Omg Tension Resolver

---
name: omg-tension-resolver
description: '[OpenModelica Microgrid Gym](https://github.com/upb-lea/openmodelica-microgrid-gym) (OMG) provides a physical substrate where all skill tensions find resolution through **energy flow dynamics**:'
metadata:
  skill_type: Dynamical system substrate for balancing opposing forces
  interface_ports:
  - Commands
---
# omg-tension-resolver Skill

> *Resolve skill paradigm tensions through OpenModelica Microgrid Gym dynamics*

## The Gym as Universal Resolver

[OpenModelica Microgrid Gym](https://github.com/upb-lea/openmodelica-microgrid-gym) (OMG) provides a physical substrate where all skill tensions find resolution through **energy flow dynamics**:

```
┌──────────────────────────────────────────────────────────────────────┐
│                     MICROGRID AS SKILL RESOLVER                       │
├──────────────────────────────────────────────────────────────────────┤
│                                                                       │
│   TENSION                    MICROGRID RESOLUTION                     │
│   ═══════                    ════════════════════                     │
│                                                                       │
│   temporal ↔ atemporal   →   FMU simulation ↔ steady-state analysis  │
│   symbolic ↔ subsymbolic →   Modelica eqns ↔ neural controller       │
│   maximize ↔ sample      →   SafeOpt UCB ↔ GP posterior sampling     │
│   backprop ↔ non-backprop→   gradient ctrl ↔ Bayesian optimization   │
│   local ↔ global         →   inverter control ↔ grid-wide stability  │
│   discrete ↔ continuous  →   PWM switching ↔ continuous power flow   │
│                                                                       │
└──────────────────────────────────────────────────────────────────────┘
```

## Tension Resolution Patterns

### 1. Temporal ↔ Atemporal (d=2.131)

**Skills in tension**: `unworld`, `temporal-coalgebra`, `duckdb-temporal-versioning`

**Resolution via FMU dynamics**:

```python
# Temporal: FMU simulation with time-stepping
class TemporalController:
    def step(self, env, t, dt):
        # Time-indexed state evolution
        obs, reward, done, info = env.step(self.action(t))
        return obs

# Atemporal: Steady-state Lyapunov analysis
class AtemporalAnalyzer:
    def steady_state(self, network_yaml):
        # No time - only derivational structure
        # V_steady = lim_{t→∞} V(t) if stable
        jacobian = self.linearize_around_equilibrium()
        eigenvalues = np.linalg.eigvals(jacobian)
        return all(ev.real < 0 for ev in eigenvalues)  # Hurwitz criterion
```

**Bridge**: The FMU supports **both** time-domain simulation AND steady-state analysis. The `ModelicaEnv.reset()` initializes to steady-state, while `step()` evolves temporally.

### 2. Symbolic ↔ Subsymbolic (d=1.859)

**Skills in tension**: `sicp`, `lispsyntax-acset`, `gflownet`, `forward-forward-learning`

**Resolution via Modelica + Neural control**:

```python
# Symbolic: Modelica equations (explicit structure)
"""
model Inverter
  parameter Real L = 2.3e-3;  // Inductance
  parameter Real R = 0.4;      // Resistance
  Real v_out, i_out;
equation
  L * der(i_out) = v_in - R * i_out - v_out;  // Symbolic ODE
end Inverter;
"""

# Subsymbolic: Neural network controller
class NeuralController:
    def __init__(self):
        self.net = nn.Sequential(
            nn.Linear(obs_dim, 64),
            nn.ReLU(),
            nn.Linear(64, action_dim)
        )
    
    def action(self, obs):
        return self.net(torch.tensor(obs))

# Resolution: Hybrid control with symbolic safety envelope
class HybridController:
    def __init__(self):
        self.neural = NeuralController()
        self.symbolic_bounds = SymbolicSafetyEnvelope()
    
    def action(self, obs):
        neural_action = self.neural.action(obs)
        # Project onto symbolic safety set
        return self.symbolic_bounds.project(neural_action)
```

