translator_flavor.hpp

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// === AUDIT STATUS ===
// internal:    { status: Planned, auditors: [], commit: }
// external_1:  { status: not started, auditors: [], commit: }
// external_2:  { status: not started, auditors: [], commit: }
// =====================
 
#pragma once
 
#include "barretenberg/commitment_schemes/commitment_key.hpp"
#include "barretenberg/commitment_schemes/kzg/kzg.hpp"
#include "barretenberg/commitment_schemes/small_subgroup_ipa/small_subgroup_ipa_utils.hpp"
#include "barretenberg/common/ref_vector.hpp"
#include "barretenberg/ecc/curves/bn254/bn254.hpp"
#include "barretenberg/flavor/flavor.hpp"
#include "barretenberg/flavor/flavor_macros.hpp"
#include "barretenberg/flavor/partially_evaluated_multivariates.hpp"
#include "barretenberg/flavor/relation_definitions.hpp"
#include "barretenberg/flavor/repeated_commitments_data.hpp"
#include "barretenberg/polynomials/polynomial.hpp"
#include "barretenberg/polynomials/univariate.hpp"
#include "barretenberg/relations/relation_parameters.hpp"
#include "barretenberg/relations/relation_tuple_helpers.hpp"
#include "barretenberg/relations/translator_vm/translator_decomposition_relation.hpp"
#include "barretenberg/relations/translator_vm/translator_decomposition_short_relation.hpp"
#include "barretenberg/relations/translator_vm/translator_delta_range_constraint_relation.hpp"
#include "barretenberg/relations/translator_vm/translator_delta_range_constraint_short_relation.hpp"
#include "barretenberg/relations/translator_vm/translator_extra_relations.hpp"
#include "barretenberg/relations/translator_vm/translator_extra_short_relations.hpp"
#include "barretenberg/relations/translator_vm/translator_non_native_field_relation.hpp"
#include "barretenberg/relations/translator_vm/translator_non_native_field_short_relation.hpp"
#include "barretenberg/relations/translator_vm/translator_permutation_relation.hpp"
#include "barretenberg/relations/translator_vm/translator_permutation_short_relation.hpp"
#include "barretenberg/relations/translator_vm/translator_shiftable_first_coeff_zero_relation.hpp"
#include "barretenberg/relations/translator_vm/translator_shiftable_first_coeff_zero_short_relation.hpp"
#include "barretenberg/translator_vm/translator_circuit_builder.hpp"
#include "barretenberg/translator_vm/translator_fixed_vk.hpp"
#include "barretenberg/translator_vm/translator_selectors.hpp"
 
namespace bb {
 
namespace detail {
template <typename> struct ref_array_extent;
template <typename T, std::size_t N> struct ref_array_extent<RefArray<T, N>> {
    static constexpr std::size_t value = N;
};
} // namespace detail
 
class TranslatorFlavor {
 
  public:
    using CircuitBuilder = TranslatorCircuitBuilder;
    using Curve = curve::BN254;
    using PCS = KZG<Curve>;
    using GroupElement = Curve::Element;
    using Commitment = Curve::AffineElement;
    using CommitmentKey = bb::CommitmentKey<Curve>;
    using VerifierCommitmentKey = bb::VerifierCommitmentKey<Curve>;
    using FF = Curve::ScalarField;
    using BF = Curve::BaseField;
    using Polynomial = bb::Polynomial<FF>;
    using Codec = FrCodec;
    using HashFunction = crypto::Poseidon2<crypto::Poseidon2Bn254ScalarFieldParams>;
    using Transcript = BaseTranscript<Codec, HashFunction>;
 
    // indicates when evaluating sumcheck, edges must be extended to be MAX_PARTIAL_RELATION_LENGTH
    static constexpr bool USE_SHORT_MONOMIALS = false;
 
    // Indicates that this flavor runs with ZK Sumcheck.
    static constexpr bool HasZK = true;
    // Translator has no disabled rows at the top of the trace.
    static constexpr size_t TRACE_OFFSET = 0;
    // Translator proof size and its recursive verifier circuit are genuinely fixed, hence no padding is needed.
    static constexpr bool USE_PADDING = false;
    // Important: these constants cannot be arbitrarily changed - please consult with a member of the Crypto team if
    // they become too small.
 
    // The number of entities added for ZK (gemini_masking_poly)
    static constexpr size_t NUM_MASKING_POLYNOMIALS = 1;
 
    // None of this parameters can be changed
    // Number of wires representing the op queue whose commitments are going to be checked against those from the
    // final round of merge
    static constexpr size_t NUM_OP_QUEUE_WIRES = 4;
 
    // How many mini_circuit_size polynomials are concatenated in one concatenated poly
    static constexpr size_t CONCATENATION_GROUP_SIZE = 16;
 
    // The fixed log size of Translator mini circuit. It should be determined by the size of the EccOpQueue.
    static constexpr size_t LOG_MINI_CIRCUIT_SIZE = CONST_TRANSLATOR_MINI_CIRCUIT_LOG_SIZE;
 
    // Log of size of concatenated and ordered polynomials
    static constexpr size_t CONST_TRANSLATOR_LOG_N = LOG_MINI_CIRCUIT_SIZE + numeric::get_msb(CONCATENATION_GROUP_SIZE);
 
    // For the translator, the genuine and virtual log circuit size coincide
    static constexpr size_t VIRTUAL_LOG_N = CONST_TRANSLATOR_LOG_N;
 
    static constexpr size_t MINI_CIRCUIT_SIZE = 1UL << LOG_MINI_CIRCUIT_SIZE;
 
    // The number of concatenated polynomials (4 range constraint groups + 1 non-range group)
    static constexpr size_t NUM_CONCATENATED_POLYS = 5;
 
    // The step in the DeltaRangeConstraint relation i.e. the maximum difference between two consecutive values
    static constexpr size_t SORT_STEP = 3;
 
    // Number of wires
    static constexpr size_t NUM_WIRES = CircuitBuilder::NUM_WIRES;
 
    // The result of evaluating the polynomials in the nonnative form in translator circuit, stored as limbs and
    // referred to as accumulated_result. This is reconstructed in it's base field form and sent to the verifier
    // responsible for checking it against the evaluations received from ECCVM.
    static constexpr size_t RESULT_ROW = CircuitBuilder::RESULT_ROW;
 
    // Number of random ops found at he end of Translator trace multiplied by 2 as each accumulation gates occupies two
    // rows.
    static constexpr size_t NUM_MASKED_ROWS_END = CircuitBuilder::NUM_RANDOM_OPS_END * 2;
 
    // Maximum number of random masking values any ordered polynomial will have at the end
    // Total scattered masking positions = CONCATENATION_GROUP_SIZE * NUM_MASKED_ROWS_END
    // This is the space reserved at the end of each ordered polynomial (contiguous)
    static constexpr size_t MAX_RANDOM_VALUES_PER_ORDERED = CONCATENATION_GROUP_SIZE * NUM_MASKED_ROWS_END;
 
    // Index at which random coefficients start (for zk) within Translator trace.
    // The first 2 rows are zeros for polynomial shiftability (one op's worth of rows).
    static constexpr size_t RANDOMNESS_START = 2;
 
    // The bitness of the range constraint
    static constexpr size_t MICRO_LIMB_BITS = CircuitBuilder::MICRO_LIMB_BITS;
 
    // Number of bits in a binary limb
    // This is not a configurable value. Relations are sepcifically designed for it to be 68
    static constexpr size_t NUM_LIMB_BITS = CircuitBuilder::NUM_LIMB_BITS;
 
    using GrandProductRelations = std::tuple<TranslatorPermutationRelation<FF>>;
    // define the tuple of Relations that comprise the Sumcheck relation
    template <typename FF>
    using Relations_ = std::tuple<TranslatorPermutationRelation<FF>,
                                  TranslatorDeltaRangeConstraintRelation<FF>,
                                  TranslatorOpcodeConstraintRelation<FF>,
                                  TranslatorAccumulatorTransferRelation<FF>,
                                  TranslatorDecompositionRelation<FF>,
                                  TranslatorNonNativeFieldRelation<FF>,
                                  TranslatorZeroConstraintsRelation<FF>,
                                  TranslatorShiftableFirstCoeffZeroRelation<FF>>;
    using Relations = Relations_<FF>;
 
    static constexpr size_t NUM_SUBRELATIONS = compute_number_of_subrelations<Relations>();
    using SubrelationSeparators = std::array<FF, NUM_SUBRELATIONS - 1>;
 
    static constexpr size_t MAX_PARTIAL_RELATION_LENGTH = compute_max_partial_relation_length<Relations>();
 
