorter than the fixed program-hash + deferred-root prefix"
    )]
    fn observe_rejects_short_aux_inputs() {
        #[derive(Default)]
        struct FeltSink {
            observed: Vec<Felt>,
        }

        impl CanObserve<Felt> for FeltSink {
            fn observe(&mut self, value: Felt) {
                self.observed.push(value);
            }
        }

        let mut challenger = FeltSink::default();
        let air_inputs = vec![Felt::ZERO; NUM_PUBLIC_VALUES];
        let multi_air = MidenMultiAir::new();

        <MidenMultiAir as MultiAir<Felt, QuadFelt>>::observe(
            &multi_air,
            &mut challenger,
            &air_inputs,
            &[],
            &[8, 8, 8],
        );
    }
}