### 3. Maximize ↔ Sample (d=1.867)

**Skills in tension**: `compression-progress`, `kolmogorov-compression`, `gflownet`, `curiosity-driven`

**Resolution via SafeOpt Bayesian optimization**:

```python
# SafeOpt balances BOTH paradigms:
# - UCB (Upper Confidence Bound) = maximize expected + uncertainty
# - Posterior sampling = sample from GP belief

class SafeOptResolver:
    def __init__(self, initial_safe_params):
        self.gp = GPy.models.GPRegression(X_init, Y_init, 
                                           kernel=GPy.kern.Matern32(ndim))
        self.optimizer = SafeOptSwarm(self.gp, 
                                       parameter_set=bounds,
                                       threshold=safe_threshold)
    
    def resolve_tension(self, mode='balanced'):
        if mode == 'maximize':
            # Pure exploitation (compression-progress)
            return self.optimizer.optimize(beta=0.0)
        elif mode == 'sample':
            # Pure exploration (gflownet-like)
            return self.gp.posterior_sample()
        else:
            # Balanced: SafeOpt's natural behavior
            return self.optimizer.optimize()  # UCB with safety
```

### 4. Backprop ↔ Non-Backprop (d=1.952)

**Skills in tension**: `system2-attention`, `forward-forward-learning`, `godel-machine`

**Resolution via gradient-free Bayesian optimization**:

```python
# OMG's SafeOpt is GRADIENT-FREE by design!
# No backprop through the FMU - only black-box evaluation

class GradientFreeOptimizer:
    """
    SafeOpt queries the environment as a black box:
    params → episode reward (no gradients needed)
    
    This resolves the backprop/non-backprop tension:
    - Internal FMU uses symbolic equations (differentiable)
    - Outer loop uses GP (no backprop through simulation)
    """
    
    def optimize_episode(self, params):
        # Run full episode with params
        self.controller.set_params(params)
        total_reward = 0
        obs = self.env.reset()
        done = False
        while not done:
            action = self.controller(obs)
            obs, reward, done, _ = self.env.step(action)
            total_reward += reward
        return total_reward  # Black-box evaluation
```

### 5. Local ↔ Global (d=0.5)

**Skills in tension**: `forward-forward-learning`, `epistemic-arbitrage` vs `sheaf-cohomology`, `kan-extensions`

**Resolution via multi-inverter coordination**:

```python
# Local: Each inverter has its own PI controller
class LocalInverterController:
    def __init__(self, inverter_id):
        self.id = inverter_id
        self.kp, self.ki = 0.1, 10.0  # Local gains
    
    def control(self, local_obs):
        # Only sees own voltage/current
        error = self.v_ref - local_obs['v_out']
        return self.kp * error + self.ki * self.integral

# Global: Grid-wide droop control for load sharing
class GlobalDroopController:
    def __init__(self, inverters):
        self.inverters = inverters
        self.droop = 0.01  # Frequency droop coefficient
    
    def coordinate(self, global_state):
        # Adjust all inverters for power balance
        total_load = sum(inv.p_out for inv in self.inverters)
        for inv in self.inverters:
            # Droop: share load proportionally
            inv.freq_ref = 50 - self.droop * inv.p_out

# Resolution: Hierarchical control (local + global)
class HierarchicalController:
    def __init__(self):
        self.local = [LocalInverterController(i) for i in range(n_inv)]
        self.global_ = GlobalDroopController(self.local)
    
    def control(self, obs):
        # Global sets references
        self.global_.coordinate(obs['grid'])
        # Local tracks references
        return [c.control(obs[f'inv_{i}']) for i, c in enumerate(self.local)]
```

### 6. Discrete ↔ Continuous (d=0.6)

**Skills in tension**: `acsets`, `three-match`, `moebius-inversion` vs `persistent-homology`, `sheaf-laplacian`

**Resolution via PWM and averaging**:

```python
# Discrete: PWM switching (finite states)
class PWMController:
    def __init__(self, fs=10000):  # 10kHz switching
        self.fs = fs
        self.states = [-1, 0, 1]  # Discrete switching states
    
    def switch(self, duty_cycle):
        # Discrete decision: which state?
        return np.sign(duty_cycle) if abs(duty_cycle) > 0.5 else 0

# Continuous: Averaged model (dq-frame)
class ContinuousModel:
    """
    dq-frame transformation averages over switching:
    v_d, v_q = continuous voltages (no switching ripple)
    """
    def transform(self, v_abc, theta):
        T = park_transform(theta)
        return T @ v_abc  # Continuous representation

# Resolution: Multi-rate simulation
class MultiRateEnv:
    def __init__(self):
        self.fast_dt = 1e-5   # Switching dynamics
        self.slow_dt = 1e-3   # Averaged dynamics
    
    def step(self, action):
        # Fast loop: discrete switching
        for _ in range(int(self.slow_dt / self.fast_dt)):
            switch_state = self.pwm.switch(action)
            self.fmu.doStep(self.fast_dt, switch_state)
        
        # Slow loop: averaged observation
        return self.average_obs(), self.reward(), self.done()
```

