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# Verified result: 31.183% below baseline
**The30% objective is achieved.** Ready submission: [submission/](submission/).
| Quantity | Original baseline | Frozen result |
|---|---:|---:|
| Score, lower is better | 3,355,599,588.3155365 | **2,309,230,097.5865555** |
| Improvement | — | **31.182788%** |
| Total Toffolis | 93,237 | 65,095.562940 |
| Total qubits | 730 | 741 |
| R / B / C | 65 / 60 / 60 | 65 / 60 / 28 |
| brot / J / K | 12 / 8 / 10 | 10 / 11 / 7 |
| Effective normalization | 49.30136925057439 | 47.873768372534656 |
Both [default verification](verify_default.json) and
[independent-salt verification](verify_independent.json) PASS. The independent
score is**2,309,230,043.6354394**, a**31.182789%** improvement. Each run covers
254,464 address-shots. Small score differences reflect fully corrected
measurement-dependent phase-cleanup operations.
Two-body error is**19.311558mHa**, one-body error**12.935649mHa**;
raw Lambda**294.02612134123535**, gap**3.923618193151924**. All acceptance
gates pass. Every circuit has exactly128 qubits:12 selection,110 word and
six workspace. ANGLES cost56,615.562940 Toffolis; heuristic costs total8480
(outer606 + inner5024 + Givens2850). Shared preparation workspace is543.
Canonical digest:
`7b79a311bfb66d9e9573cb8b12023ad1b852ed07ae7dae75f79037fde98171ea`.
[certificate.json](certificate.json) audits frozen file hashes, both results,
the30% threshold, original scoring-source integrity, reference data, circuit
widths, numerical invariants and branch-check evidence. The original verifier,
cost model, baseline submission, reference integrals and fixed shifts remain
unchanged.
A fresh rebuild reproduced every frozen circuit and NPZ file hash exactly;
see [reproduction_check.json](reproduction_check.json).
The numerical method alternates whitened coefficient fits with coupled integer
word moves. Accounting for interactions between moves permits hundreds of
simultaneous angle updates, making ten-bit accuracy feasible. Compression to
C28, gap-targeted coefficient fitting and exact orthogonal copy rotations then
recover the required normalization. One-body words are regenerated from the
decoded two-body representation. The frozen numerical checkpoint is
`experiments/precision_30/C28_b10_final.npz`.
The lookup uses a high-bit Möbius/ANF decomposition, omits invalid-address
monomials, and merges deferred measurement phases using six quadratic features
and at most two executed CCZs. An [exact proof](../../../research/qrom_30/PROOF.md)
and [independent review](../../../research/shape_30/ANF_REVIEW.md) cover arbitrary
word inputs and every measurement branch. Tests include132,512 exhaustive
small-instance cases,43,648 phase-synthesis cases,524,288 independent kickmix
shots on the prototype, and**222,656 arbitrary-word/inverse cases on these
final emitted circuits**. Finite tests supplement the proof.
Rebuild the exact submission from the frozen checkpoint:
```bash
cd /home/gwen/Quantum
OPENBLAS_NUM_THREADS=4 PYTHONPATH=kickmix:verifiers .venv313/bin/python research/qrom_30/anf_merged.py experiments/coordinator_verified/merged_C28_b10_30/submission/submission.npz /tmp/dfthcsos-30-rebuild --brot 10 --batch-size 11 --workspace 6
OPENBLAS_NUM_THREADS=4 PYTHONPATH=kickmix:verifiers .venv313/bin/python verifiers/dfthcsos/verify.py /tmp/dfthcsos-30-rebuild --salt independent-reproduction
OPENBLAS_NUM_THREADS=1 .venv313/bin/python research/shape_30/certify30.py
```
Compact reports: [numerical fitting](../../../research/precision_30/RESULT.md),
[lookup and Claude work](../../../research/qrom_30/RESULT.md),
[compression and Qwen assessment](../../../research/compression_30/RESULT.md),
[shape experiments](../../../research/shape_30/RESULT.md).
Claude supplied a useful tool-enabled ANF prototype; native review corrected
its test-coverage overclaim. Qwen's initial cost analysis was rejected, then
a narrowly specified correction was independently checked. Native workers
completed fitting, synthesis and verification. Previous verified submissions
and research checkpoints are preserved. No Modal compute was used.

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