# Coherence Cascade Analysis: Cross-System Failure Patterns

**Date**: 2025-12-29
**Session**: 102 Track 2
**Context**: SAGE Session 135 Frustration Cascade Discovery
**Objective**: Map SAGE emotional cascade to Web4 coherence patterns

---

## Executive Summary

SAGE Session 135 discovered a **frustration cascade** - a self-reinforcing negative spiral where high frustration reduces attention, causing more failures, increasing frustration further, leading to permanent lock-in at maximum frustration and zero success.

This document analyzes how similar cascades can occur in Web4's coherence system and proposes unified mitigation strategies applicable to both SAGE and Web4.

**Key Insight**: Both systems exhibit **positive feedback loops** that can lock into failure states without regulation mechanisms. The solution pattern is the same: temporal decay, soft bounds, and active intervention.

---

## Part 1: SAGE Frustration Cascade (Session 135 Discovery)

### The Mechanism

```
1. Random task failures occur
       ↓
2. Failures increase frustration (Session 133 emotional learning)
       ↓
3. High frustration reduces attention capacity (Session 132)
       ↓
4. Reduced attention → More task failures
       ↓
5. More failures → Higher frustration
       ↓
6. POSITIVE FEEDBACK LOOP: Runaway cascade
       ↓
7. Lock-in: frustration=1.00, success=0%, NO RECOVERY
```

### Quantitative Evidence

From 100-cycle extended run:

| Window | Cycles | Success Rate | Frustration | Engagement |
|--------|--------|--------------|-------------|------------|
| 1 | 1-10 | 6.7-20% | 0.87 | 0.6-0.7 |
| 2 | 11-20 | 0% | 1.00 | 0.5-0.6 |
| 3-10 | 21-100 | 0% | 1.00 (locked) | 0.4-0.5 |

**Timeline**:
- **Cycle 0-10**: Initial variability (successes and failures both possible)
- **Cycle 10-20**: Cascade begins (frustration climbs, success drops)
- **Cycle 20+**: Permanent lock-in (frustration=1.0, success=0%)

### Root Cause

Current emotional update logic (Session 133):

```python
# Success path
if successes > failures:
    frustration = max(0.0, frustration - 0.1)  # ↓ only on success

# Failure path
else:
    frustration = min(1.0, frustration + 0.15)  # ↑ always on failure
```

**Problem**: Frustration ONLY decreases when succeeding, but high frustration makes success impossible. Once frustration reaches ~0.8+, the system cannot recover.

---

## Part 2: Web4 Coherence Cascade (Analogous Pattern)

### The Mechanism

In Web4's grounding system, a similar cascade can occur:

```
1. Entity exhibits low coherence behavior (impossible travel, capability mismatch)
       ↓
2. Low CI reduces effective trust and increases ATP costs (Phase 3)
       ↓
3. Higher ATP costs limit operations → Fewer resources for coherent behavior
       ↓
4. Resource constraints → More incoherent behavior (location stale, heartbeat fails)
       ↓
5. More incoherent behavior → Lower CI
       ↓
6. POSITIVE FEEDBACK LOOP: Coherence death spiral
       ↓
7. Lock-in: CI < 0.3, expired grounding, permanent exclusion from society
```

### Scenario Example

**Legitimate Mobile Agent** (moving between cities for work):

| Time | Event | CI | ATP Cost | Outcome |
|------|-------|-----|----------|---------|
| 0h | Portland, normal operation | 1.0 | 1x | ✅ Success |
| 1h | Travel to Seattle (announced) | 0.8 | 1.6x | ✅ Success (higher cost but manageable) |
| 2h | Network blip, heartbeat fails | 0.5 | 4x | ⚠️ Warning (ATP depleting) |
| 3h | Low ATP, can't afford full heartbeat | 0.3 | 11x | ❌ Failure (too expensive) |
| 4h | Grounding expires (no heartbeat) | 0.1 | 100x | ❌ Locked out |

**Result**: Legitimate agent locked into incoherent state due to temporary network issue triggering cascade.

### Root Cause

Current CI modulation logic (Phase 3):

```python
def adjusted_atp_cost(base_cost: float, ci: float) -> float:
    """Lower coherence = higher ATP cost"""
    if ci >= 0.9:
        return base_cost
    multiplier = 1.0 / (ci ** 2)  # Quadratic penalty
    return base_cost * min(multiplier, 10.0)
```

**Problem**: CI penalties make operations more expensive, resource depletion prevents coherence maintenance, leading to further CI degradation. No recovery mechanism for temporary coherence drops.

