A.Appendix
A.1 Repository
The Nanometers harness is implemented as a single-file Python script ( nanometers.py) with full source available on GitHub:
Python 3.11+ · MIT License · async/await architecture
A.2 Usage
# Compute
python nanometers.py 728
# Manual problem input
python nanometers.py --manual
# Run only, skip verification
python nanometers.py 728 --models claude --skip-aristotle
A.3 Dependencies
The harness requires the following Python packages:
| Package | Role |
|---|---|
| httpx | Async HTTP client for problem acquisition |
| openai | Inference operator |
| anthropic | Inference operator and synthesis |
| beautifulsoup4 | HTML parsing for |
| python-dotenv | API key management |
A.4 Prompt Specification
The system prompt for (GPT-5.4 Pro) constrains outputs to deductive strategies:
“You are an expert mathematician specializing in combinatorics, number theory, and additive combinatorics. Produce a rigorous, publication-quality proof. Require: precise logical structure with clearly stated lemmas, complete epsilon-delta arguments where applicable, explicit bounds and constants, and citation of relevant known results.”
The system prompt for (Claude Opus 4.6) constrains outputs to constructive strategies:
“You are a research mathematician known for creative, non-obvious constructions and unexpected connections between subfields. Prioritize: probabilistic method arguments, algebraic and explicit constructions, applications of the Lovász Local Lemma, and novel approaches outside standard techniques.”
A.5 Transparency
All model outputs are logged without modification. The harness performs no filtering, editing, or post-processing of mathematical content beyond the synthesis step described in Section 2.3. Every generated file includes an attribution header identifying it as AI-generated output.
This project makes no claims of having solved any open problem. All results are presented as candidate proofs subject to verification via the predicate defined in Section 2.4.