    // BATCHED_RELATION_PARTIAL_LENGTH = algebraic degree of sumcheck relation *after* multiplying by the `pow_zeta`
    // random polynomial e.g. For \sum(x) [A(x) * B(x) + C(x)] * PowZeta(X), relation length = 2 and random relation
    // length = 3.
    // The degree has to be further increased because the relation is multiplied by the Row Disabling Polynomial
    // total degree = sumcheck relation degree + 1 (PowZeta) + 1 (masking)
    static constexpr size_t BATCHED_RELATION_PARTIAL_LENGTH = MAX_PARTIAL_RELATION_LENGTH + 2;
    static_assert(BATCHED_RELATION_PARTIAL_LENGTH == Curve::LIBRA_UNIVARIATES_LENGTH,
                  "LIBRA_UNIVARIATES_LENGTH must be equal to Translator::BATCHED_RELATION_PARTIAL_LENGTH");
    static constexpr size_t NUM_RELATIONS = std::tuple_size_v<Relations>;
 
    static constexpr size_t num_frs_comm = FrCodec::calc_num_fields<Commitment>();
    static constexpr size_t num_frs_fr = FrCodec::calc_num_fields<FF>();
    static constexpr size_t num_frs_fq = FrCodec::calc_num_fields<BF>();
 
    template <typename DataType_> class PrecomputedEntities {
      public:
        bool operator==(const PrecomputedEntities& other) const = default;
        using DataType = DataType_;
        DEFINE_FLAVOR_MEMBERS(DataType,
                              ordered_extra_range_constraints_numerator, // column 0
                              lagrange_first,                            // column 1
                              lagrange_last,                             // column 2
                              lagrange_odd_in_minicircuit,               // column 3
                              lagrange_even_in_minicircuit,              // column 4
                              lagrange_result_row,                       // column 5
                              lagrange_last_in_minicircuit,              // column 6
                              lagrange_masking,                          // column 7
                              lagrange_mini_masking,                     // column 8
                              lagrange_real_last,                        // column 9
                              lagrange_ordered_masking);                 // column 10
    };
 
    template <typename DataType> class ConcatenatedPolynomials {
      public:
        DEFINE_FLAVOR_MEMBERS(DataType,
                              concatenated_range_constraints_0, // column 0
                              concatenated_range_constraints_1, // column 1
                              concatenated_range_constraints_2, // column 2
                              concatenated_range_constraints_3, // column 3
                              concatenated_non_range)           // column 4
    };
    template <typename DataType> class NonRangeMainWires {
      public:
        DEFINE_FLAVOR_MEMBERS(DataType,
                              p_x_low_limbs,               // column 0
                              p_x_high_limbs,              // column 1
                              p_y_low_limbs,               // column 2
                              p_y_high_limbs,              // column 3
                              z_low_limbs,                 // column 4
                              z_high_limbs,                // column 5
                              accumulators_binary_limbs_0, // column 6
                              accumulators_binary_limbs_1, // column 7
                              accumulators_binary_limbs_2, // column 8
                              accumulators_binary_limbs_3, // column 9
                              quotient_low_binary_limbs,   // column 10
                              quotient_high_binary_limbs,  // column 11
                              relation_wide_limbs)         // column 12
    };
 
    template <typename DataType> class RangeConstraintWires {
      public:
        DEFINE_FLAVOR_MEMBERS(DataType,
                              p_x_low_limbs_range_constraint_0,             // column 0
                              p_x_low_limbs_range_constraint_1,             // column 17
                              p_x_low_limbs_range_constraint_2,             // column 18
                              p_x_low_limbs_range_constraint_3,             // column 19
                              p_x_low_limbs_range_constraint_4,             // column 20
                              p_x_low_limbs_range_constraint_tail,          // column 21
                              p_x_high_limbs_range_constraint_0,            // column 22
                              p_x_high_limbs_range_constraint_1,            // column 23
                              p_x_high_limbs_range_constraint_2,            // column 24
                              p_x_high_limbs_range_constraint_3,            // column 25
                              p_x_high_limbs_range_constraint_4,            // column 26
                              p_x_high_limbs_range_constraint_tail,         // column 27
                              p_y_low_limbs_range_constraint_0,             // column 28
                              p_y_low_limbs_range_constraint_1,             // column 29
                              p_y_low_limbs_range_constraint_2,             // column 30
                              p_y_low_limbs_range_constraint_3,             // column 31
                              p_y_low_limbs_range_constraint_4,             // column 32
                              p_y_low_limbs_range_constraint_tail,          // column 33
                              p_y_high_limbs_range_constraint_0,            // column 34
                              p_y_high_limbs_range_constraint_1,            // column 35
                              p_y_high_limbs_range_constraint_2,            // column 36
                              p_y_high_limbs_range_constraint_3,            // column 37
                              p_y_high_limbs_range_constraint_4,            // column 38
                              p_y_high_limbs_range_constraint_tail,         // column 39
                              z_low_limbs_range_constraint_0,               // column 40
                              z_low_limbs_range_constraint_1,               // column 41
                              z_low_limbs_range_constraint_2,               // column 42
                              z_low_limbs_range_constraint_3,               // column 43
                              z_low_limbs_range_constraint_4,               // column 44
                              z_low_limbs_range_constraint_tail,            // column 45
                              z_high_limbs_range_constraint_0,              // column 46
                              z_high_limbs_range_constraint_1,              // column 47
                              z_high_limbs_range_constraint_2,              // column 48
                              z_high_limbs_range_constraint_3,              // column 49
                              z_high_limbs_range_constraint_4,              // column 50
                              z_high_limbs_range_constraint_tail,           // column 51
                              accumulator_low_limbs_range_constraint_0,     // column 52
                              accumulator_low_limbs_range_constraint_1,     // column 53
                              accumulator_low_limbs_range_constraint_2,     // column 54
                              accumulator_low_limbs_range_constraint_3,     // column 55
                              accumulator_low_limbs_range_constraint_4,     // column 56
                              accumulator_low_limbs_range_constraint_tail,  // column 57
                              accumulator_high_limbs_range_constraint_0,    // column 58
                              accumulator_high_limbs_range_constraint_1,    // column 59
                              accumulator_high_limbs_range_constraint_2,    // column 60
                              accumulator_high_limbs_range_constraint_3,    // column 61
                              accumulator_high_limbs_range_constraint_4,    // column 62
                              accumulator_high_limbs_range_constraint_tail, // column 63
                              quotient_low_limbs_range_constraint_0,        // column 64
                              quotient_low_limbs_range_constraint_1,        // column 65
                              quotient_low_limbs_range_constraint_2,        // column 66
                              quotient_low_limbs_range_constraint_3,        // column 67
                              quotient_low_limbs_range_constraint_4,        // column 68
                              quotient_low_limbs_range_constraint_tail,     // column 69
                              quotient_high_limbs_range_constraint_0,       // column 70
                              quotient_high_limbs_range_constraint_1,       // column 71
                              quotient_high_limbs_range_constraint_2,       // column 72
                              quotient_high_limbs_range_constraint_3,       // column 73
                              quotient_high_limbs_range_constraint_4,       // column 74
                              quotient_high_limbs_range_constraint_tail,    // column 75
                              relation_wide_limbs_range_constraint_0,       // column 76
                              relation_wide_limbs_range_constraint_1,       // column 77
                              relation_wide_limbs_range_constraint_2,       // column 62
                              relation_wide_limbs_range_constraint_3);      // column 63
    };
 
    template <typename DataType>
    class NonOpQueueWiresToBeShiftedEntities : public NonRangeMainWires<DataType>,
                                               public RangeConstraintWires<DataType> {
      public:
        DEFINE_COMPOUND_GET_ALL(NonRangeMainWires<DataType>, RangeConstraintWires<DataType>)
    };
 
    template <typename DataType> class OpQueueWiresToBeShiftedEntities {
      public:
        DEFINE_FLAVOR_MEMBERS(DataType,
                              x_lo_y_hi, // column 0
                              x_hi_z_1,  // column 1
                              y_lo_z_2)  // column 2
    };
 
    template <typename DataType>
    class WireToBeShiftedEntities : public OpQueueWiresToBeShiftedEntities<DataType>,
                                    public NonOpQueueWiresToBeShiftedEntities<DataType> {
      public:
        DEFINE_COMPOUND_GET_ALL(OpQueueWiresToBeShiftedEntities<DataType>, NonOpQueueWiresToBeShiftedEntities<DataType>)
    };
 