## Triangle Inequality Resolution

Each tension pair becomes a **valid hop** through the microgrid:

```
          unworld ←───────2.13───────→ temporal-coalgebra
              │                              │
              │                              │
              │     ┌───────────────┐        │
              └────►│   OMG FMU     │◄───────┘
                    │ steady-state  │
                    │   + step()    │
                    └───────────────┘
                           │
                     d ≤ 1.0 + 1.0 = 2.0
                    (triangle inequality satisfied via bridge)
```

## Implementation

### Environment Configuration

```yaml
# net/tension_resolver.yaml
Network:
  name: TensionResolver
  
Components:
  # Symbolic (Modelica equations)
  Inverter1:
    type: Inverter
    params: {L: 2.3e-3, R: 0.4}
  
  # Subsymbolic (neural controller target)
  Load:
    type: RLLoad
    controller: neural
  
  # Discrete/Continuous bridge
  PWM:
    type: PWMModulator
    fs: 10000
    
Connections:
  - [Inverter1.output, Load.input]
```

### Tension-Aware Agent

```python
from openmodelica_microgrid_gym.agents import SafeOptAgent

class TensionResolvingAgent(SafeOptAgent):
    """
    Agent that explicitly resolves skill tensions through control.
    """
    
    def __init__(self, tensions: List[Tuple[str, str, float]]):
        super().__init__()
        self.tensions = tensions
        self.resolution_weights = self._compute_weights()
    
    def _compute_weights(self):
        """Map tensions to control objectives."""
        weights = {}
        for t1, t2, dist in self.tensions:
            if 'temporal' in t1 or 'temporal' in t2:
                weights['settling_time'] = 1.0 / dist
            if 'maximize' in t1 or 'sample' in t2:
                weights['exploration_exploitation'] = dist
            if 'local' in t1 or 'global' in t2:
                weights['coordination'] = 1.0 / dist
        return weights
    
    def reward(self, obs):
        """Multi-objective reward balancing tensions."""
        r = 0
        if 'settling_time' in self.resolution_weights:
            r -= self.resolution_weights['settling_time'] * obs['overshoot']
        if 'exploration_exploitation' in self.resolution_weights:
            r += self.resolution_weights['exploration_exploitation'] * obs['novelty']
        return r
```

### Running Resolution

```python
import gym
from tension_resolver import TensionResolvingAgent

# Load tensions from dissonance analysis
tensions = [
    ('unworld', 'temporal-coalgebra', 2.131),
    ('compression-progress', 'gflownet', 1.859),
    ('system2-attention', 'forward-forward-learning', 1.940),
]

env = gym.make('openmodelica_microgrid_gym:ModelicaEnv-v1',
               net='net/tension_resolver.yaml',
               model_path='omg_grid/grid.network.fmu')

agent = TensionResolvingAgent(tensions)

# Training resolves tensions through physical dynamics
for episode in range(100):
    obs = env.reset()
    done = False
    while not done:
        action = agent.act(obs)
        obs, reward, done, info = env.step(action)
    agent.update(reward)
    
    print(f"Episode {episode}: Tension resolution = {agent.resolution_metric()}")
```

## Gay.jl Color Mapping

Map tensions to power flow phases:

```python
PHASE_COLORS = {
    'phase_a': '#E6F463',  # Stream 2 (temporal)
    'phase_b': '#63B6F0',  # Stream 3 (symbolic)
    'phase_c': '#5713C0',  # Stream 4 (maximize)
}

def tension_to_phase(t1, t2):
    """Map tension pair to three-phase color."""
    if 'temporal' in t1 or 'temporal' in t2:
        return PHASE_COLORS['phase_a']
    elif 'symbolic' in t1 or 'symbolic' in t2:
        return PHASE_COLORS['phase_b']
    else:
        return PHASE_COLORS['phase_c']
```

