# Kernel-lane demonstration — matmul (n=512, f32)

## 1. Equivalence: byte-identical is the wrong gate
byte-identical: FAIL — 244901 of 262144 result values differ (accumulation reordered)

diff-test FP-tolerance policy (targets/matmul/equivalence.toml):
  policy: FpTolerance { abs: 0.0001, rel: 0.001 }
  EQUIVALENT under policy

in-process reference differential test:
  kernel differential test (opt vs reference):
    max_abs_err = 3.815e-05
    max_rel_err = 2.173e-02 (dominated by near-zero elements; see abs floor)
    tolerance   = abs 1.000e-04 + rel 1.000e-03 * |ref|
    byte_identical   = NO (accumulation reordered by design)
    within_tolerance = YES
    verdict = EQUIVALENT

control — a genuine wrong result IS caught by the tolerance:
  tolerance correctly REJECTS a +0.5 perturbation of one element

## 2. Speedup: interleaved A/B, bootstrap 95% CI
  speedup (baseline/candidate): median 3.2301, 95% CI [3.1600, 3.2594]
  verdict: accepted

## What it demonstrates
A real matmul speedup (transpose for cache locality + eight-accumulator
ILP) that reorders the reduction. Byte-identical rejects it; the
FP-tolerance gate accepts it (abs 1e-4 + rel 1e-3) while still catching
a wrong result; the bench measures it with the same CI machinery as
every other target. The GPU extension (Triton/CUDA vs a reference
kernel) is the same shape — only the timer and the hardware change.