    // Note: These are technically derived from wires but do not depend on challenges (like z_perm). They are committed
    // to in the wires commitment round.
    template <typename DataType> class OrderedRangeConstraints {
      public:
        DEFINE_FLAVOR_MEMBERS(DataType,
                              ordered_range_constraints_0,  // column 0
                              ordered_range_constraints_1,  // column 1
                              ordered_range_constraints_2,  // column 2
                              ordered_range_constraints_3,  // column 3
                              ordered_range_constraints_4); // column 4
    };
 
    template <typename DataType> class OpQueueWireNonshiftedEntities {
      public:
        DEFINE_FLAVOR_MEMBERS(DataType,
                              op // column 0
        );
    };
 
    template <typename DataType> class WireNonshiftedEntities : public OpQueueWireNonshiftedEntities<DataType> {
      public:
        DEFINE_COMPOUND_GET_ALL(OpQueueWireNonshiftedEntities<DataType>)
    };
 
    template <typename DataType> class DerivedWitnessEntities {
      public:
        DEFINE_FLAVOR_MEMBERS(DataType,
                              z_perm); // column 0
    };
    template <typename DataType>
    class WitnessEntities : public WireNonshiftedEntities<DataType>,
                            public WireToBeShiftedEntities<DataType>,
                            public OrderedRangeConstraints<DataType>,
                            public DerivedWitnessEntities<DataType>,
                            public ConcatenatedPolynomials<DataType> {
      public:
        DEFINE_COMPOUND_GET_ALL(WireNonshiftedEntities<DataType>,
                                WireToBeShiftedEntities<DataType>,
                                OrderedRangeConstraints<DataType>,
                                DerivedWitnessEntities<DataType>,
                                ConcatenatedPolynomials<DataType>)
 
        
        auto get_wires()
        {
            return concatenate(WireNonshiftedEntities<DataType>::get_all(),
                               WireToBeShiftedEntities<DataType>::get_all());
        };
 
        auto get_non_opqueue_wires_and_ordered_range_constraints()
        {
            return concatenate(ConcatenatedPolynomials<DataType>::get_all(),
                               OrderedRangeConstraints<DataType>::get_all());
        };
 
        auto get_all_to_be_shifted()
        {
            return concatenate(WireToBeShiftedEntities<DataType>::get_all(),
                               OrderedRangeConstraints<DataType>::get_all(),
                               DerivedWitnessEntities<DataType>::get_all());
        };
 
        auto get_concatenated() { return ConcatenatedPolynomials<DataType>::get_all(); }
 
        std::vector<RefVector<DataType>> get_groups_to_be_concatenated()
        {
            static DataType zero_value = DataType(0);
            return partition_minicircuit_wires_into_groups<DataType>(
                NonOpQueueWiresToBeShiftedEntities<DataType>::get_all(), zero_value);
        };
    };
 
    template <typename DataType> class OpQueueShiftedEntities {
      public:
        DEFINE_FLAVOR_MEMBERS(DataType,
                              x_lo_y_hi_shift, // column 0
                              x_hi_z_1_shift,  // column 1
                              y_lo_z_2_shift)  // column 2
    };
 
    template <typename DataType> class NonOpQueueShiftedEntities {
      public:
        DEFINE_FLAVOR_MEMBERS(DataType,
                              p_x_low_limbs_shift,                                // column 3
                              p_x_high_limbs_shift,                               // column 10
                              p_y_low_limbs_shift,                                // column 17
                              p_y_high_limbs_shift,                               // column 24
                              z_low_limbs_shift,                                  // column 31
                              z_high_limbs_shift,                                 // column 38
                              accumulators_binary_limbs_0_shift,                  // column 45
                              accumulators_binary_limbs_1_shift,                  // column 46
                              accumulators_binary_limbs_2_shift,                  // column 47
                              accumulators_binary_limbs_3_shift,                  // column 48
                              quotient_low_binary_limbs_shift,                    // column 61
                              quotient_high_binary_limbs_shift,                   // column 62
                              relation_wide_limbs_shift,                          // column 75
                              p_x_low_limbs_range_constraint_0_shift,             // column 4
                              p_x_low_limbs_range_constraint_1_shift,             // column 5
                              p_x_low_limbs_range_constraint_2_shift,             // column 6
                              p_x_low_limbs_range_constraint_3_shift,             // column 7
                              p_x_low_limbs_range_constraint_4_shift,             // column 8
                              p_x_low_limbs_range_constraint_tail_shift,          // column 9
                              p_x_high_limbs_range_constraint_0_shift,            // column 11
                              p_x_high_limbs_range_constraint_1_shift,            // column 12
                              p_x_high_limbs_range_constraint_2_shift,            // column 13
                              p_x_high_limbs_range_constraint_3_shift,            // column 14
                              p_x_high_limbs_range_constraint_4_shift,            // column 15
                              p_x_high_limbs_range_constraint_tail_shift,         // column 16
                              p_y_low_limbs_range_constraint_0_shift,             // column 18
                              p_y_low_limbs_range_constraint_1_shift,             // column 19
                              p_y_low_limbs_range_constraint_2_shift,             // column 20
                              p_y_low_limbs_range_constraint_3_shift,             // column 21
                              p_y_low_limbs_range_constraint_4_shift,             // column 22
                              p_y_low_limbs_range_constraint_tail_shift,          // column 23
                              p_y_high_limbs_range_constraint_0_shift,            // column 25
                              p_y_high_limbs_range_constraint_1_shift,            // column 26
                              p_y_high_limbs_range_constraint_2_shift,            // column 27
                              p_y_high_limbs_range_constraint_3_shift,            // column 28
                              p_y_high_limbs_range_constraint_4_shift,            // column 29
                              p_y_high_limbs_range_constraint_tail_shift,         // column 30
                              z_low_limbs_range_constraint_0_shift,               // column 32
                              z_low_limbs_range_constraint_1_shift,               // column 33
                              z_low_limbs_range_constraint_2_shift,               // column 34
                              z_low_limbs_range_constraint_3_shift,               // column 35
                              z_low_limbs_range_constraint_4_shift,               // column 36
                              z_low_limbs_range_constraint_tail_shift,            // column 37
                              z_high_limbs_range_constraint_0_shift,              // column 39
                              z_high_limbs_range_constraint_1_shift,              // column 40
                              z_high_limbs_range_constraint_2_shift,              // column 41
                              z_high_limbs_range_constraint_3_shift,              // column 42
                              z_high_limbs_range_constraint_4_shift,              // column 43
                              z_high_limbs_range_constraint_tail_shift,           // column 44
                              accumulator_low_limbs_range_constraint_0_shift,     // column 49
                              accumulator_low_limbs_range_constraint_1_shift,     // column 50
                              accumulator_low_limbs_range_constraint_2_shift,     // column 51
                              accumulator_low_limbs_range_constraint_3_shift,     // column 52
                              accumulator_low_limbs_range_constraint_4_shift,     // column 53
                              accumulator_low_limbs_range_constraint_tail_shift,  // column 54
                              accumulator_high_limbs_range_constraint_0_shift,    // column 55
                              accumulator_high_limbs_range_constraint_1_shift,    // column 56
                              accumulator_high_limbs_range_constraint_2_shift,    // column 57
                              accumulator_high_limbs_range_constraint_3_shift,    // column 58
                              accumulator_high_limbs_range_constraint_4_shift,    // column 59
                              accumulator_high_limbs_range_constraint_tail_shift, // column 60
                              quotient_low_limbs_range_constraint_0_shift,        // column 63
                              quotient_low_limbs_range_constraint_1_shift,        // column 64
                              quotient_low_limbs_range_constraint_2_shift,        // column 65
                              quotient_low_limbs_range_constraint_3_shift,        // column 66
                              quotient_low_limbs_range_constraint_4_shift,        // column 67
                              quotient_low_limbs_range_constraint_tail_shift,     // column 68
                              quotient_high_limbs_range_constraint_0_shift,       // column 69
                              quotient_high_limbs_range_constraint_1_shift,       // column 70
                              quotient_high_limbs_range_constraint_2_shift,       // column 71
                              quotient_high_limbs_range_constraint_3_shift,       // column 72
                              quotient_high_limbs_range_constraint_4_shift,       // column 73
                              quotient_high_limbs_range_constraint_tail_shift,    // column 74
                              relation_wide_limbs_range_constraint_0_shift,       // column 76
                              relation_wide_limbs_range_constraint_1_shift,       // column 77
                              relation_wide_limbs_range_constraint_2_shift,       // column 78
                              relation_wide_limbs_range_constraint_3_shift)       // column 79
    };
 
