pragma circom 2.1.0;

// HDGL Lattice Blending ZK Circuit - Production Version
// Verifies φ-delta evolution and lattice commitment integrity

include "circomlib/circuits/poseidon.circom";
include "circomlib/circuits/comparators.circom";
include "circomlib/circuits/bitify.circom";

// Constants
template Constants() {
    // φ * 10^9 (scaled for integer arithmetic)
    var PHI_SCALED = 1618033988;
    // φ^2 * 10^9
    var PHI_SQ_SCALED = 2618033988;
    // 1/φ * 10^9  
    var PHI_INV_SCALED = 618033988;
    // Scale factor
    var SCALE = 1000000000;
    
    // Fibonacci sequence (first 13 elements)
    var FIBONACCI[13] = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233];
}

// φ-power computation using repeated squaring
template PhiPower(n) {
    signal input base; // PHI_SCALED
    signal output result;
    
    component bits = Num2Bits(8);
    bits.in <== n;
    
    signal powers[8];
    powers[0] <== base;
    
    for (var i = 1; i < 8; i++) {
        powers[i] <== powers[i-1] * powers[i-1];
    }
    
    signal accumulator[9];
    accumulator[0] <== 1;
    
    for (var i = 0; i < 8; i++) {
        signal selector <== bits.out[i] * (powers[i] - 1) + 1;
        accumulator[i+1] <== accumulator[i] * selector;
    }
    
    result <== accumulator[8];
}

// Modular cosine approximation using Taylor series
template CosApprox() {
    signal input x; // Input angle * SCALE
    signal output cos_x;
    
    // Normalize input to [0, 2π) approximately
    signal x_norm <== x % 6283185307; // 2π * SCALE
    
    // Taylor series: cos(x) ≈ 1 - x²/2! + x⁴/4! - x⁶/6!
    signal x2 <== x_norm * x_norm;
    signal x4 <== x2 * x2;
    signal x6 <== x4 * x2;
    
    // Compute terms with proper scaling
    signal term2 <== x2 \ (2 * 1000000000000000000); // x²/2! scaled
    signal term4 <== x4 \ (24 * 1000000000000000000000000000000000000); // x⁴/4! scaled  
    signal term6 <== x6 \ (720 * 1000000000000000000000000000000000000000000000000000000); // x⁶/6! scaled
    
    cos_x <== 1000000000 - term2 + term4 - term6; // 1 - x²/2! + x⁴/4! - x⁶/6!
}

// Core D_n operator computation
template DnOperator() {
    signal input n;
    signal input r_dim_scaled;
    signal input omega_scaled;
    signal output d_n;
    
    // Compute φ^n
    component phi_n = PhiPower(8); // Max 8 bits for n
    phi_n.base <== 1618033988; // PHI_SCALED
    phi_n.n <== n;
    
    // Compute φ^(-n) ≈ (1/φ)^n
    component phi_inv_n = PhiPower(8);
    phi_inv_n.base <== 618033988; // PHI_INV_SCALED
    phi_inv_n.n <== n;
    
    // Compute r^n (approximation for small n)
    signal r_power;
    component r_pow_comp = PhiPower(8);
    r_pow_comp.base <== r_dim_scaled;
    r_pow_comp.n <== n;
    r_power <== r_pow_comp.result;
    
    // Compute oscillatory terms
    signal omega_n <== omega_scaled * n;
    signal omega_phi_n <== omega_n * 618033988 \ 1000000000; // ω*n/φ
    
    component cos_comp = CosApprox();
    cos_comp.x <== omega_n;
    
    component sin_comp = CosApprox(); 
    sin_comp.x <== omega_phi_n + 1570796327; // Add π/2 for sin approximation
    
    // Combine components: φ^n * r^n * cos(ωn) + φ^(-n) * sin(ωn/φ)
    signal primary <== phi_n.result * r_power * cos_comp.cos_x \ (1000000000 * 1000000000);
    signal secondary <== phi_inv_n.result * sin_comp.cos_x \ 1000000000;
    
    d_n <== primary + secondary;
}

// Blend raw slots into D-slots
template SlotBlender(num_slots) {
    signal input raw_slots[num_slots];
    signal input r_dim_scaled;
    signal input slot_index;
    signal output blended_slot;
    
