# Asked AI to do a mini math breakthrough. It did a mini breakthrough

> Source: <https://github.com/learademacher/ai-refines-ai-zeta-bound>
> Published: 2026-08-11 21:17:08+00:00

**A reproducible candidate improvement to the 67.25% zeta-zero bound.**

One AI system produced Anthropic's new Theorem D. A second AI-generated research draft found a small strengthening. This repository packages the stronger argument, its exact interval-arithmetic verifier, and a clean-room reproduction of the only computer-assisted lemma.

The candidate bound is

Here

Important

This is an unreviewed candidate refinement. It does not prove the Riemann hypothesis and it does not independently replace the analytic results imported from Anthropic's Theorem D. The finite interval certificate has been reproduced exactly; broader expert review is still needed.

[Paper (PDF)](/learademacher/ai-refines-ai-zeta-bound/blob/main/paper/riemann.pdf) · [LaTeX source](/learademacher/ai-refines-ai-zeta-bound/blob/main/paper/riemann.tex) ·
[technical audit](/learademacher/ai-refines-ai-zeta-bound/blob/main/AUDIT.md) · [reproduction guide](/learademacher/ai-refines-ai-zeta-bound/blob/main/REPRODUCIBILITY.md)

The strengthened source is isolated in commit
[ 0faebf367ffb780951845d014e2e3d9a4a04adb1](https://github.com/learademacher/ai-refines-ai-zeta-bound/commit/0faebf367ffb780951845d014e2e3d9a4a04adb1).
Starting from the public verifier, it changes the target to

A clean x86_64 Linux run with CPython 3.12.3 and `python-flint==0.8.0`

returned:

```
verified=true
target=F6 >= 191/50000
grid=4000
precision_bits=128
initial_boxes=729
nodes=786215
pruned=393472
splits=392743
maximum_depth=43
kernel_table_sha256=f79a9147ffc37692b84330e98422fb94cbf601c51d4f9f8ae749982f23838571
second_derivative_table_sha256=cc98102590dba6e1a982a5a4c9fcd755848a93483db67edd6634813a35e5e3f5
```

The exact expected report is committed in
[ certificates/seven-point.expected.json](/learademacher/ai-refines-ai-zeta-bound/blob/main/certificates/seven-point.expected.json).
CI reruns the exhaustive verifier from a clean checkout and compares every
deterministic field.

Anthropic's Theorem D gives

The seven-point refinement proves, using those imported analytic inputs,

for all nonnegative gaps. With block size

The matrix inequality, kernel normalization, seven-point combinatorics,
shifted-block pinching, and final arithmetic are covered in the
[audit](/learademacher/ai-refines-ai-zeta-bound/blob/main/AUDIT.md). The analytic trace estimates, tail bounds, and optimized
test family remain dependencies of the cited Anthropic paper and its Lean 4
artifact.

The most exact route uses the pinned container image:

```
docker build -t ai-refines-ai-zeta-bound .
docker run --rm ai-refines-ai-zeta-bound
```

For a local CPython 3.12 installation:

```
python3 -m venv .venv
source .venv/bin/activate
python -m pip install --require-hashes -r requirements.lock
PYTHONPATH=src python -m unittest discover -s tests -v
PYTHONPATH=src python scripts/verify_release.py
```

The exhaustive verification usually takes a few minutes. An unresolved terminal cell is a hard failure; the program never treats it as verified.

- Upstream artifact:
, commit`ainta/zeta-simple-zeros`

`040c5e899e658aed7b56a2a87f501798fe10761d`

. - The upstream repository identifies the research draft as generated by GPT-5.6 Sol.
- Anthropic foundation:
[research article](https://www.anthropic.com/research/riemann-zeta),[paper](https://www-cdn.anthropic.com/564f962e60643842f5fcb4a17c9dbc8f608f1c37.pdf), and[Lean 4 artifact](https://github.com/anthropics/zeta-23-lean). - This release preserves the upstream MIT license and history. See
[PROVENANCE.md](/learademacher/ai-refines-ai-zeta-bound/blob/main/PROVENANCE.md)for the exact chain.

AI-generated research draft. Computer-assisted lemma independently reproduced. No human peer review is claimed. Attempts to falsify the argument or reproduce the certificate on another architecture are welcome once the repository is made public.

MIT, inherited from the upstream artifact.