Bounded verification
Small checks. Specific claims.
These checks exercise simplified mathematical or systems mechanisms using Python’s standard library. They do not run the archived frameworks, train a model or certify the original implementations. Article-specific proposed tests remain proposals unless named here.
Executed 2026-09-19 · 14 checks passed.
- Patch boundary arithmetic
An 8×4 patch on 32×31 pixels gives 32 SAME-padded patches versus 28 complete VALID patches.
- Attention head dimensions
A 32-channel total split over four heads gives eight per head; four 32-channel heads give 128 projected channels.
- Topology survives softmax only with a mask
Zero logits assign positive mass to nonedges; a separate exclusion mask removes it.
- Pooled statistics do not freeze old predictions
The scalar ridge optimum changes 0.5→0 while old squared error rises 0.25→1.
- Floating addition is not bitwise order invariant
Changing positive-term summation order changes a binary64 result.
- Nominal bits versus packed bytes
Three four-bit values need two whole payload bytes; an int32 workspace needs twelve payload bytes.
- Embedded header and timestamp width
A packed little-endian H/I/b/H header has nine bytes; uint32 microseconds wrap after about 71.58 minutes.
- Modulo pointer updates do not wrap a memcpy
A twelve-byte packet at offset sixty in a 64-byte ring crosses the allocation even though the equality overflow check does not fire.
- Bucket identity differs from emission time
A bar in bucket zero is emitted only when a later bucket arrives; absent buckets cannot be inferred as observations.
- Single-tone recurrence
The independent sinusoid recurrence recovers a synthetic 20 kHz tone within 1e-7 Hz; this is not a noisy physiological test.
- Causal versus unmasked attention
An unmasked earlier query mixes in a future value; a causal mask excludes it.
- Blockwise reverse chain rule
A two-layer scalar adjoint sweep matches finite-difference parameter gradients within 1e-9; no PyTorch equivalence is claimed.
- Checkpoint input expansion
Zero sensor columns preserve an actor affine map; relocating the critic action columns preserves its old input/action map.
- Integrity is distinct from accuracy
A payload mutation changes its digest. This says nothing about whether the stored scientific answer is correct.