    template <typename DataType> class DerivedShiftedEntities {
      public:
        DEFINE_FLAVOR_MEMBERS(DataType,
                              ordered_range_constraints_0_shift, // column 80
                              ordered_range_constraints_1_shift, // column 81
                              ordered_range_constraints_2_shift, // column 82
                              ordered_range_constraints_3_shift, // column 83
                              ordered_range_constraints_4_shift, // column 84
                              z_perm_shift)                      // column 85
    };
 
    template <typename DataType>
    class ShiftedEntities : public OpQueueShiftedEntities<DataType>,
                            public NonOpQueueShiftedEntities<DataType>,
                            public DerivedShiftedEntities<DataType> {
      public:
        DEFINE_COMPOUND_GET_ALL(OpQueueShiftedEntities<DataType>,
                                NonOpQueueShiftedEntities<DataType>,
                                DerivedShiftedEntities<DataType>)
 
        
        auto get_pcs_shifted()
        {
            return concatenate(OpQueueShiftedEntities<DataType>::get_all(),
                               DerivedShiftedEntities<DataType>::get_all());
        }
 
        std::vector<RefVector<DataType>> get_groups_to_be_concatenated_shifted()
        {
            static DataType zero_value = DataType(0);
            return partition_minicircuit_wires_into_groups<DataType>(NonOpQueueShiftedEntities<DataType>::get_all(),
                                                                     zero_value);
        };
    };
 
    template <typename DataType> class MaskingEntities {
      public:
        DEFINE_FLAVOR_MEMBERS(DataType, gemini_masking_poly)
    };
 
    template <typename DataType>
    class AllEntities : public MaskingEntities<DataType>,
                        public PrecomputedEntities<DataType>,
                        public WitnessEntities<DataType>,
                        public ShiftedEntities<DataType> {
      public:
        DEFINE_COMPOUND_GET_ALL(MaskingEntities<DataType>,
                                PrecomputedEntities<DataType>,
                                WitnessEntities<DataType>,
                                ShiftedEntities<DataType>)
 
        
        auto get_concatenated() { return ConcatenatedPolynomials<DataType>::get_all(); };
 
        auto get_ordered_range_constraints() { return OrderedRangeConstraints<DataType>::get_all(); };
 
        auto get_pcs_unshifted()
        {
            return concatenate(
                MaskingEntities<DataType>::get_all(),                                     // gemini_masking_poly
                RefArray<DataType, 1>{ this->ordered_extra_range_constraints_numerator }, // non-computable precomputed
                WireNonshiftedEntities<DataType>::get_all(),                              // op (from merge protocol)
                OpQueueWiresToBeShiftedEntities<DataType>::get_all(), // x_lo_y_hi, x_hi_z_1, y_lo_z_2
                OrderedRangeConstraints<DataType>::get_all(),         // ordered_0..4
                DerivedWitnessEntities<DataType>::get_all(),          // z_perm
                ConcatenatedPolynomials<DataType>::get_all());        // concat_0..4
        }
 
        auto get_pcs_to_be_shifted()
        {
            return concatenate(OpQueueWiresToBeShiftedEntities<DataType>::get_all(), // x_lo_y_hi, x_hi_z_1, y_lo_z_2
                               OrderedRangeConstraints<DataType>::get_all(),         // ordered_0..4
                               DerivedWitnessEntities<DataType>::get_all(),          // z_perm
                               ConcatenatedPolynomials<DataType>::get_all());        // concat_0..4
        }
 
        auto get_shifted() { return ShiftedEntities<DataType>::get_all(); };
        auto get_pcs_shifted() { return ShiftedEntities<DataType>::get_pcs_shifted(); };
 
        auto get_full_circuit_entities()
        {
            return concatenate(MaskingEntities<DataType>::get_all(),
                               RefArray<DataType, 1>{ this->ordered_extra_range_constraints_numerator },
                               WireNonshiftedEntities<DataType>::get_all(),
                               OpQueueWiresToBeShiftedEntities<DataType>::get_all(),
                               OrderedRangeConstraints<DataType>::get_all(),
                               DerivedWitnessEntities<DataType>::get_all(),
                               ShiftedEntities<DataType>::get_pcs_shifted());
        }
 
        auto get_minicircuit_wires() { return NonOpQueueWiresToBeShiftedEntities<DataType>::get_all(); }
 
        auto get_minicircuit_wires_shifted() { return NonOpQueueShiftedEntities<DataType>::get_all(); }
 
        friend std::ostream& operator<<(std::ostream& os, const AllEntities& a)
        {
            os << "{ ";
            std::ios_base::fmtflags f(os.flags());
            auto entities = a.get_all();
            for (size_t i = 0; i < entities.size() - 1; i++) {
                os << "e[" << std::setw(2) << i << "] = " << (entities[i]) << ",\n";
            }
            os << "e[" << std::setw(2) << (entities.size() - 1) << "] = " << entities[entities.size() - 1] << " }";
 
            os.flags(f);
            return os;
        }
    };
 
    class AllValues : public AllEntities<FF> {
      public:
        using Base = AllEntities<FF>;
        using Base::Base;
    };
 
    // ========================================
    // Derived entity counts (from entity class sizes)
    // ========================================
    static constexpr size_t NUM_PRECOMPUTED_ENTITIES = PrecomputedEntities<FF>::_members_size;
    static constexpr size_t NUM_WIRES_NON_SHIFTED = WireNonshiftedEntities<FF>::_members_size;
    static constexpr size_t NUM_ORDERED_RANGE = OrderedRangeConstraints<FF>::_members_size;
 
    // Witness = WireNonshifted + WireToBeShifted + OrderedRange + Derived + Concatenated
    static constexpr size_t NUM_WITNESS_ENTITIES =
        WireNonshiftedEntities<FF>::_members_size + OpQueueWiresToBeShiftedEntities<FF>::_members_size +
        NonRangeMainWires<FF>::_members_size + RangeConstraintWires<FF>::_members_size +
        OrderedRangeConstraints<FF>::_members_size + DerivedWitnessEntities<FF>::_members_size +
        ConcatenatedPolynomials<FF>::_members_size;
 