    // Base value
    signal base_value <== raw_slots[slot_index];
    
    // φ-factor computation
    component phi_factor = PhiPower(4);
    phi_factor.base <== 1618033988;
    phi_factor.n <== slot_index % 13; // Cycle through powers
    
    // Cross-slot influence calculation
    signal influence_sum;
    signal weights[num_slots];
    signal influences[num_slots];
    
    for (var i = 0; i < num_slots; i++) {
        signal distance <== (i - slot_index) * (i - slot_index); // |i - slot_index|²
        
        // Weight = φ^(-distance) approximation
        component weight_comp = PhiPower(6);
        weight_comp.base <== 618033988; // PHI_INV_SCALED
        weight_comp.n <== distance % 64; // Limit exponent
        weights[i] <== weight_comp.result;
        
        influences[i] <== raw_slots[i] * weights[i];
    }
    
    // Sum influences (simplified for circuit constraints)
    signal partial_sums[num_slots];
    partial_sums[0] <== influences[0];
    for (var i = 1; i < num_slots; i++) {
        partial_sums[i] <== partial_sums[i-1] + influences[i];
    }
    influence_sum <== partial_sums[num_slots - 1];
    
    // Normalize influence
    signal normalized_influence <== influence_sum \ (num_slots * 1000000000);
    
    // r-dimension scaling
    component r_factor = PhiPower(4);
    r_factor.base <== r_dim_scaled;
    r_factor.n <== slot_index + 1;
    
    // Combine: base * φ^i * r^(i+1) + influence * φ^(-1)
    signal phi_scaled_base <== base_value * phi_factor.result * r_factor.result \ (1000000000 * 1000000000);
    signal phi_scaled_influence <== normalized_influence * 618033988 \ 1000000000;
    
    blended_slot <== phi_scaled_base + phi_scaled_influence;
}

// Lattice commitment hash computation
template LatticeCommitment(num_slots) {
    signal input D_slots[num_slots];
    signal input r_dim_scaled;
    signal input omega_scaled;
    signal input WAVES;
    signal input STRANDS;
    signal output commitment;
    
    // Use Poseidon hash for efficient ZK-friendly commitment
    component hasher = Poseidon(num_slots + 4);
    
    // Add D-slots to hash input
    for (var i = 0; i < num_slots; i++) {
        hasher.inputs[i] <== D_slots[i];
    }
    
    // Add parameters
    hasher.inputs[num_slots] <== r_dim_scaled;
    hasher.inputs[num_slots + 1] <== omega_scaled;
    hasher.inputs[num_slots + 2] <== WAVES;
    hasher.inputs[num_slots + 3] <== STRANDS;
    
    commitment <== hasher.out;
}

// Fibonacci constraint verification
template FibonacciConstraint(num_slots) {
    signal input lattice_slots[num_slots];
    signal input fold_step;
    signal output valid;
    
    // Fibonacci sequence embedded in circuit
    signal fibonacci[13];
    fibonacci[0] <== 1;
    fibonacci[1] <== 1;
    fibonacci[2] <== 2;
    fibonacci[3] <== 3;
    fibonacci[4] <== 5;
    fibonacci[5] <== 8;
    fibonacci[6] <== 13;
    fibonacci[7] <== 21;
    fibonacci[8] <== 34;
    fibonacci[9] <== 55;
    fibonacci[10] <== 89;
    fibonacci[11] <== 144;
    fibonacci[12] <== 233;
    
    // Select appropriate Fibonacci number based on fold step
    signal fib_index <== fold_step % 13;
    signal expected_fib;
    
    component selector = Multiplexer(1, 13);
    for (var i = 0; i < 13; i++) {
        selector.inp[i][0] <== fibonacci[i];
    }
    selector.sel <== fib_index;
    expected_fib <== selector.out[0];
    
    // Compute sum of first 8 lattice slots
    signal slot_sum;
    signal partial_sums[num_slots];
    partial_sums[0] <== lattice_slots[0];
    for (var i = 1; i < num_slots && i < 8; i++) {
        partial_sums[i] <== partial_sums[i-1] + lattice_slots[i];
    }
    slot_sum <== partial_sums[7]; // Sum of first 8 slots
    
