witness.u8_air

U8Air AIR witness generation.

U8Air proves U8 range lookups used by SimpleLeft. The table covers all 256 U8 values (0–255) packed two per row across 128 rows:

Row i covers values: [2i, 2i+1] Column mul[0] at row i: count of value 2i Column mul[1] at row i: count of value 2i+1

SimpleLeft’s columns subject to U8 range checks (bus ids 100):

k[0]: range_check(k[0], 0, 255) k[2]: range_check(k[2]-1, 0, 254) — i.e. k[2] in 1..255 k[3]: range_check(k[3], 0, 255) and range_check(256-k[3], 1, 256)

Stage-2 intermediates and grand sums are handled by the bytecode adapter.

Classes

U8AirWitness

Stage-1 witness generator for U8Air AIR.

Module Contents

class witness.u8_air.U8AirWitness

Bases: witness.base.WitnessModule

Stage-1 witness generator for U8Air AIR.

Computes multiplicity columns mul[0], mul[1] by counting how many times each U8 value (0–255) appears across SimpleLeft’s U8 range-check columns.

For byte-identical C++ comparison tests, Stage-1 trace is loaded directly from C++ test vectors and this module is not invoked.

static compute_trace(simple_left_k0: numpy.ndarray, simple_left_k2: numpy.ndarray, simple_left_k3: numpy.ndarray, N: int = 128) → numpy.ndarray

Compute U8Air’s cm1 trace from SimpleLeft’s U8 range-check columns.

Args:

simple_left_k0: SimpleLeft’s k[0] column (8 elements, values 0..255) simple_left_k2: SimpleLeft’s k[2] column (8 elements, values 1..255) simple_left_k3: SimpleLeft’s k[3] column (8 elements, values 0..255) N: Trace size = 128 rows

Returns:

cm1 buffer (128 * 2 field elements) interleaved as [mul0_0, mul1_0, …] mul[j] at row i = count of value (2*i + j) across k[0], k[2]-1, k[3]

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

Delegated to bytecode adapter; this module only computes Stage 1.

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

Delegated to bytecode adapter; this module only computes Stage 1.