A / THE OBSERVATION 14 × 16 RGB
Pixels are read once to write W. Subsequent probes use only the byte-valued conductance fields.
What if the image doesn't survive as pixels, but as a changed propagation medium? Two different orders of probing the same conductance graph may reveal different relationships.
Interactive *analytic* demonstration. Conductances are computed from the image, not produced by the trained Python writer.
Pixels are read once to write W. Subsequent probes use only the byte-valued conductance fields.
The four edge fields occupy exactly 14 × 16 × 4 bytes, including forbidden-edge padding.
First transport along B's edges, then along A's.
The identical graph and query, interrogated in reverse order.
Signed order-sensitive differences. Bright means amplitude, not proven semantic significance.
A matched two-order read that removes the antisymmetric component.
Nonzero difference = order matters for this operator and query. It does not prove a mark was decoded. Run the trained held-out experiment below.
Input-written edge values replace pixel activity as the stored state. A new query can then traverse the same graph by different paths.
Encode one image into four directed uint8 conductance fields. The trained PyTorch version uses a convolutional writer with byte rounding in the forward pass.
W = round(255 × Eθ(I))Apply A and B to a fresh, question-conditioned signal. Uniform filters commute; image-written edge weights generally need not.
ABq ≠ BAqAsk whether the antisymmetric component predicts an unseen answer better than matched order-blind reads and a direct-graph decoder.
Δ = ABq − BAqOne trainable writer, five comparison arms, untouched held-out scenes. The code records results rather than inventing a successful benchmark.
The synthetic image contains two textured objects and 2×2 red/blue marks. The reader receives only 896-byte W and a query for left or right. The source pixels are inaccessible after writing.
Heads for ordered pair, commutator, symmetric mean, isotropic two-step, and raw W have matched trainable parameters. Ordered and commutator probes consume four transports. Direct-W is an explicit memory-access upper baseline, not compute-matched.
Read frozen protocol ↗pip install -r requirements.txt pytest -q python train.py --seed 41 --steps 450 python train.py --seed 97 --steps 450
JSON receipts → results/seed*.json