# Lattice Error-Feedback Residual Blocks

## Run

```bash
/home/maxwelhelp/main/bin/python3 toy_experiment.py
```

This writes `results.json` and prints the same JSON.

## What is tested

The toy residual stream uses scalar increments (a scalar is one component of the claimed componentwise result), nearest-lattice rounding, and fixed lattice spacing `h`.

- `identity_check`: verifies `z_D = sum(Delta_t) - c_D` and checks the nearest-rounding carry bound.
- `depth_sweep`: uses the adversarial constant increment `Delta=0.49h`. Full-state write-back accumulates a `0.49h` error each layer, while feedback remains bounded by `h/2`.
- `scale_sweep`: repeats the same relative increment for several `h`; the normalized carry remains `0.5h` and absolute error scales linearly with `h`.
- `random_comparison`: compares full-state write-back, increment feedback, and stochastic absolute-state rounding on random residual proposals.

The experiment intentionally has no learned network: it isolates the quantization mechanism and its conservation law. No claim about CIFAR accuracy or wall-clock speed is made.