diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..bd5590b
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,21 @@
+node_modules/
+.npmrc
+.env
+.env.*
+__tests__/
+coverage/
+.nyc_output/
+dist/
+build/
+.cache/
+*.log
+.DS_Store
+tmp/
+.tmp/
+__pycache__/
+*.pyc
+.venv/
+venv/
+*.egg-info/
+.pytest_cache/
+READY_TO_PUBLISH
diff --git a/AGENTS.md b/AGENTS.md
new file mode 100644
index 0000000..74b9b99
--- /dev/null
+++ b/AGENTS.md
@@ -0,0 +1,24 @@
+Repository: CatOpt-Play (prototype)
+
+Architecture
+- Language: Python 3.8+
+- Layout: src/ package layout (src/idea36_catopt_play_category)
+- Core components:
+  - contracts: pydantic models for LocalProblem, SharedVariables, DualVariables, PlanDelta, PrivacyBudget, AuditLog
+  - solver: an ADMM-lite consensus solver (prototype)
+
+Tech stack
+- Python with pydantic for data contracts
+- pytest for tests
+- setuptools/pyproject for packaging
+
+Testing & Commands
+- Run tests: `pytest`
+- Build package: `python3 -m build`
+- Full automation: `bash test.sh` (installs build+pytest in the environment, installs package editable, runs tests, then builds)
+
+Rules for AI agents and contributors
+- Make minimal, well-scoped edits. Prefer small changes.
+- Follow src/ layout and put package code under `src/idea36_catopt_play_category`.
+- Add tests for new behaviour. CI expects `pytest` to pass.
+- Do not create READY_TO_PUBLISH unless the full original spec is implemented and tests pass.
diff --git a/README.md b/README.md
index 5a573e1..5748abf 100644
--- a/README.md
+++ b/README.md
@@ -1,3 +1,17 @@
-# idea36-catopt-play-category
+# CatOpt-Play (prototype)
 
-Source logic for Idea #36
\ No newline at end of file
+This repository contains a Python prototype for CatOpt-Play — a category-theory-inspired compositional optimizer for distributed multi-agent coordination. The goal of this prototype is to provide a canonical IR for local problems and data contracts, plus a small ADMM-lite solver demonstrating distributed consensus and delta-style plan deltas.
+
+Contents
+- src/idea36_catopt_play_category: core library (contracts, solver)
+- tests: basic tests for solver convergence and schema generation
+- AGENTS.md: repository architecture and contribution rules
+- test.sh: runs tests and builds the package
+
+Quickstart
+1. Install dev tools: `pip install -U build pytest`
+2. Install package in editable mode: `pip install -e .`
+3. Run tests: `pytest`
+4. Build distribution: `python3 -m build`
+
+This prototype focuses on a small, well-tested chunk: the canonical data contracts and an ADMM-lite consensus solver. It is intentionally minimal and designed to be extended with engine adapters, transports, and governance ledgers in follow-up work.
diff --git a/pyproject.toml b/pyproject.toml
new file mode 100644
index 0000000..b61373e
--- /dev/null
+++ b/pyproject.toml
@@ -0,0 +1,3 @@
+[build-system]
+requires = ["setuptools>=61.0", "wheel"]
+build-backend = "setuptools.build_meta"
diff --git a/setup.cfg b/setup.cfg
new file mode 100644
index 0000000..924c4a7
--- /dev/null
+++ b/setup.cfg
@@ -0,0 +1,16 @@
+[metadata]
+name = idea36-catopt-play-category
+version = 0.1.0
+description = CatOpt-Play: Category-Theoretic Compositional Optimizer (prototype)
+long_description = file: README.md
+long_description_content_type = text/markdown
+author = OpenCode
+license = MIT
+
+[options]
+package_dir =
+    = src
+packages = find:
+python_requires = >=3.8
+install_requires =
+    pydantic>=1.10
diff --git a/src/idea36_catopt_play_category/__init__.py b/src/idea36_catopt_play_category/__init__.py
new file mode 100644
index 0000000..1d06289
--- /dev/null
+++ b/src/idea36_catopt_play_category/__init__.py
@@ -0,0 +1,4 @@
+"""CatOpt-Play prototype package."""
+from . import contracts, solver
+
+__all__ = ["contracts", "solver"]
diff --git a/src/idea36_catopt_play_category/contracts.py b/src/idea36_catopt_play_category/contracts.py
new file mode 100644
index 0000000..89d56b6
--- /dev/null
+++ b/src/idea36_catopt_play_category/contracts.py
@@ -0,0 +1,57 @@
+from typing import Dict, Any, List, Optional
+from pydantic import BaseModel, Field
+from datetime import datetime
+
+
+class LocalProblem(BaseModel):
+    """Canonical representation of a local agent planning problem.
+
+    For the prototype we model simple quadratic objectives with coefficients
+    so the ADMM updates can be computed analytically in tests.
