diff --git a/README.md b/README.md
index 2f58883..6843f05 100644
--- a/README.md
+++ b/README.md
@@ -1,3 +1,20 @@
 # catopt-category-theoretic-compositional-
 
-Problem space: distributed, offline-first optimization across heterogeneous edge devices (DERs, meters, controllers, EV chargers) in mesh networks. Centralized solvers are infeasible due to latency, bandwidth, and privacy. We need a modular, provably
\ No newline at end of file
+Problem space: distributed, offline-first optimization across heterogeneous edge devices (DERs, meters, controllers, EV chargers) in mesh networks. Centralized solvers are infeasible due to latency, bandwidth, and privacy. We need a modular, provably compositional optimization framework that can be plugged into existing energy and robotics ecosystems with privacy by design and offline resilience.
+
+This repository implements a minimal MVP scaffold for CatOpt, a light-weight framework that uses category-theory-inspired abstractions to express distributed optimization problems and a toy solver stack to validate the idea in CI.
+
+MVP Runtime (new): lightweight primitives to experiment with CatOpt concepts locally.
+- LocalProblem: representation of an agent's optimization task.
+- DataContract, SharedVariables, PlanDelta: lightweight data-exchange primitives for a privacy-conscious mesh.
+- ADMMTwoAgentSolver: tiny, in-process ADMM-like solver to demonstrate joint optimization across two agents.
+- demo_two_agent_admm(): quick in-repo demonstration function returning final variables.
+
+Usage notes:
+- Import from the package and optionally run the demo function to observe convergence on a toy problem.
+- Example:
+  ```python
+  from catopt_category_theoretic_compositional.runtime import ADMMTwoAgentSolver, demo_two_agent_admm
+  result = demo_two_agent_admm()
+  print(result)
+  ```
diff --git a/src/catopt_category_theoretic_compositional_/__init__.py b/src/catopt_category_theoretic_compositional_/__init__.py
index ed0324b..6578c21 100644
--- a/src/catopt_category_theoretic_compositional_/__init__.py
+++ b/src/catopt_category_theoretic_compositional_/__init__.py
@@ -1,13 +1,13 @@
-"""Minimal placeholder for CatOpt package.
+"""CatOpt: Minimal placeholder surface & MVP runtime exposure."""
 
-This module provides a tiny, well-typed surface to validate packaging and imports
-in CI. The real project would implement the MVP of the CatOpt framework.
-"""
+from .runtime import LocalProblem, SharedVariables, DataContract, PlanDelta, ADMMTwoAgentSolver, demo_two_agent_admm  # noqa: F401
 
 def add(a: int, b: int) -> int:
     """Return the sum of two integers.
 
