翻訳待ち：Asked AI to do a mini math breakthrough. It did a mini breakthrough

AI サービスが一時的に利用できないため、復旧後に翻訳を補完します。

Notifications You must be signed in to change notification settings Fork 0 Star 0 BranchesTags Open more actions menu Folders and files NameName Last commit message Last commit date Latest commit History 7 Commits 7 Commits .github/workflows .github/workflows certificates certificates docs docs paper paper scripts scripts src/zeta_simple_zeros src/zeta_simple_zeros tests tests .dockerignore .dockerignore .gitignore .gitignore .python-version .python-version AUDIT.md AUDIT.md CITATION.cff CITATION.cff Dockerfile Dockerfile LICENSE LICENSE Makefile Makefile PROVENANCE.md PROVENANCE.md README.md README.md REPRODUCIBILITY.md REPRODUCIBILITY.md pyproject.toml pyproject.toml requirements.lock requirements.lock Repository files navigation 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 $$ \liminf_{T\to\infty}\frac{N_0^s(T,2T)}{N(T,2T)} \ge 0.6730213619501665335\ldots. $$ Here $N(T,2T)$ counts nontrivial zeros with multiplicity, while $N_0^s(T,2T)$ counts simple zeros on the critical line. 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) · LaTeX source · technical audit · reproduction guide What reproduced exactly The strengthened source is isolated in commit 0faebf367ffb780951845d014e2e3d9a4a04adb1. Starting from the public verifier, it changes the target to $191/50000$ and derives the matching pressure cutoff of 45,840 grid cells. 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. CI reruns the exhaustive verifier from a clean checkout and compares every deterministic field. Result and scope Anthropic's Theorem D gives $$ H_{\mathrm{MT}} =\frac32-\frac1{\sqrt2}\cot\frac1{\sqrt2} =0.672500703679\ldots. $$ The seven-point refinement proves, using those imported analytic inputs, $$ F_6(g_1,\ldots,g_6)\ge\frac{191}{50000} $$ for all nonnegative gaps. With block size $m=267$, the final deduction is $$ \frac{13{,}350{,}000H_{\mathrm{MT}}-26{,}600}{13{,}300{,}149} =0.6730213619501665335\ldots. $$ The matrix inequality, kernel normalization, seven-point combinatorics, shifted-block pinching, and final arithmetic are covered in the audit. The analytic trace estimates, tail bounds, and optimized test family remain dependencies of the cited Anthropic paper and its Lean 4 artifact. Reproduce it 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. Provenance Upstream artifact: ainta/zeta-simple-zeros, commit 040c5e899e658aed7b56a2a87f501798fe10761d. The upstream repository identifies the research draft as generated by GPT-5.6 Sol. Anthropic foundation: research article, paper, and Lean 4 artifact. This release preserves the upstream MIT license and history. See PROVENANCE.md for the exact chain. Status 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. License MIT, inherited from the upstream artifact. MIT license Activity Stars 0 stars Watchers 0 watching Forks 0 forks Report repository