# Holographic Hasse-Weil Oracle

This run applies a Nagao-style drift observable to three LMFDB-verified elliptic curves and estimates rank with a robust holographic horizon score.

Important: this is a numerical heuristic validation artifact. It is not a proof of the Birch and Swinnerton-Dyer conjecture.

## Results

Prime horizon: `12000`

| Curve | Expected rank | Late-slope rank | Oracle score | Oracle rank | Confidence | R2 |
| --- | ---: | ---: | ---: | ---: | ---: | ---: |
| 11a1 / rank 0 | 0 | 0.0578 | 0.0000 | 0 | 1.000 | 0.0005 |
| 37a1 / rank 1 | 1 | 0.8585 | 0.7861 | 1 | 0.572 | 0.1704 |
| 389a1 / rank 2 | 2 | 2.3834 | 1.6887 | 2 | 0.377 | 0.5437 |

## Verdict

Status: `pass`

The robust horizon score passes this small verified smoke test. This is still a numerical heuristic, not a proof or a substitute for analytic-rank computation.

## Outputs

- `output/bsd_holographic_drift.csv`
- `output/bsd_rank_summary.csv`
- `output/bsd_rank_collapse.svg`

## Next Validation Step

Run the same estimator over a larger LMFDB/Cremona corpus, use leave-one-conductor-out evaluation, and report classification error, confidence intervals, and failure cases.