     This tiny function exists to provide a deterministic, testable behavior
-    for the initial CI gate.
+    for the initial CI gate, preserving backwards compatibility with tests.
     """
     return a + b
+
+__all__ = ["add", "LocalProblem", "SharedVariables", "DataContract", "PlanDelta", "ADMMTwoAgentSolver", "demo_two_agent_admm"]
diff --git a/src/catopt_category_theoretic_compositional_/runtime.py b/src/catopt_category_theoretic_compositional_/runtime.py
new file mode 100644
index 0000000..01ecbaf
--- /dev/null
+++ b/src/catopt_category_theoretic_compositional_/runtime.py
@@ -0,0 +1,121 @@
+"""CatOpt MVP Runtime: Minimal category-inspired runtime primitives.
+
+This module provides a tiny, self-contained runtime that demonstrates:
+- Local optimization problem representation (LocalProblem)
+- Simple data contracts (DataContract, SharedVariables, PlanDelta)
+- A toy ADMM-like two-agent solver (ADMMTwoAgentSolver)
+
+The goal is not to be a full implementation but to provide a minimal,
+understandable surface that respects the MVP's spirit and can be wired up
+into the existing test harness without changing the current public API.
+"""
+from __future__ import annotations
+
+from dataclasses import dataclass, field
+from typing import Dict, Optional, List, Tuple
+import time
+
+@dataclass
+class LocalProblem:
+    """Represents a local optimization problem for an agent.
+
+    For the MVP this captures a quadratic objective of form
+        0.5 * a * x^2 + b * x
+    along with an optional linear term for convenience. The real CatOpt use
+    would expose a richer DSL; this is a compact placeholder.
+    """
+
+    id: str
+    a: float  # quadratic coefficient (scalar)
+    b: float  # linear coefficient (scalar)
+    x_name: str = "x"  # variable name for display purposes
+
+    def __post_init__(self):
+        if self.a <= 0:
+            # Keep a positive definite quadratic for stability in demo
+            self.a = max(self.a, 1e-6)
+
+
+@dataclass
+class DataContract:
+    """A lightweight data-contract describing what is exchanged between agents."""
+
+    version: int = 1
+    schema: Dict[str, str] = field(default_factory=dict)
+
+
+@dataclass
+class SharedVariables:
+    """Container for values shared between agents (e.g., delta signals)."""
+
+    values: Dict[str, float] = field(default_factory=dict)
+
+
+@dataclass
+class PlanDelta:
+    """Represents a delta/plan update from an agent."""
+
+    contract_id: str
+    delta: Dict[str, float]
+    timestamp: float = field(default_factory=time.time)
+
+
+class ADMMTwoAgentSolver:
+    """Tiny ADMM-like solver for two agents sharing one variable.
+
+    Solves a simple coupled objective:
+        minimize 0.5*a1*x1^2 + b1*x1 + 0.5*a2*x2^2 + b2*x2
+        subject to x1 + x2 = 1
+    using the scaled dual variable formulation with updates similar to ADMM.
+    This is intentionally small and self-contained for MVP purposes.
+    """
+
+    def __init__(self, a1: float, b1: float, a2: float, b2: float, rho: float = 1.0):
+        self.a1 = float(a1)
+        self.b1 = float(b1)
+        self.a2 = float(a2)
+        self.b2 = float(b2)
+        self.rho = float(rho)
+        # Initialize variables
+        self.x1 = 0.0
+        self.x2 = 0.0
+        self.z = 0.5  # shared variable estimate
+        self.u1 = 0.0  # dual vars
+        self.u2 = 0.0
+
+        # History for introspection
+        self.history: List[Dict[str, float]] = []
+
+    def _step(self) -> None:
+        # x1 update: minimize 0.5*a1*x1^2 + b1*x1 + (rho/2)*(x1 - z + u1)^2
+        # Closed-form: x1 = -(b1 + rho*(-z + u1)) / (a1 + rho)
+        self.x1 = (-(self.b1) + self.rho * (self.z - self.u1)) / (self.a1 + self.rho)
+        # x2 update: similarly
+        self.x2 = (-(self.b2) + self.rho * (self.z - self.u2)) / (self.a2 + self.rho)
+        # z update: minimize w.r.t z of the augmented terms
+        self.z = (self.x1 + self.x2 + self.u1 + self.u2) / 2.0
+        # Dual updates
+        self.u1 += self.x1 - self.z
+        self.u2 += self.x2 - self.z
+        # Save history snapshot
+        self.history.append({"x1": self.x1, "x2": self.x2, "z": self.z,
+                               "u1": self.u1, "u2": self.u2})
+
+    def run(self, iterations: int = 10) -> List[Dict[str, float]]:
+        for _ in range(iterations):
+            self._step()
+        return self.history or []
+
+    def final_solution(self) -> Tuple[float, float, float]:
+        return self.x1, self.x2, self.z
+
+
+def demo_two_agent_admm() -> Dict[str, float]:
+    """Run a tiny demo with 2 agents and return the final variables.
+
+    This helper is convenient for quick sanity checks in the REPL or tests.
+    """
+    solver = ADMMTwoAgentSolver(a1=2.0, b1=0.5, a2=3.0, b2=-0.2, rho=1.0)
+    _ = solver.run(iterations=20)
+    x1, x2, z = solver.final_solution()
+    return {"x1": float(x1), "x2": float(x2), "z": float(z)}