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Examples

Curated, runnable demonstrations of the EML tool layer and the multi-agent investigations built on top of it. Every example in this directory is self-contained and runnable with python examples/<name>.py after pip install -e ..

File What it shows
01_eml_basics.py The seven EML tools in one pass — translate, evaluate, verify, search
02_hard_problems_via_sympy.py sympy_compute solving the five graduate-level hard problems
03_riemann_zeros_on_critical_line.py Computes the first 20 non-trivial zeros of ζ and verifies they sit on Re(s)=½
04_riemann_li_criterion.py Computes Li's λₙ for n=1..10 and confirms positivity (RH-equivalent, Li 1997)
05_riemann_robin_criterion.py Checks σ(n) < e^γ·n·log log n for 5040 < n ≤ 10000 (RH-equivalent, Robin 1984)
06_riemann_pair_correlation.py Empirical pair correlation of normalized zero spacings vs Montgomery's GUE form

Running them

pip install -e .
python examples/01_eml_basics.py
python examples/03_riemann_zeros_on_critical_line.py   # takes ~1 min; high precision

All six run offline and require no Claude API key. The subagent-orchestration flow (which needs Claude Code) is documented in ../RESULTS.md and ../RIEMANN_REPORT.md; the examples here are the pure computation half of those runs and can be used to verify the agents' numerical claims independently.

Subagent prompt templates

The exact prompts used to spawn Claude Code subagents for the benchmark and Riemann runs are embedded in ../src/eml_research/benchmark.py (for the general math benchmark via the Anthropic SDK) and in ../src/eml_research/riemann/README.md (for the RH investigation). See those files for the templates and the track-split (EML-first vs Classical-only) rules.