witness.u16_air

U16Air AIR witness generation.

U16Air proves U16 range lookups used by SimpleLeft. The table covers all 65536 U16 values (0–65535) packed four per row across 16384 rows:

Row i covers values: [4i, 4i+1, 4i+2, 4i+3] Column mul[j] at row i: count of value 4i+j

SimpleLeft’s column subject to U16 range check (bus id 101):

k[1]: range_check(k[1], 0, 65535) Also: k[3] range check via 256-k[3] contributes to U16 space

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

Classes

U16AirWitness

Stage-1 witness generator for U16Air AIR.

Module Contents

class witness.u16_air.U16AirWitness

Bases: witness.base.WitnessModule

Stage-1 witness generator for U16Air AIR.

Computes multiplicity columns mul[0..3] by counting how many times each U16 value (0–65535) appears in SimpleLeft’s k[1] column (and related 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_k1: numpy.ndarray, simple_left_k3: numpy.ndarray, N: int = 16384) → numpy.ndarray

Compute U16Air’s cm1 trace from SimpleLeft’s U16 range-check columns.

Args:

simple_left_k1: SimpleLeft’s k[1] column (8 elements, values 0..65535) simple_left_k3: SimpleLeft’s k[3] column (8 elements); contributes

256-k[3] to U16 range (values 1..256)

N: Trace size = 16384 rows

Returns:

cm1 buffer (16384 * 4 field elements) interleaved as [mul0_0, …, mul3_0, …] mul[j] at row i = count of value (4*i + j) across all U16 sources

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.