    // Shifted = OpQueueShifted + NonOpQueueShifted + DerivedShifted
    static constexpr size_t NUM_SHIFTED_ENTITIES = OpQueueShiftedEntities<FF>::_members_size +
                                                   NonOpQueueShiftedEntities<FF>::_members_size +
                                                   DerivedShiftedEntities<FF>::_members_size;
 
    static constexpr size_t NUM_ALL_ENTITIES =
        NUM_MASKING_POLYNOMIALS + NUM_PRECOMPUTED_ENTITIES + NUM_WITNESS_ENTITIES + NUM_SHIFTED_ENTITIES;
 
    // All precomputed selectors except ordered_extra_range_constraints_numerator are computable
    static constexpr size_t NUM_COMPUTABLE_PRECOMPUTED = NUM_PRECOMPUTED_ENTITIES - 1;
 
    // Minicircuit wires: NonRangeMain + RangeConstraint (the non-op-queue wires that get shifted)
    static constexpr size_t NUM_MINICIRCUIT_WIRES =
        NonRangeMainWires<FF>::_members_size + RangeConstraintWires<FF>::_members_size;
    static_assert(NUM_MINICIRCUIT_WIRES == NonOpQueueShiftedEntities<FF>::_members_size,
                  "Shifted minicircuit wires must match unshifted");
    // 77 unshifted + 77 shifted minicircuit wire evaluations are sent mid-sumcheck
    static constexpr size_t NUM_MINICIRCUIT_EVALUATIONS = 2 * NUM_MINICIRCUIT_WIRES;
 
    // Number of evaluations sent in proof (all minus computable precomputed minus reconstructed concat evals)
    static constexpr size_t NUM_SENT_EVALUATIONS =
        NUM_ALL_ENTITIES - NUM_COMPUTABLE_PRECOMPUTED - NUM_CONCATENATED_POLYS;
    static constexpr size_t NUM_FULL_CIRCUIT_EVALUATIONS = NUM_SENT_EVALUATIONS - NUM_MINICIRCUIT_EVALUATIONS;
 
    // Total number of minicircuit wires across all concatenation groups
    static constexpr size_t NUM_CONCATENATED_WIRES = NUM_CONCATENATED_POLYS * CONCATENATION_GROUP_SIZE;
    static_assert(ConcatenatedPolynomials<FF>::_members_size == NUM_CONCATENATED_POLYS);
    static_assert(RangeConstraintWires<FF>::_members_size == (NUM_CONCATENATED_POLYS - 1) * CONCATENATION_GROUP_SIZE,
                  "Range constraint wires must fill exactly 4 concatenation groups");
 
    // PCS batch sizes
    // Note: op-queue to-be-shifted wires (x_lo_y_hi, x_hi_z_1, y_lo_z_2) are registered in BOTH the
    // unshifted and shifted PCS batches because the decomposition relation reads them in both forms.
    static constexpr size_t NUM_UNSHIFTED_WITNESSES_WITHOUT_CONCATENATED =
        WireNonshiftedEntities<FF>::_members_size + OpQueueWiresToBeShiftedEntities<FF>::_members_size +
        OrderedRangeConstraints<FF>::_members_size + DerivedWitnessEntities<FF>::_members_size;
    static constexpr size_t NUM_TO_BE_SHIFTED = OpQueueWiresToBeShiftedEntities<FF>::_members_size +
                                                OrderedRangeConstraints<FF>::_members_size +
                                                DerivedWitnessEntities<FF>::_members_size;
    static constexpr size_t NUM_PCS_UNSHIFTED = NUM_MASKING_POLYNOMIALS +
                                                (NUM_PRECOMPUTED_ENTITIES - NUM_COMPUTABLE_PRECOMPUTED) +
                                                NUM_UNSHIFTED_WITNESSES_WITHOUT_CONCATENATED + NUM_CONCATENATED_POLYS;
    static constexpr size_t NUM_PCS_TO_BE_SHIFTED = NUM_TO_BE_SHIFTED + NUM_CONCATENATED_POLYS;
 
    // Indices for partitioning AllEntities
    static constexpr size_t TO_BE_SHIFTED_WITNESSES_START = NUM_PRECOMPUTED_ENTITIES + NUM_WIRES_NON_SHIFTED;
    static constexpr size_t SHIFTED_WITNESSES_START = NUM_SHIFTED_ENTITIES + TO_BE_SHIFTED_WITNESSES_START;
 
    // Commitments sent in wire round: concatenated + ordered range constraints
    static constexpr size_t NUM_COMMITMENTS_IN_PROOF = NUM_CONCATENATED_POLYS + NUM_ORDERED_RANGE;
 
    // A container to be fed to ShpleminiVerifier to avoid redundant scalar muls.
    // Identifies commitments that appear in both the unshifted and shifted batches:
    //   Unshifted batch: masking(1) + ordered_extra(1) + op(1) + op_queue_tbs(3) + ordered(5) + z_perm(1) + concat(5)
    //                  = 17
    //   Shifted batch:   op_queue(3) + ordered(5) + z_perm(1) + concat(5) = 14
    // Range 1: op_queue_tbs(3) + ordered(5) + z_perm(1) = 9 (contiguous in both batches)
    //          stored indices 2..10 (unshifted) ↔ 16..24 (shifted)
    // Range 2: concatenated(5) — stored indices 11..15 (unshifted) ↔ 25..29 (shifted)
    // (Stored indices are 0-based after ZK offset; offset=2 accounts for Q_commitment + gemini_masking_poly)
    static constexpr size_t NUM_OP_QUEUE_TO_BE_SHIFTED = OpQueueWiresToBeShiftedEntities<FF>::_members_size;
    static constexpr RepeatedCommitmentsData REPEATED_COMMITMENTS =
        RepeatedCommitmentsData(2,
                                2 + NUM_PCS_TO_BE_SHIFTED,
                                NUM_OP_QUEUE_TO_BE_SHIFTED + NUM_ORDERED_RANGE + 1,
                                2 + NUM_OP_QUEUE_TO_BE_SHIFTED + NUM_ORDERED_RANGE + 1,
                                2 + NUM_PCS_TO_BE_SHIFTED + NUM_OP_QUEUE_TO_BE_SHIFTED + NUM_ORDERED_RANGE + 1,
                                NUM_CONCATENATED_POLYS);
 
    static constexpr size_t PROOF_LENGTH =
        /* 1. Gemini masking poly commitment */ (num_frs_comm) +
        /* 2. Wire commitments: concatenated + ordered */
        (NUM_COMMITMENTS_IN_PROOF * num_frs_comm) +
        /* 3. Z_PERM commitment */ (num_frs_comm) +
        /* 4. Libra concatenation commitment */ (num_frs_comm) +
        /* 5. Libra sum */ (num_frs_fr) +
        /* 6. CONST_TRANSLATOR_LOG_N sumcheck univariates */
        (CONST_TRANSLATOR_LOG_N * BATCHED_RELATION_PARTIAL_LENGTH * num_frs_fr) +
        /* 7. sumcheck evaluations (computable precomputed and concat evals excluded) */
        (NUM_SENT_EVALUATIONS * num_frs_fr) +
        /* 8. Libra claimed evaluation */ (num_frs_fr) +
        /* 9. Libra grand sum commitment */ (num_frs_comm) +
        /* 10. Libra quotient commitment */ (num_frs_comm) +
        /* 11. CONST_TRANSLATOR_LOG_N - 1 Gemini Fold commitments */
        ((CONST_TRANSLATOR_LOG_N - 1) * num_frs_comm) +
        /* 12. CONST_TRANSLATOR_LOG_N Gemini a evaluations */
        (CONST_TRANSLATOR_LOG_N * num_frs_fr) +
        /* 13. NUM_SMALL_IPA_TRANSCRIPT_EVALS libra evals */
        (NUM_SMALL_IPA_TRANSCRIPT_EVALS * num_frs_fr) +
        /* 14. Shplonk Q commitment */ (num_frs_comm) +
        /* 15. KZG W commitment */ (num_frs_comm);
 