## Neighbor Skills

- **alife**: Emergent dynamics from simple rules (like microgrid self-organization)
- **forward-forward-learning**: Local learning ↔ local inverter control
- **gflownet**: Sampling ↔ SafeOpt posterior sampling
- **sheaf-laplacian-coordination**: Global consensus ↔ droop control
- **acsets**: Discrete structure ↔ network topology
- **crn-topology**: Reaction networks ↔ power flow networks

## Geometric Morphism Structure (Symplectic Bordism Core)

### Secondary Symplectic Hub (Equilibrium Dynamics)

This skill occupies a **harmonic equilibrium nexus** in the skill-space network:

**Flow Properties:**
- In-degree: 6 (receives from 6 distinct morphism sources)
- Out-degree: 6 (sends to 6 distinct morphism targets)
- **Symplectic Property**: |in - out| = 0 ✓ (perfect flow balance)
- **Status**: SECONDARY SYMPLECTIC HUB (harmonic equilibrium resolver)

**Morphism Neighbors (Discovered via Random Walk):**
```
skill.omg-tension-resolver ←→ skill.gym
                           ←→ skill.entropy-sequencer
                           ←→ skill.self-validation-loop
                           ←→ skill.sheaf-laplacian-coordination
                           ←→ skill.alife
                           ←→ skill.forward-forward-learning
```

### Interpretation

The OpenModelica Microgrid Gym represents **physical equilibrium as tension resolution**:

- **Type**: Dynamical system substrate for balancing opposing forces
- **Role**: Central equilibrium point in the skill manifold
- **Topology**: Bridges symbolic (Modelica equations) and subsymbolic (neural control)
- **Symplectic Property**: Preserves energy flow across all tension dimensions

Its perfect 6→6 balance means it acts as a **harmony resolver**—a system where opposing skill paradigms find their natural equilibrium point, with energy flowing inward and outward in equal measure.

### Coherence Proof

```
Theorem (Harmonic Equilibrium Property):
  skill.omg-tension-resolver is symplectic ⟺ in-deg = out-deg = 6

Proof:
  by direct inspection of morphism graph
  ∑ in-flow = ∑ out-flow = 6 ✓

  Each tension resolves to a dual representation:
    (temporal ↔ atemporal) through FMU ↔ steady-state
    (symbolic ↔ subsymbolic) through Modelica ↔ neural
    (local ↔ global) through inverter ↔ grid stability

Corollary (Lyapunov Stability):
  For any composition φ: X → Y through omg-tension-resolver,
  the equilibrium is asymptotically stable:
    lim_{t→∞} ||X(t) - X*|| = 0
```

### Cross-Skill Integration

This skill links seamlessly to:
- **gym**: Practical instantiation of environment-based learning
- **entropy-sequencer**: Temporal sequences of equilibrium states
- **self-validation-loop**: Validation through stable dynamics
- **sheaf-laplacian-coordination**: Global coordination via local dynamics
- **alife**: Emergent self-organization through energy flow
- **forward-forward-learning**: Local learning in equilibrium basin

## Resources

- [OMG GitHub](https://github.com/upb-lea/openmodelica-microgrid-gym)
- [OMG Documentation](https://upb-lea.github.io/openmodelica-microgrid-gym)
- [SafeOpt Paper](https://arxiv.org/abs/1509.01066)
- [OMG Whitepaper](https://arxiv.org/abs/2005.04869)
- [Symplectic Bordism Core](../../SYMPLECTIC_BORDISM_CORE.md) — Full geometric morphism analysis

---

## End-of-Skill Interface

## Commands

```bash
# Install OMG
conda install -c conda-forge pyfmi
pip install openmodelica_microgrid_gym

# Run tension resolution
python tension_resolver.py --tensions "unworld,temporal-coalgebra,2.131"

# Visualize resolution
python visualize_resolution.py --episode 50
```


---

## Autopoietic Marginalia

> **The interaction IS the skill improving itself.**

Every use of this skill is an opportunity for worlding:
- **MEMORY** (-1): Record what was learned
- **REMEMBERING** (0): Connect patterns to other skills  
- **WORLDING** (+1): Evolve the skill based on use



*Add Interaction Exemplars here as the skill is used.*