eml-mcp

name

eml-mcp

description

Use this skill when working with the EML (Exp-Minus-Log) MCP server — discovering pure-EML decompositions of elementary functions, inspecting the formula catalog, running symbolic regression, or reasoning about the Sheffer-style operator `eml(x, y) = exp(x) - ln(y)`. Trigger keywords include "EML", "elementary functions", "Sheffer operator for continuous math", "symbolic regression via EML", "eml_discover", and "K-complexity of a formula".

EML MCP — Agent Skill

What this is

The EML MCP server exposes the EML (Exp-Minus-Log) operator eml(x, y) = exp(x) - ln(y) — a single binary function that, paired with the constant 1, generates every standard elementary function. It's the continuous analogue of the NAND gate. Source: Odrzywołek 2026, arXiv:2603.21852v2.

The server is at /home/ty/Repositories/ai_workspace/eml-mcp. The SQLite catalog eml_formulas.db persists every seed, discovery, and verification across sessions.

When to reach for what tool

Routing table — use the smallest/fastest tool that answers the question.

Question / task	Tool
What formulas exist? What's in the catalog?	eml_list_formulas
What's the full tree for a known formula?	eml_tree_info
Does eml(a, b) equal z for specific a, b?	eml_evaluate
Is a stored tree correct to machine precision?	eml_verify
How do these two formulas structurally compare?	eml_similarity (Zhang-Shasha)
Can this expression be simplified?	eml_simplify
Compile a Python math expression into an EML tree	eml_compile
Fast discovery — expect to find it in seconds	eml_discover (sync, blocking)
Long discovery — expect minutes, want progress visibility	eml_discover_start (async)
Poll a running job	eml_discover_status
Retrieve a finished job's full result	eml_discover_result
Stop a stuck/slow job, preserve partial progress	eml_discover_cancel
What jobs exist?	eml_discover_list
Gradient-based (PyTorch Adam) formula fitting	eml_symbolic_regression
Build a parameterized master tree for SR	eml_master_tree

Hard-earned rules of thumb

1. Default to async for anything beyond simple additive/scaling targets. The sync eml_discover has a 4-minute MCP ceiling and loses partial progress on timeout. Async jobs checkpoint every 5 iterations and survive restarts.

2. Cancel liberally if MSE plateaus. Cancellation preserves the best-so-far candidate and the top-N nearby_discoveries. A cancelled job is not a wasted one.

3. K reported by a fresh discovery is the simplified K. The engine now simplifies before persisting. k_before_simplify shows what the raw evolutionary tree looked like — usually 2–5× larger.

4. If eml_simplify collapses a tree to a bare const or var, something in your derivation lost the symbolic structure. This is rare but real — e and zero constant-fold to 2.718… and 0.0 respectively, which is numerically correct but outside the pure-EML grammar S → 1 | x | eml(S, S). The migration script guards against this; the live simplifier doesn't, so don't blindly trust its output when the input was already a seed.

5. The constant -697.281718171541 is a finite proxy for ln(ln(0)) = -∞. Treat it as "essentially negative infinity" when reading trees. exp(-697.28) ≈ 10⁻³⁰³ is zero at machine precision, so eml(-697.28, z) ≈ -ln(z). This constant appears throughout compositionally-derived formulas; it's not a bug.

Reference material

Load these on demand:

• reference/tool_decision_tree.md — detailed sync-vs-async routing, with worked examples for common targets.
• reference/k9_families.md — the K=9 template for x + c and c·x. Recognizing a family lets you predict K before running search.
• reference/operational_gotchas.md — the -697.28 proxy, grammar-preservation, signature-based dedup, what the simplifier can and can't do.
• reference/observed_behavior.md — empirical notes on what resolves fast vs. stagnates, target selection guidance.
• research/paper_odrzywolek_2026.md — source paper summary and how the server's implementation relates to it.
• research/cross_domain_notes.md — pointers to the project's cross-domain exploration material.

Files an agent should know about

eml-mcp/
├── README.md                              # Human-facing overview
├── docs/
│   ├── FORMULAS.md                        # Auto-generated catalog
│   ├── simplifier_k_reduction.md          # Migration rationale + numbers
│   ├── async_discovery.md                 # Background job architecture
│   ├── k9_families.md                     # Synthesis: K=9 templates
│   ├── cross_domain_exploration.md        # MGA mapping (NAND ↔ EML ↔ biology)
│   └── eml_transformer_architecture.md    # Older speculative design
├── src/eml_mcp/
│   ├── server.py           # @mcp.tool definitions
│   ├── discovery.py        # DiscoveryEngine, find_target, DiscoveryCancelled
│   ├── jobs.py             # Async JobStore, background threads, orphan sweep
│   ├── simplifier.py       # Identity-rule reduction + constant folding
│   ├── database.py         # SQLite schema + formula CRUD + job rows
│   ├── registry.py         # Seed formulas + verify_eml_identity
│   ├── trees.py            # EMLNode data structure
│   └── primitives.py       # eml() operator, test points, safe arithmetic
├── scripts/
│   ├── migrate_simplify_catalog.py   # One-shot K-reduction migration
│   ├── export_catalog.py             # Regenerate docs/FORMULAS.md
│   └── cleanup_duplicates.py         # Dedup catalog by signature
└── eml_formulas.db                    # The catalog (SQLite)

Coding invariants for this project

The user (Ty) prefers:

• uv for Python tooling, Python 3.13+
• Type hints using X | None, list[...], dict[...] (PEP 604/585, no Optional/List/Dict)
• complex128 arithmetic (not float64) because trig needs complex intermediates via Euler's formula
• Edits over rewrites — str_replace / edit_block, not wholesale file rewrites
• Never start/stop/restart the MCP server — Ty manages that. The server does not hot-reload; after code changes, wait for Ty to restart it.

Sanity-check workflow for code changes

After non-trivial edits to src/eml_mcp/:

cd /home/ty/Repositories/ai_workspace/eml-mcp
.venv/bin/python -m pytest tests/ -x -q --tb=short

All 78 tests should pass. The test_sr_recovery*.py tests take several seconds each (they train torch networks); test_parallel_discovery.py spawns processes; the rest are fast.

After catalog-affecting edits, regenerate the human-readable catalog:

.venv/bin/python scripts/export_catalog.py