    // Proof length when using committed sumcheck: each round sends a commitment + 2 scalar evaluations
    // instead of BATCHED_RELATION_PARTIAL_LENGTH scalars.
    static constexpr size_t COMMITTED_SUMCHECK_PROOF_LENGTH =
        PROOF_LENGTH +
        CONST_TRANSLATOR_LOG_N * (num_frs_comm + 2 * num_frs_fr - BATCHED_RELATION_PARTIAL_LENGTH * num_frs_fr);
 
    // ===== Static assert to ensure a valid trace can be proven ======
 
    // The number of "steps" inserted in ordered range constraint polynomials to ensure that the
    // DeltaRangeConstraintRelation can always be satisfied if the polynomial is within the appropriate range.
    static constexpr size_t SORTED_STEPS_COUNT = ((1 << MICRO_LIMB_BITS) / SORT_STEP) + 1;
 
    // The number of masking values in the overflow columns used for the ordered range constraint
    static constexpr size_t MASKING_OVERFLOW_COLUMN =
        MAX_RANDOM_VALUES_PER_ORDERED * (NUM_ORDERED_RANGE - 1) / NUM_ORDERED_RANGE;
 
    static_assert(SORTED_STEPS_COUNT * NUM_ORDERED_RANGE + MASKING_OVERFLOW_COLUMN <
                      MINI_CIRCUIT_SIZE * CONCATENATION_GROUP_SIZE,
                  "Translator circuit is too small for defined number of steps "
                  "(TranslatorDeltaRangeConstraintRelation). ");
 
    // ================================================================
 
    template <typename DataType, typename WireRefs>
    static std::vector<RefVector<DataType>> partition_minicircuit_wires_into_groups(WireRefs wire_refs,
                                                                                    DataType& zero_value)
    {
        constexpr size_t num_non_range = NonRangeMainWires<DataType>::_members_size;
        constexpr size_t num_range = RangeConstraintWires<DataType>::_members_size;
        static_assert(num_range % CONCATENATION_GROUP_SIZE == 0);
        constexpr size_t num_range_groups = num_range / CONCATENATION_GROUP_SIZE;
 
        std::vector<RefVector<DataType>> groups;
        // Groups 0..num_range_groups-1: sequential chunks of range constraint wires
        for (size_t g = 0; g < num_range_groups; g++) {
            RefVector<DataType> group;
            for (size_t j = 0; j < CONCATENATION_GROUP_SIZE; j++) {
                group.push_back(wire_refs[num_non_range + g * CONCATENATION_GROUP_SIZE + j]);
            }
            groups.push_back(std::move(group));
        }
        // Last group: non-range main wires + zero padding
        RefVector<DataType> group;
        for (size_t j = 0; j < num_non_range; j++) {
            group.push_back(wire_refs[j]);
        }
        for (size_t j = num_non_range; j < CONCATENATION_GROUP_SIZE; j++) {
            group.push_back(zero_value);
        }
        groups.push_back(std::move(group));
        return groups;
    }
 
    template <typename FFType>
    static void compute_computable_precomputed(AllEntities<FFType>& evals, std::span<const FFType> challenge)
    {
        TranslatorSelectorEvaluations<FFType, LOG_MINI_CIRCUIT_SIZE>::compute(challenge).populate(evals);
    }
 
    template <typename PolyContainer>
    static std::array<FF, NUM_MINICIRCUIT_EVALUATIONS> get_minicircuit_evaluations(PolyContainer& polys)
    {
        std::array<FF, NUM_MINICIRCUIT_EVALUATIONS> result;
        size_t dst = 0;
        for (auto& wire : polys.get_minicircuit_wires()) {
            result[dst++] = wire[0];
        }
        for (auto& wire : polys.get_minicircuit_wires_shifted()) {
            result[dst++] = wire[0];
        }
        return result;
    }
 
    template <typename FFType>
    static void set_minicircuit_evaluations(AllEntities<FFType>& evals,
                                            const std::array<FFType, NUM_MINICIRCUIT_EVALUATIONS>& mid)
    {
        size_t src = 0;
        for (auto& wire : evals.get_minicircuit_wires()) {
            wire = mid[src++];
        }
        for (auto& wire : evals.get_minicircuit_wires_shifted()) {
            wire = mid[src++];
        }
    }
 
    template <typename FFType>
    static void complete_claimed_evaluations(AllEntities<FFType>& evals, std::span<const FFType> challenge)
    {
        // 1. Compute the computable precomputed selector evaluations
        compute_computable_precomputed(evals, challenge);
 
        // 2. Scale minicircuit wire evaluations by L_0(u_top) = Π_{i=0}^{3} (1 - u_{LOG_MINI + i})
        FFType l0 = FFType(1);
        for (size_t i = 0; i < CONST_TRANSLATOR_LOG_N - LOG_MINI_CIRCUIT_SIZE; i++) {
            l0 *= (FFType(1) - challenge[LOG_MINI_CIRCUIT_SIZE + i]);
        }
        for (auto& wire : evals.get_minicircuit_wires()) {
            wire *= l0;
        }
        for (auto& wire : evals.get_minicircuit_wires_shifted()) {
            wire *= l0;
        }
    }
 
    template <typename FFType>
    static void complete_full_circuit_evaluations(AllEntities<FFType>& evals,
                                                  const std::array<FFType, NUM_FULL_CIRCUIT_EVALUATIONS>& full_circuit,
                                                  std::span<const FFType> challenge)
    {
        set_full_circuit_evaluations(evals, full_circuit);
        complete_claimed_evaluations(evals, challenge);
 
        // Reconstruct the 5 concatenated polynomial evaluations from (now L0-scaled) wire evaluations
        auto groups = evals.get_groups_to_be_concatenated();
        auto concat_evals = reconstruct_concatenated_evaluations(groups, challenge);
        auto concat_refs = evals.get_concatenated();
        for (size_t g = 0; g < NUM_CONCATENATED_POLYS; g++) {
            concat_refs[g] = concat_evals[g];
        }
    }
 
    template <typename FFType>
    static std::array<FFType, NUM_CONCATENATED_POLYS> reconstruct_concatenated_evaluations(
        const std::vector<RefVector<FFType>>& groups, std::span<const FFType> challenge)
    {
        static constexpr size_t NUM_TOP_BITS = numeric::get_msb(CONCATENATION_GROUP_SIZE);
 
        // Compute CONCATENATION_GROUP_SIZE-point Lagrange basis over the top challenges
        // a = u[N - 4], b = u[N - 3], c = u[N - 2], d = u[N - 1]
        // L(0) = (1 - d) * (1 - c) * (1 - b) * (1 - a)
        // L(1) = (1 - d) * (1 - c) * (1 - b) * (    a)
        // L(2) = (1 - d) * (1 - c) * (    b) * (1 - a)
        // L(3) = (1 - d) * (1 - c) * (    b) * (    a)
        // ...
        std::array<FFType, CONCATENATION_GROUP_SIZE> lagrange_basis;
        for (size_t j = 0; j < CONCATENATION_GROUP_SIZE; j++) {
            lagrange_basis[j] = FFType(1);
            for (size_t bit = 0; bit < NUM_TOP_BITS; bit++) {
                const FFType& u = challenge[CONST_TRANSLATOR_LOG_N - NUM_TOP_BITS + bit];
                lagrange_basis[j] *= ((j >> bit) & 1) ? u : (FFType(1) - u);
            }
        }
 