+    """
+
+    id: str
+    # objective: 0.5 * a * x^2 + b * x
+    a: float = Field(..., description="Quadratic coefficient (>=0)")
+    b: float = Field(..., description="Linear coefficient")
+    constraints: Optional[Dict[str, Any]] = None
+
+
+class SharedVariables(BaseModel):
+    values: Dict[str, float]
+    version: str
+    timestamp: datetime
+
+
+class DualVariables(BaseModel):
+    values: Dict[str, float]
+    version: str
+    timestamp: datetime
+
+
+class PlanDelta(BaseModel):
+    agent_id: str
+    delta: Dict[str, float]
+    version: str
+    timestamp: datetime
+    nonce: Optional[str] = None
+
+
+class PrivacyBudget(BaseModel):
+    remaining: float
+    used: float = 0.0
+    budget_id: Optional[str] = None
+
+
+class AuditLog(BaseModel):
+    event_id: str
+    actor: str
+    action: str
+    details: Optional[Dict[str, Any]] = None
+    timestamp: datetime
+
+
+def export_json_schemas() -> Dict[str, Any]:
+    """Return JSON schemas for canonical contracts."""
+    models = [LocalProblem, SharedVariables, DualVariables, PlanDelta, PrivacyBudget, AuditLog]
+    return {m.__name__: m.schema() for m in models}
diff --git a/src/idea36_catopt_play_category/solver.py b/src/idea36_catopt_play_category/solver.py
new file mode 100644
index 0000000..d824413
--- /dev/null
+++ b/src/idea36_catopt_play_category/solver.py
@@ -0,0 +1,46 @@
+from typing import List, Dict
+import math
+
+
+def admm_consensus(local_problems: List[Dict[str, float]], rho: float = 1.0, max_iter: int = 200, tol: float = 1e-4):
+    """
+    Simple ADMM consensus solver for scalar variables.
+
+    local_problems: list of dicts with keys 'a' and 'b' representing local objective
+      0.5 * a * x^2 + b * x
+
+    Returns tuple (z, history) where z is consensus variable and history a list of z over iterations.
+    """
+    n = len(local_problems)
+    # initialize
+    x = [0.0 for _ in range(n)]
+    u = [0.0 for _ in range(n)]
+    z = 0.0
+    history = []
+
+    for k in range(max_iter):
+        # x-update (closed-form for quadratic)
+        for i, p in enumerate(local_problems):
+            a = p.get("a", 0.0)
+            b = p.get("b", 0.0)
+            denom = a + rho
+            # minimize 0.5*a*x^2 + b*x + (rho/2)*(x - z + u)^2
+            x[i] = (-b + rho * (z - u[i])) / denom
+
+        # z-update: average of x + u
+        z_old = z
+        z = sum(x[i] + u[i] for i in range(n)) / n
+
+        # u-update
+        for i in range(n):
+            u[i] = u[i] + x[i] - z
+
+        history.append(z)
+
+        # check convergence (primal residual)
+        r_norm = math.sqrt(sum((x[i] - z) ** 2 for i in range(n)))
+        s_norm = math.sqrt(n) * abs(rho * (z - z_old))
+        if r_norm < tol and s_norm < tol:
+            break
+
+    return z, history
diff --git a/test.sh b/test.sh
new file mode 100644
index 0000000..2491dac
--- /dev/null
+++ b/test.sh
@@ -0,0 +1,16 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+echo "Installing dev dependencies (build, pytest)..."
+pip install -U build pytest >/dev/null
+
+echo "Installing package in editable mode..."
+pip install -e . >/dev/null
+
+echo "Running pytest..."
+pytest -q
+
+echo "Building distribution..."
+python3 -m build
+
+echo "All done."
diff --git a/tests/test_schema.py b/tests/test_schema.py
new file mode 100644
index 0000000..e5f9152
--- /dev/null
+++ b/tests/test_schema.py
@@ -0,0 +1,9 @@
+from idea36_catopt_play_category import contracts
+
+
+def test_export_schemas_contains_models():
+    schemas = contracts.export_json_schemas()
+    expected = ["LocalProblem", "PlanDelta", "AuditLog"]
+    for name in expected:
+        assert name in schemas
+        assert isinstance(schemas[name], dict)
diff --git a/tests/test_solver.py b/tests/test_solver.py
new file mode 100644
index 0000000..86290f5
--- /dev/null
+++ b/tests/test_solver.py
@@ -0,0 +1,16 @@
+from idea36_catopt_play_category.solver import admm_consensus
+
+
+def test_admm_consensus_converges_to_average():
+    # two agents with objectives 0.5*(x - c)^2 => a=1, b=-c
+    c1 = 2.0
+    c2 = -1.0
+    local = [
+        {"a": 1.0, "b": -c1},
+        {"a": 1.0, "b": -c2},
+    ]
+
+    z, history = admm_consensus(local, rho=1.0, max_iter=500, tol=1e-6)
+    # analytic centralized optimum is average of c1 and c2
+    expected = (c1 + c2) / 2.0
+    assert abs(z - expected) < 1e-3