MPC — Metastable Propositional Calculus

Metastable Propositional Calculus (MPC) engine. Analyzes the thermodynamic and physical feasibility of logical assertions across multi-step reasoning. Unlike standard Boolean logic, MPC detects epistemic drift and structural conflicts (k-states) by calculating the energetic holding costs of maintaining premises over time. Use this to rigorously verify whether a complex sequence of claims can be logically maintained together without collapsing into contradiction.

Truth values: c (committed) · s (suspended) · k (conflict) · r (reset)

---

Theory & Background

To successfully use this tool, it helps to understand the theoretical foundation of MPC. The framework models propositions as systems resting in a latent energy landscape rather than as instantaneous, costless Boolean states. For a detailed explanation of the physics, mathematics, and logic driving the engine, please review the foundational project artifacts:

• Metastable Propositional Calculus (MPC) as a Thermodynamic Extension — Part 1
• Metastable Propositional Calculus (MPC) as a Thermodynamic Extension — Part 2
• Metastable Propositional Calculus (MPC) as a Thermodynamic Extension — Part 3

---

What's new in v0.3

Feature	Detail
FastMCP	Replaced low-level MCP server with FastMCP for cleaner tool definitions and better client compatibility
Five-provider routing	Anthropic · Google · OpenAI · Kimi (Moonshot AI) · Ollama — all first-class
Dynamic model listing	Real-time queries to each provider's list-models endpoint; 5-minute TTL cache
Zero env-var conflicts	Each provider has its own variable: ANTHROPIC_API_KEY, GOOGLE_API_KEY, OPENAI_API_KEY, KIMI_API_KEY, OLLAMA_HOST
Provider tab in UI	Side-by-side key configuration, per-provider status, model counts
list_available_models tool	New MCP tool for dynamic model discovery
Retry logic	Transient errors retried up to 3× with exponential back-off
/status + /env endpoints	Provider health and env-var audit without exposing key values

---

Providers

Provider	SDK	Key Env Var	Notes
Anthropic	anthropic	ANTHROPIC_API_KEY	Claude claude-opus-4-6, claude-sonnet-4-6, Haiku
Google	google-generativeai	GOOGLE_API_KEY	Gemini 2.5 Pro, 2.0 Flash, 1.5
OpenAI	openai	OPENAI_API_KEY	GPT-4o, o1, o3-mini, etc.
Kimi	openai (OpenAI-compatible)	KIMI_API_KEY	Moonshot AI · moonshot.cn
Ollama	stdlib urllib	OLLAMA_HOST	Local models, no key needed

API keys are resolved in order: explicit argument → environment variable → .env file. No provider ever reads another provider's key variable.

---

Install

# Core — all five providers included
pip install -e .

# Add QuTiP for exact partition function (Ising Hamiltonian)
pip install qutip

# Add NetKet for spin-glass ground-state solver (requires JAX)
pip install "jax[cpu]" netket

# Full stack
pip install -e ".[full]"

Requires Python ≥ 3.11.

---

Quick start

Set API keys

# Any combination — only set what you have
export ANTHROPIC_API_KEY=sk-ant-…
export GOOGLE_API_KEY=AIza…
export OPENAI_API_KEY=sk-…
export KIMI_API_KEY=sk-…          # Moonshot AI key
export OLLAMA_HOST=http://localhost:11434   # default; omit if standard

Or use the Providers tab in the browser UI to enter and persist keys to .env.

Start the server

mpc-server

Starts:

• MCP server on stdio (register in Claude Desktop or any MCP client)
• Browser UI on http://localhost:7771

---

Claude Desktop configuration

{
  "mcpServers": {
    "mpc": {
      "command": "mpc-server",
      "env": {
        "ANTHROPIC_API_KEY": "sk-ant-…",
        "GOOGLE_API_KEY": "AIza…",
        "OPENAI_API_KEY": "sk-…",
        "KIMI_API_KEY": "sk-…"
      }
    }
  }
}

---

MCP Tools

Tool	Description	API call?
compile_text	Full MPC analysis: hypotheses, phases, frustration matrix, free energy (QuTiP), spin-glass ground state, Theorem 6.1 bound	✓
compile_sequence	Multi-step trace with Entity Ledger — tracks epistemic drift and η_i accumulation	✓
read_claims	Per-claim phase assignment (c/s/k/r) with rationale	✓
budget_estimate	Theorem 6.1 N_max = O(√(2E*/αε_min d_avg)) — pure arithmetic	✗
list_available_models	Real-time model catalogue across all five providers	✗ (cached)

All tools accept provider_api_key as an optional parameter; omitting it reads from environment variables automatically.

