{"slug": "asked-ai-to-do-a-mini-math-breakthrough-it-did-a-mini-breakthrough", "title": "Asked AI to do a mini math breakthrough. It did a mini breakthrough", "summary": "A second AI system has produced a candidate improvement to the 67.25% zeta-zero bound, refining Anthropic's Theorem D. The new repository packages a stronger argument with an exact interval-arithmetic verifier, and a clean-room reproduction of the computer-assisted lemma. The candidate bound is unreviewed and does not prove the Riemann hypothesis.", "body_md": "**A reproducible candidate improvement to the 67.25% zeta-zero bound.**\n\nOne 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.\n\nThe candidate bound is\n\nHere\n\nImportant\n\nThis 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.\n\n[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) ·\n[technical audit](/learademacher/ai-refines-ai-zeta-bound/blob/main/AUDIT.md) · [reproduction guide](/learademacher/ai-refines-ai-zeta-bound/blob/main/REPRODUCIBILITY.md)\n\nThe strengthened source is isolated in commit\n[ 0faebf367ffb780951845d014e2e3d9a4a04adb1](https://github.com/learademacher/ai-refines-ai-zeta-bound/commit/0faebf367ffb780951845d014e2e3d9a4a04adb1).\nStarting from the public verifier, it changes the target to\n\nA clean x86_64 Linux run with CPython 3.12.3 and `python-flint==0.8.0`\n\nreturned:\n\n```\nverified=true\ntarget=F6 >= 191/50000\ngrid=4000\nprecision_bits=128\ninitial_boxes=729\nnodes=786215\npruned=393472\nsplits=392743\nmaximum_depth=43\nkernel_table_sha256=f79a9147ffc37692b84330e98422fb94cbf601c51d4f9f8ae749982f23838571\nsecond_derivative_table_sha256=cc98102590dba6e1a982a5a4c9fcd755848a93483db67edd6634813a35e5e3f5\n```\n\nThe exact expected report is committed in\n[ certificates/seven-point.expected.json](/learademacher/ai-refines-ai-zeta-bound/blob/main/certificates/seven-point.expected.json).\nCI reruns the exhaustive verifier from a clean checkout and compares every\ndeterministic field.\n\nAnthropic's Theorem D gives\n\nThe seven-point refinement proves, using those imported analytic inputs,\n\nfor all nonnegative gaps. With block size\n\nThe matrix inequality, kernel normalization, seven-point combinatorics,\nshifted-block pinching, and final arithmetic are covered in the\n[audit](/learademacher/ai-refines-ai-zeta-bound/blob/main/AUDIT.md). The analytic trace estimates, tail bounds, and optimized\ntest family remain dependencies of the cited Anthropic paper and its Lean 4\nartifact.\n\nThe most exact route uses the pinned container image:\n\n```\ndocker build -t ai-refines-ai-zeta-bound .\ndocker run --rm ai-refines-ai-zeta-bound\n```\n\nFor a local CPython 3.12 installation:\n\n```\npython3 -m venv .venv\nsource .venv/bin/activate\npython -m pip install --require-hashes -r requirements.lock\nPYTHONPATH=src python -m unittest discover -s tests -v\nPYTHONPATH=src python scripts/verify_release.py\n```\n\nThe exhaustive verification usually takes a few minutes. An unresolved terminal cell is a hard failure; the program never treats it as verified.\n\n- Upstream artifact:\n, commit`ainta/zeta-simple-zeros`\n\n`040c5e899e658aed7b56a2a87f501798fe10761d`\n\n. - The upstream repository identifies the research draft as generated by GPT-5.6 Sol.\n- Anthropic foundation:\n[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\n[PROVENANCE.md](/learademacher/ai-refines-ai-zeta-bound/blob/main/PROVENANCE.md)for the exact chain.\n\nAI-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.\n\nMIT, inherited from the upstream artifact.", "url": "https://wpnews.pro/news/asked-ai-to-do-a-mini-math-breakthrough-it-did-a-mini-breakthrough", "canonical_source": "https://github.com/learademacher/ai-refines-ai-zeta-bound", "published_at": "2026-08-11 21:17:08+00:00", "updated_at": "2026-08-11 21:41:51.895131+00:00", "lang": "en", "topics": ["artificial-intelligence", "ai-research"], "entities": ["Anthropic", "GPT-5.6 Sol", "CPython", "python-flint", "Lean 4"], "alternates": {"html": "https://wpnews.pro/news/asked-ai-to-do-a-mini-math-breakthrough-it-did-a-mini-breakthrough", "markdown": "https://wpnews.pro/news/asked-ai-to-do-a-mini-math-breakthrough-it-did-a-mini-breakthrough.md", "text": "https://wpnews.pro/news/asked-ai-to-do-a-mini-math-breakthrough-it-did-a-mini-breakthrough.txt", "jsonld": "https://wpnews.pro/news/asked-ai-to-do-a-mini-math-breakthrough-it-did-a-mini-breakthrough.jsonld"}}