witness.permutation1_6

Permutation1_6 AIR witness generation.

Permutation1_6 uses both sum-based (logup) and product-based permutation:

Sum-based logup terms (5 terms, 0-indexed): 0. Permutation assumes, busid=1, sel=1, cols=[a1, b1] -> goes to gsum direct 1. Permutation proves, busid=1, sel=-1, cols=[c1, d1] 2. Permutation assumes, busid=2, sel=1, cols=[a2, b2] 3. Permutation assumes, busid=3, sel=sel1, cols=[a3, b3] 4. Permutation proves, busid=3, sel=-sel2, cols=[c2, d2]

Intermediate columns clustering (from constraint module): - im_cluster[0]: terms 1,2 (proves busid=1 + assumes busid=2) - im_cluster[1]: terms 3,4 (assumes busid=3 + proves busid=3) - Term 0 goes directly to gsum, not into im_cluster

Product-based term (for gprod): Permutation assumes, busid=4, sel=sel3, cols=[a4, b4]

Classes

Permutation1_6Witness

Witness generation for Permutation1_6 AIR.

Module Contents

class witness.permutation1_6.Permutation1_6Witness

Bases: witness.base.WitnessModule

Witness generation for Permutation1_6 AIR.

Computes 2 im_cluster columns, 1 gsum column, and 1 gprod column.

compute_intermediates(ctx: constraints.base.ConstraintContext) → dict[str, dict[int, primitives.field.FF3Poly]]

Compute intermediate polynomials directly from constraint equations.

From constraint module: - im_cluster[0]: (D2 - D1)/(D1*D2) where D1=compress(1,[c1,d1]), D2=compress(2,[a2,b2]) - im_cluster[1]: ((-sel1)*D2 + sel2*D1)/(D1*D2) where D1=compress(3,[a3,b3]), D2=compress(3,[c2,d2])

Returns:

{

‘im_cluster’: {0: im_cluster_0, 1: im_cluster_1}

}

compute_grand_sums(ctx: constraints.base.ConstraintContext) → dict[str, primitives.field.FF3Poly]

Compute gsum and gprod polynomials.

From constraint 2: gsum recurrence (gsum - prev_gsum*(1-L1) - sum_im) * direct_den + 1 = 0 So gsum[i] = gsum[i-1] + sum_im[i] - 1/direct_den[i] where direct_den = compress(1,[a1,b1])

From constraint 4: gprod recurrence gprod * denom = prev_gprod * (1-L1) + L1 where denom = sel3 * (e + gamma - 1) + 1, e = (b4*alpha + a4)*alpha + 4 For i>0: gprod[i] = gprod[i-1] / denom[i] For i=0: gprod[0] = 1 / denom[0]

Returns:

{‘gsum’: gsum_polynomial, ‘gprod’: gprod_polynomial}