        // L_0 is the "padding" factor from wires having support in [1, MINI)
        // The reason we need to divide by L_0 is because L_j(u) already accounts for the challenges a, b, c, d:
        // L_j(u) = (1 - d) * (1 - c) * (1 - b) * (1 - a) * L_j(0, u_bottom)
        FFType padding_inv = lagrange_basis[0].invert();
 
        auto reconstruct = [&](const auto& group) -> FFType {
            FFType result = FFType(0);
            for (size_t j = 0; j < CONCATENATION_GROUP_SIZE; j++) {
                result += lagrange_basis[j] * group[j];
            }
            return result * padding_inv;
        };
 
        std::array<FFType, NUM_CONCATENATED_POLYS> result;
        for (size_t g = 0; g < NUM_CONCATENATED_POLYS; g++) {
            result[g] = reconstruct(groups[g]);
        }
        return result;
    }
 
    template <typename FFType>
    static std::array<FFType, NUM_FULL_CIRCUIT_EVALUATIONS> get_full_circuit_evaluations(AllEntities<FFType>& evals)
    {
        std::array<FFType, NUM_FULL_CIRCUIT_EVALUATIONS> result;
        size_t dst = 0;
        for (auto& entity : evals.get_full_circuit_entities()) {
            result[dst++] = entity;
        }
        return result;
    }
 
    template <typename FFType>
    static void set_full_circuit_evaluations(AllEntities<FFType>& evals,
                                             const std::array<FFType, NUM_FULL_CIRCUIT_EVALUATIONS>& full_circuit)
    {
        size_t src = 0;
        for (auto& entity : evals.get_full_circuit_entities()) {
            entity = full_circuit[src++];
        }
    }
 
    class ProverPolynomials : public AllEntities<Polynomial> {
      public:
        ProverPolynomials()
        {
 
            const size_t circuit_size = 1 << CONST_TRANSLATOR_LOG_N;
            for (auto& ordered_range_constraint : get_ordered_range_constraints()) {
                ordered_range_constraint = Polynomial{ /*size*/ circuit_size - 1,
                                                       /*largest possible index*/ circuit_size,
                                                       1 };
            }
 
            // Initialize 5 concatenated polynomials (full circuit_size, shiftable with start_index=1)
            // Row 0 of block 0 is the no-op row where all values are zero.
            for (auto& concat_poly : get_concatenated()) {
                concat_poly = Polynomial{ /*size*/ circuit_size - 1,
                                          /*virtual_size*/ circuit_size,
                                          /*start_index*/ 1 };
            }
            z_perm = Polynomial{ /*size*/ circuit_size - 1,
                                 /*virtual_size*/ circuit_size,
                                 /*start_index*/ 1 };
 
            op = Polynomial{ MINI_CIRCUIT_SIZE, circuit_size };
 
            // All minicircuit wires (non-op-queue) are only non-zero in [1, MINI_CIRCUIT_SIZE)
            for (auto& poly : NonOpQueueWiresToBeShiftedEntities<Polynomial>::get_all()) {
                if (poly.is_empty()) {
                    poly = Polynomial{ /*size*/ MINI_CIRCUIT_SIZE - 1,
                                       /*virtual_size*/ circuit_size,
                                       /*start_index*/ 1 };
                }
            }
 
            // Op queue wires to be shifted
            for (auto& poly : OpQueueWiresToBeShiftedEntities<Polynomial>::get_all()) {
                if (poly.is_empty()) {
                    poly = Polynomial{ /*size*/ MINI_CIRCUIT_SIZE - 1,
                                       /*virtual_size*/ circuit_size,
                                       /*start_index*/ 1 };
                }
            }
 
            // Initialize lagrange polynomials and the ordered extra range constraints numerator (the precomputed
            // polynomials) within the appropriate range they operate on
            lagrange_first = Polynomial{ /*size*/ 1, /*virtual_size*/ circuit_size };
            lagrange_result_row = Polynomial{ /*size*/ 1, /*virtual_size*/ circuit_size, /*start_index*/ RESULT_ROW };
            lagrange_even_in_minicircuit = Polynomial{ /*size*/ MINI_CIRCUIT_SIZE - RESULT_ROW - NUM_MASKED_ROWS_END,
                                                       /*virtual_size*/ circuit_size,
                                                       /*start_index=*/RESULT_ROW };
            lagrange_odd_in_minicircuit = Polynomial{ /*size*/ MINI_CIRCUIT_SIZE - RESULT_ROW - NUM_MASKED_ROWS_END - 1,
                                                      /*virtual_size*/ circuit_size,
                                                      /*start_index=*/RESULT_ROW + 1 };
            lagrange_last_in_minicircuit = Polynomial{ /*size*/ 1,
                                                       /*virtual_size*/ circuit_size,
                                                       /*start_index=*/MINI_CIRCUIT_SIZE - NUM_MASKED_ROWS_END - 1 };
            lagrange_mini_masking = Polynomial{ /*size*/ MINI_CIRCUIT_SIZE - RANDOMNESS_START,
                                                /*virtual_size*/ circuit_size,
                                                /*start_index=*/RANDOMNESS_START };
            // With concatenation, masking rows are scattered in concatenated polys: end of each of the 16 blocks
            // Must span full circuit since values go up to position 15*MINI+(MINI-1)
            lagrange_masking = Polynomial{ circuit_size, circuit_size };
            // Ordered masking: contiguous at the end (marks masking positions in ordered polynomials)
            lagrange_ordered_masking = Polynomial{ /*size*/ MAX_RANDOM_VALUES_PER_ORDERED,
                                                   /*virtual_size*/ circuit_size,
                                                   /*start_index*/ circuit_size - MAX_RANDOM_VALUES_PER_ORDERED };
            lagrange_last = Polynomial{ /*size*/ 1,
                                        /*virtual_size*/ circuit_size,
                                        /*start_index*/ circuit_size - 1 };
            // lagrange_real_last marks the last position with sorted values in ordered polynomials
            // (where we check maximum value = 2^14 - 1). With contiguous masking at the end,
            // this is at position circuit_size - MAX_RANDOM_VALUES_PER_ORDERED - 1.
            lagrange_real_last = Polynomial{ /*size*/ 1,
                                             /*virtual_size*/ circuit_size,
                                             /*start_index*/ circuit_size - MAX_RANDOM_VALUES_PER_ORDERED - 1 };
            ordered_extra_range_constraints_numerator =
                Polynomial{ /*size*/ SORTED_STEPS_COUNT * NUM_CONCATENATED_POLYS + MASKING_OVERFLOW_COLUMN,
                            /*virtual_size*/ circuit_size,
                            /*start_index*/ 0 };
 
            set_shifted();
        }
        ProverPolynomials& operator=(const ProverPolynomials&) = delete;
        ProverPolynomials(const ProverPolynomials& o) = delete;
        ProverPolynomials(ProverPolynomials&& o) noexcept = default;
        ProverPolynomials& operator=(ProverPolynomials&& o) noexcept = default;
        ~ProverPolynomials() = default;
        [[nodiscard]] static size_t get_polynomial_size() { return 1UL << CONST_TRANSLATOR_LOG_N; }
        [[nodiscard]] AllValues get_row(size_t row_idx) const
        {
            AllValues result;
            for (auto [result_field, polynomial] : zip_view(result.get_all(), this->get_all())) {
                // Translator polynomials have different support regions (start_index/end_index)
                // Return 0 for out-of-bounds access (which is the correct value outside support)
                if (row_idx >= polynomial.start_index() && row_idx < polynomial.end_index()) {
                    result_field = polynomial[row_idx];
                } else {
                    result_field = FF(0);
                }
            }
            return result;
        }
        // Set all shifted polynomials based on their to-be-shifted counterpart.
        // Uses get_all_to_be_shifted() (86 entries for Sumcheck), not get_to_be_shifted() (9 entries for PCS).
        void set_shifted()
        {
            for (auto [shifted, to_be_shifted] : zip_view(get_shifted(), get_all_to_be_shifted())) {
                shifted = to_be_shifted.shifted();
            }
        }
    };
 
    class ProvingKey {
      public:
        size_t circuit_size = 1UL << CONST_TRANSLATOR_LOG_N;
        size_t log_circuit_size = CONST_TRANSLATOR_LOG_N;
 
        ProverPolynomials polynomials; // storage for all polynomials evaluated by the prover
        CommitmentKey commitment_key;
 