    // Constraint: sum should NOT be divisible by Fibonacci number
    // valid = 1 if (slot_sum % expected_fib) != 0
    signal remainder <== slot_sum % expected_fib;
    component is_zero = IsZero();
    is_zero.in <== remainder;
    valid <== 1 - is_zero.out; // valid = 1 when remainder != 0
}

// Range check to ensure values are within expected bounds
template RangeCheck(bits) {
    signal input in;
    signal output valid;
    
    component lt = LessThan(bits + 1);
    lt.in[0] <== in;
    lt.in[1] <== 1 << bits; // 2^bits
    
    component gte = GreaterEqThan(bits + 1);
    gte.in[0] <== in;
    gte.in[1] <== 0;
    
    valid <== lt.out * gte.out;
}

// φ-delta evolution verification
template PhiDeltaEvolution(lattice_size) {
    signal input prev_lattice[lattice_size];
    signal input new_lattice[lattice_size];
    signal input fold_step;
    signal input strand_id;
    signal output valid;
    
    // Evolution radius calculation
    signal evolution_radius;
    signal base_radius <== 4;
    signal expansion <== fold_step < 6 ? fold_step : 6; // min(fold_step, 6)
    signal power_of_two[7];
    power_of_two[0] <== 1;
    for (var i = 1; i < 7; i++) {
        power_of_two[i] <== power_of_two[i-1] * 2;
    }
    evolution_radius <== base_radius * power_of_two[expansion];
    
    // Strand offset
    signal strand_offset <== strand_id * 8;
    
    // φ² scaled value for delta computation
    signal phi_sq_scaled <== 2618033988;
    
    // Fibonacci modulation
    signal fib_mod;
    component fib_selector = Multiplexer(1, 13);
    signal fibonacci[13] = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233];
    for (var i = 0; i < 13; i++) {
        fib_selector.inp[i][0] <== fibonacci[i];
    }
    fib_selector.sel <== fold_step % 13;
    fib_mod <== fib_selector.out[0];
    
    // Verify evolution for each affected slot
    signal evolution_checks[lattice_size];
    for (var i = 0; i < lattice_size; i++) {
        signal in_evolution_radius;
        component radius_check = LessThan(32);
        radius_check.in[0] <== i;
        radius_check.in[1] <== evolution_radius;
        in_evolution_radius <== radius_check.out;
        
        // If within evolution radius, verify φ-delta transformation
        signal base_idx <== (strand_offset + i) % lattice_size;
        signal phi_delta <== phi_sq_scaled * fib_mod \ 1000000;
        signal position_mod <== (i * 618033988) % 1000000000;
        
        signal expected_delta <== phi_delta + position_mod;
        signal expected_new <== (prev_lattice[i] + expected_delta) % 10000000000;
        
        // Check if evolution is correct when in radius, or unchanged when outside
        signal diff <== new_lattice[i] - prev_lattice[i];
        signal expected_diff <== in_evolution_radius * expected_delta;
        
        component diff_check = IsEqual();
        diff_check.in[0] <== diff;
        diff_check.in[1] <== expected_diff;
        evolution_checks[i] <== diff_check.out;
    }
    
    // All evolution checks must pass
    signal check_product;
    signal partial_products[lattice_size];
    partial_products[0] <== evolution_checks[0];
    for (var i = 1; i < lattice_size; i++) {
        partial_products[i] <== partial_products[i-1] * evolution_checks[i];
    }
    valid <== partial_products[lattice_size - 1];
}

// Main HDGL Blending Circuit
template HDGLBlending(num_slots, lattice_size) {
    // Public inputs
    signal input commitment;
    
    // Private inputs  
    signal input D_slots[num_slots];
    signal input WAVES;
    signal input STRANDS;
    signal input r_dim_scaled;
    signal input Omega_scaled;
    signal input fold_step;
    signal input strand_id;
    signal input raw_lattice[lattice_size];
    