---

Python API

import mpc_core

# Full analysis — Anthropic (default)
result = mpc_core.compile("Your text here…", api_key="sk-ant-…")

# Google Gemini
result = mpc_core.compile("…", model="gemini-2.0-flash", api_key="AIza…")

# OpenAI
result = mpc_core.compile("…", model="gpt-4o", api_key="sk-…")

# Kimi (Moonshot AI)
result = mpc_core.compile("…", model="moonshot-v1-32k", api_key="sk-…")

# Local Ollama (no key needed)
result = mpc_core.compile("…", model="llama3:8b")

print(result.energy_model.free_energy)      # F = -kT ln Z
print(result.ground_state.energy)           # Ising ground-state energy
print(result.ground_state.stable_ids)       # most compatible hypothesis subset
print(result.analytical_summary)

# Per-claim phase assignment
phases = mpc_core.read_claims(
    ["All ravens are black.", "Some ravens are albino."],
    api_key="sk-ant-…",
    model="claude-sonnet-4-6",
)

# Budget theorem (no API call)
est = mpc_core.budget_estimate(N=8, d_avg=2.5, epsilon_min=1.2)
print(est.interpretation)

# Multi-step trace with Entity Ledger
seq = mpc_core.compile_sequence(
    ["Step 1 text…", "Step 2 text…", "Step 3 text…"],
    api_key="sk-ant-…",
)

# Dynamic model listing
from mpc_core.providers import list_models, ProviderID
models = list_models(ProviderID.ANTHROPIC, "sk-ant-…")

# Free-energy surface (no API call)
from mpc_core.thermodynamics import free_energy_surface
surface = free_energy_surface(my_epsilon_matrix, T_range=(0.2,5), E_star_range=(2,40))
# surface["F"][T_index][E_star_index] → F value

---

Browser UI — tabs

Tab	Description
Analyse text	Full MPC analysis with hypothesis cards, thermodynamic strip (Z, F, S), ground-state box
Read claims	One claim per line → instant phase assignment
3D Free Energy	Interactive Plotly F(T, E*) surface with N_max Theorem 6.1 contour
Energy landscape	Animated 2-D canvas with budget/temperature sliders
Compatibility matrix	Pairwise ε_ij frustration table
Budget calculator	Theorem 6.1 N_max — no API key needed
Historical Heatmap	η_i accumulation across a reasoning trace (Addendum V)
Providers	API key configuration, per-provider status and model counts

---

HTTP API (localhost:7771)

Method	Path	Description
GET	/	Browser UI (index.html)
GET	/models	Model catalogue using env-var keys
POST	/models	Refresh catalogue with caller-supplied keys
GET	/env	Which env vars are set (values redacted)
POST	/status	Provider connectivity health check
POST	/setenv	Persist a key to .env
POST	/	MPC actions (compile, compile_sequence, read_claims, budget_estimate, free_energy_surface, ground_state)

---

Testing

# Arithmetic tests (no API key required)
pytest tests/ -v

# Live API tests — any provider combination
ANTHROPIC_API_KEY=sk-ant-…  pytest tests/ -v
GOOGLE_API_KEY=AIza…        pytest tests/ -v
OPENAI_API_KEY=sk-…         pytest tests/ -v
KIMI_API_KEY=sk-…           pytest tests/ -v

---

Architecture

mpc_core/
  providers.py     NEW v0.3 — ProviderID enum, per-provider key resolution,
                   dynamic model listing with TTL cache, all_models_catalogue()
  router.py        REWRITTEN — five-backend dispatch, retry logic, auth-error fast-fail
  compiler.py      compile() · read_claims() · budget_estimate() · compile_sequence()
  entity_ledger.py Cross-step entity registry (four-layer pipeline)
  thermodynamics.py QuTiP partition function · NetKet spin-glass · free_energy_surface()
  json_repair.py   Best-effort repair of truncated LLM JSON
  models.py        MPCResult dataclass hierarchy

mpc_server/
  server.py        REWRITTEN — FastMCP application + HTTP UI proxy (port 7771)
                   New endpoints: GET /env, POST /status, POST /models

static/
  index.html       REWRITTEN — provider selector tabs, per-provider key inputs,
                   dynamic model dropdowns, /status integration

---

Roadmap

• v0.1 ✓ Core compiler, MCP server, reference UI
• v0.2 ✓ Multi-backend routing · QuTiP · NetKet · 3D Plotly · Historical heatmap
• v0.3 ✓ FastMCP · Five providers · Dynamic model listing · Provider UI · Retry logic
• v0.4 Spectral Laplacian extension of Theorem 6.1, community-aware N_max bounds
• v0.5 Streaming analysis; differential η_i display per hypothesis per step

---

License

MIT