        ProvingKey() = default;
    };
 
    template <typename DataType_> class VKEntities {
      public:
        bool operator==(const VKEntities& other) const = default;
        using DataType = DataType_;
        DEFINE_FLAVOR_MEMBERS(DataType, ordered_extra_range_constraints_numerator);
    };
 
    using VerificationKey = FixedVKAndHash_<VKEntities<Commitment>, FF, TranslatorHardcodedVKAndHash>;
 
    using PartiallyEvaluatedMultivariates =
        PartiallyEvaluatedMultivariatesBase<AllEntities<Polynomial>, ProverPolynomials, Polynomial>;
 
    template <size_t LENGTH> using ProverUnivariates = AllEntities<bb::Univariate<FF, LENGTH>>;
 
    using ExtendedEdges = ProverUnivariates<MAX_PARTIAL_RELATION_LENGTH>;
 
    class CommitmentLabels : public AllEntities<std::string> {
      public:
        CommitmentLabels()
        {
            // Concatenated polynomials (sent via get_non_opqueue_wires_and_ordered_range_constraints)
            this->concatenated_range_constraints_0 = "CONCATENATED_RANGE_CONSTRAINTS_0";
            this->concatenated_range_constraints_1 = "CONCATENATED_RANGE_CONSTRAINTS_1";
            this->concatenated_range_constraints_2 = "CONCATENATED_RANGE_CONSTRAINTS_2";
            this->concatenated_range_constraints_3 = "CONCATENATED_RANGE_CONSTRAINTS_3";
            this->concatenated_non_range = "CONCATENATED_NON_RANGE";
 
            // Ordered range constraints (sent via get_non_opqueue_wires_and_ordered_range_constraints)
            this->ordered_range_constraints_0 = "ORDERED_RANGE_CONSTRAINTS_0";
            this->ordered_range_constraints_1 = "ORDERED_RANGE_CONSTRAINTS_1";
            this->ordered_range_constraints_2 = "ORDERED_RANGE_CONSTRAINTS_2";
            this->ordered_range_constraints_3 = "ORDERED_RANGE_CONSTRAINTS_3";
            this->ordered_range_constraints_4 = "ORDERED_RANGE_CONSTRAINTS_4";
 
            // Grand product (committed separately)
            this->z_perm = "Z_PERM";
        };
    };
 
    template <typename Commitment, typename VerificationKey>
    class VerifierCommitments_ : public AllEntities<Commitment> {
      public:
        VerifierCommitments_(const std::shared_ptr<VerificationKey>& verification_key)
        {
            // Only ordered_extra_range_constraints_numerator needs a VK commitment for PCS.
            // All other precomputed selectors are computable (evaluations derived from sumcheck challenge).
            this->ordered_extra_range_constraints_numerator =
                verification_key->ordered_extra_range_constraints_numerator;
        }
    };
 
    template <typename ProverPolynomialsOrPartiallyEvaluatedMultivariates, typename EdgeType>
    static bool skip_entire_row([[maybe_unused]] const ProverPolynomialsOrPartiallyEvaluatedMultivariates& polynomials,
                                [[maybe_unused]] const EdgeType edge_idx)
    {
        auto s0 = polynomials.ordered_range_constraints_0_shift[edge_idx];
        auto s1 = polynomials.ordered_range_constraints_1_shift[edge_idx];
        auto s2 = polynomials.ordered_range_constraints_2_shift[edge_idx];
        auto s3 = polynomials.ordered_range_constraints_3_shift[edge_idx];
        auto s4 = polynomials.ordered_range_constraints_4_shift[edge_idx];
        auto s5 = polynomials.ordered_range_constraints_0_shift[edge_idx + 1];
        auto s6 = polynomials.ordered_range_constraints_1_shift[edge_idx + 1];
        auto s7 = polynomials.ordered_range_constraints_2_shift[edge_idx + 1];
        auto s8 = polynomials.ordered_range_constraints_3_shift[edge_idx + 1];
        auto s9 = polynomials.ordered_range_constraints_4_shift[edge_idx + 1];
        auto shift_0 = (s0 == 0) && (s1 == 0) && (s2 == 0) && (s3 == 0) && (s4 == 0) && (s5 == 0) && (s6 == 0) &&
                       (s7 == 0) && (s8 == 0) && (s9 == 0);
        return shift_0 && (polynomials.z_perm[edge_idx] == polynomials.z_perm_shift[edge_idx]) &&
               (polynomials.z_perm[edge_idx + 1] == polynomials.z_perm_shift[edge_idx + 1]) &&
               polynomials.lagrange_last[edge_idx] == 0 && polynomials.lagrange_last[edge_idx + 1] == 0;
    }
    using VerifierCommitments = VerifierCommitments_<Commitment, VerificationKey>;
};
 
class TranslatorShortMonomialFlavor : public TranslatorFlavor {
  public:
    using FF = TranslatorFlavor::FF;
    using Curve = TranslatorFlavor::Curve;
 
    static constexpr bool USE_SHORT_MONOMIALS = true;
 
    using GrandProductRelations = std::tuple<TranslatorPermutationShortRelation<FF>>;
    template <typename FF_>
    using Relations_ = std::tuple<TranslatorPermutationShortRelation<FF_>,
                                  TranslatorDeltaRangeConstraintShortRelation<FF_>,
                                  TranslatorOpcodeConstraintShortRelation<FF_>,
                                  TranslatorAccumulatorTransferShortRelation<FF_>,
                                  TranslatorDecompositionShortRelation<FF_>,
                                  TranslatorNonNativeFieldShortRelation<FF_>,
                                  TranslatorZeroConstraintsShortRelation<FF_>,
                                  TranslatorShiftableFirstCoeffZeroShortRelation<FF_>>;
    using Relations = Relations_<FF>;
 
    static constexpr size_t NUM_SUBRELATIONS = compute_number_of_subrelations<Relations>();
    using SubrelationSeparators = std::array<FF, NUM_SUBRELATIONS - 1>;
    static constexpr size_t MAX_PARTIAL_RELATION_LENGTH = compute_max_partial_relation_length<Relations>();
    static constexpr size_t BATCHED_RELATION_PARTIAL_LENGTH = MAX_PARTIAL_RELATION_LENGTH + 2;
    static constexpr size_t NUM_RELATIONS = std::tuple_size_v<Relations>;
 
    template <size_t LENGTH> using ProverUnivariates = TranslatorFlavor::ProverUnivariates<LENGTH>;
    using ExtendedEdges = ProverUnivariates<MAX_PARTIAL_RELATION_LENGTH>;
 
    static_assert(MAX_PARTIAL_RELATION_LENGTH == TranslatorFlavor::MAX_PARTIAL_RELATION_LENGTH);
    static_assert(BATCHED_RELATION_PARTIAL_LENGTH == TranslatorFlavor::BATCHED_RELATION_PARTIAL_LENGTH);
    static_assert(BATCHED_RELATION_PARTIAL_LENGTH == Curve::LIBRA_UNIVARIATES_LENGTH);
    static_assert(NUM_SUBRELATIONS == TranslatorFlavor::NUM_SUBRELATIONS);
};
 
// Guard against drift between the runtime PCS entity lists and their compile-time counts;
// REPEATED_COMMITMENTS and PROOF_LENGTH depend on these counts and desync silently otherwise.
static_assert(detail::ref_array_extent<decltype(std::declval<TranslatorFlavor::AllEntities<TranslatorFlavor::FF>&>()
                                                    .get_pcs_unshifted())>::value ==
                  TranslatorFlavor::NUM_PCS_UNSHIFTED,
              "get_pcs_unshifted() entity count must equal NUM_PCS_UNSHIFTED. If you added a witness entity, "
              "update both the runtime list and NUM_UNSHIFTED_WITNESSES_WITHOUT_CONCATENATED.");
static_assert(detail::ref_array_extent<decltype(std::declval<TranslatorFlavor::AllEntities<TranslatorFlavor::FF>&>()
                                                    .get_pcs_to_be_shifted())>::value ==
                  TranslatorFlavor::NUM_PCS_TO_BE_SHIFTED,
              "get_pcs_to_be_shifted() entity count must equal NUM_PCS_TO_BE_SHIFTED. If you added a to-be-shifted "
              "entity, update both the runtime list and NUM_TO_BE_SHIFTED.");
 
} // namespace bb