    // Range checks for all inputs
    component r_dim_check = RangeCheck(32);
    r_dim_check.in <== r_dim_scaled;
    r_dim_check.valid === 1;
    
    component omega_check = RangeCheck(33);
    omega_check.in <== Omega_scaled;
    omega_check.valid === 1;
    
    component fold_check = RangeCheck(8);
    fold_check.in <== fold_step;
    fold_check.valid === 1;
    
    component strand_check = RangeCheck(3);
    strand_check.in <== strand_id;
    strand_check.valid === 1;
    
    // Verify D-slot blending
    component blenders[num_slots];
    for (var i = 0; i < num_slots; i++) {
        blenders[i] = SlotBlender(lattice_size);
        for (var j = 0; j < lattice_size && j < 64; j++) { // Limit to prevent circuit size explosion
            blenders[i].raw_slots[j] <== raw_lattice[j];
        }
        blenders[i].r_dim_scaled <== r_dim_scaled;
        blenders[i].slot_index <== i;
        
        // Constrain that computed D-slot matches input
        blenders[i].blended_slot === D_slots[i];
    }
    
    // Verify lattice commitment
    component commitment_hasher = LatticeCommitment(num_slots);
    for (var i = 0; i < num_slots; i++) {
        commitment_hasher.D_slots[i] <== D_slots[i];
    }
    commitment_hasher.r_dim_scaled <== r_dim_scaled;
    commitment_hasher.omega_scaled <== Omega_scaled;
    commitment_hasher.WAVES <== WAVES;
    commitment_hasher.STRANDS <== STRANDS;
    
    // Constrain commitment matches
    commitment_hasher.commitment === commitment;
    
    // Verify Fibonacci constraint
    component fib_constraint = FibonacciConstraint(lattice_size);
    for (var i = 0; i < lattice_size && i < 64; i++) {
        fib_constraint.lattice_slots[i] <== raw_lattice[i];
    }
    fib_constraint.fold_step <== fold_step;
    fib_constraint.valid === 1;
    
    // Additional constraints for φ-coherence
    // Verify that r_dim and Omega maintain φ-relationships
    signal phi_scaled <== 1618033988;
    signal phi_inv_scaled <== 618033988;
    
    // r_dim should be influenced by φ
    signal r_dim_phi_mod <== r_dim_scaled * phi_inv_scaled \ 1000000000;
    component r_dim_bound_check = LessThan(32);
    r_dim_bound_check.in[0] <== r_dim_phi_mod;
    r_dim_bound_check.in[1] <== 2000000000; // Upper bound
    r_dim_bound_check.out === 1;
    
    // Omega should maintain reasonable bounds relative to φ
    signal omega_phi_ratio <== Omega_scaled * 1000000000 \ phi_scaled;
    component omega_bound_check = LessThan(32);
    omega_bound_check.in[0] <== omega_phi_ratio;
    omega_bound_check.in[1] <== 10000000000; // 10x φ maximum
    omega_bound_check.out === 1;
}

// Main component instantiation
component main = HDGLBlending(8, 256);

// Component for multiplexer (selector circuit)
template Multiplexer(wIn, nIn) {
    signal input inp[nIn][wIn];
    signal input sel;
    signal output out[wIn];
    
    component calcTotal = CalculateTotal(nIn);
    component eqs[nIn];
    
    for (var i = 0; i < nIn; i++) {
        eqs[i] = IsEqual();
        eqs[i].in[0] <== sel;
        eqs[i].in[1] <== i;
        calcTotal.nums[i] <== eqs[i].out;
    }
    
    calcTotal.sum === 1;
    
    for (var w = 0; w < wIn; w++) {
        component calcOutSignal = CalculateTotal(nIn);
        for (var i = 0; i < nIn; i++) {
            calcOutSignal.nums[i] <== inp[i][w] * eqs[i].out;
        }
        out[w] <== calcOutSignal.sum;
    }
}

// Helper template for calculating totals
template CalculateTotal(n) {
    signal input nums[n];
    signal output sum;
    
    signal sums[n];
    sums[0] <== nums[0];
    
    for (var i = 1; i < n; i++) {
        sums[i] <== sums[i-1] + nums[i];
    }
    
    sum <== sums[n-1];
}