# Archived solid-start Fourier atom-hole campaign

```{admonition} Stopped initialization study
:class: warning
This optimizer was stopped on 2026-08-24 after 665 updates. Its complete
checkpoint is preserved, but it is not the active design campaign.
```

This run established that a zero-coefficient Fourier initialization cannot be
combined safely with immediate exact binarization. Zero latent coefficients
decode to density 0.5; the binary tie convention made the nominal design a
solid silicon slab, while the initial erosion and dilation thresholds saw
nearly opposite material states. That was an initialization artifact, not a
physics-motivated seed.

## Frozen outcome

| Quantity | Value |
|---|---:|
| Updates | 665 |
| Best recorded LDOS / vacuum | 0.963590 |
| Final LDOS / vacuum | 0.729534 |
| Final silicon fill | 73.756% |
| Independent Fourier coefficients | 13,725 |
| Hard atom hole | 1 µm diameter |
| Final forward material | exact binary |

The best result remained below vacuum LDOS after hundreds of updates. The
experiment therefore provides useful negative evidence: a full Fourier basis
does not rescue a poorly posed solid-slab cold start.

## Initial and final geometry

```{figure} ../_static/generated/fourier_atom_hole_solid_start_final_geometry.png
:alt: Solid slab initialization and final binary geometry

The immutable atom hole remained clear, but the topology began from an almost
entirely solid design.
```

## Complete optimization history

```{figure} ../_static/generated/fourier_atom_hole_solid_start_final_progress.png
:alt: LDOS and Fourier optimization history for the stopped solid-start run

All 665 executed updates are retained. Threshold-dependent oscillation is
visible rather than removed from the record.
```

## Final Fourier spectrum and field

```{figure} ../_static/generated/fourier_atom_hole_solid_start_final_spectrum.png
:alt: Final Fourier coefficient spectrum
```

```{figure} ../_static/generated/fourier_atom_hole_solid_start_final_field.png
:alt: Final Ez field of the stopped solid-start campaign
```

## Reproducibility

The immutable archive is
`benchmarks/artifacts/invdes_fourier_atom_hole_ldos_dense_fft_v1.rejected_solid_start_20260824.npz`
with SHA-256
`a2ac63cd230a43de1a42b9ee730758edad53d22a8fe4622656bd3679b61eb0b2`.
It contains the parameters, optimizer moments, literal densities, Ez field,
and complete per-update JSON history.