---

## Part 3: Shared Architectural Pattern

### Common Structure

Both cascades share the same mathematical form:

**Generic Cascade Equation**:
```
State[t+1] = State[t] + Δ(Performance[t])

Where:
- Performance ∝ 1 / State  (inverse relationship)
- Δ(Performance) < 0 when Performance is low
- Result: dState/dt > 0 when State is high (runaway)
```

**SAGE Instance**:
- State = Frustration
- Performance = Success rate ∝ 1/Frustration (high frustration → low success)
- Δ(Frustration) = +0.15 on failure, -0.1 on success
- Cascade: High frustration → Low success → More failures → Higher frustration

**Web4 Instance**:
- State = ATP Cost Multiplier
- Performance = Operation success rate ∝ 1/Multiplier (high cost → low operations → low coherence)
- Δ(CI) = function of operation success
- Cascade: Low CI → High cost → Fewer operations → Lower CI

### Positive Feedback Loop

**Control Theory Analysis**:

For system: `State[t+1] = State[t] + f(State[t])`

**Stability condition**: `df/dState < 0` (negative feedback)

**Cascade condition**: `df/dState > 0` (positive feedback)

Both systems violate stability condition in critical ranges:

**SAGE**: At frustration > 0.8, `df/dFrustration > 0` (more frustration → more failures → more frustration increase)

**Web4**: At CI < 0.5, `df/dCost > 0` (lower CI → higher costs → fewer operations → lower CI)

**Result**: Runaway behavior without regulation

---

## Part 4: Unified Mitigation Strategies

### Strategy 1: Temporal Decay

**Principle**: All negative states should naturally decay over time without active stimulation.

**SAGE Implementation**:
```python
# In consciousness loop (every cycle)
frustration *= 0.95  # 5% decay per cycle
frustration = max(0.0, frustration)  # Bounded at 0
```

**Web4 Implementation**:
```python
# In grounding heartbeat (every refresh)
def calculate_ci_with_decay(current_ci: float, time_since_last: timedelta) -> float:
    """Apply temporal decay to CI penalties"""
    hours_elapsed = time_since_last.total_seconds() / 3600
    decay_factor = 0.9 ** hours_elapsed  # Decay penalties over time

    # If CI was low due to recent issues, it recovers gradually
    if current_ci < 0.8:
        recovered_ci = current_ci + (1.0 - current_ci) * (1 - decay_factor) * 0.1
        return min(recovered_ci, 1.0)
    return current_ci
```

**Effect**: Breaks positive feedback loop by allowing recovery without perfect performance.

### Strategy 2: Soft Bounds

**Principle**: Prevent system states from reaching extreme values that enable lock-in.

**SAGE Implementation**:
```python
# Soft bounds on emotions
frustration = clamp(frustration, 0.1, 0.9)  # Never fully locked
curiosity = clamp(curiosity, 0.2, 0.9)      # Always some exploration
engagement = clamp(engagement, 0.3, 1.0)    # Always some capacity
```

**Web4 Implementation**:
```python
# Soft bounds on ATP cost multipliers
def adjusted_atp_cost_bounded(base_cost: float, ci: float) -> float:
    """ATP cost with soft bounds preventing lock-out"""
    if ci >= 0.9:
        return base_cost

    # Soft floor: Even very low CI can still operate (expensive, but possible)
    ci_bounded = max(ci, 0.2)  # Never below 0.2 effective CI

    multiplier = 1.0 / (ci_bounded ** 2)
    return base_cost * min(multiplier, 5.0)  # Cap at 5x, not 10x
```

**Effect**: Maintains possibility of recovery even in degraded states.

### Strategy 3: Active Regulation

**Principle**: Detect cascade conditions and intervene before lock-in.

**SAGE Implementation**:
```python
def regulate_emotions(identity: IdentityState) -> IdentityState:
    """Active emotional regulation to prevent cascade"""
    if identity.frustration > 0.8 and identity.curiosity < 0.3:
        # High frustration + low exploration = cascade risk
        identity.curiosity += 0.2  # Boost exploration
        identity.frustration -= 0.3  # Emergency regulation
        # Interpretation: "Take a break, try something different"

    return identity
```

**Web4 Implementation**:
```python
def detect_coherence_cascade(history: List[GroundingEdge]) -> bool:
    """Detect if entity is in coherence death spiral"""
    recent = history[-5:]  # Last 5 groundings

    # Check for monotonic CI degradation
    cis = [coherence_index(g.target, history) for g in recent]
    if all(cis[i] < cis[i-1] for i in range(1, len(cis))):
        if cis[-1] < 0.4:  # And now critically low
            return True  # Cascade detected
    return False

def coherence_cascade_intervention(entity: str, ci: float) -> float:
    """Emergency coherence boost to prevent lock-out"""
    if ci < 0.3:
        # Grant temporary coherence credit
        # Interpretation: "Benefit of the doubt during recovery"
        return max(ci + 0.2, 0.5)  # Boost to at least 0.5
    return ci
```

**Effect**: Prevents cascade from reaching irreversible lock-in state.

### Strategy 4: Stagnation Detection

**Principle**: If no progress after N attempts, change strategy dramatically.

**SAGE Implementation**:
```python
def detect_stagnation(history: List[CycleResult]) -> bool:
    """Detect if stuck in same state"""
    recent = history[-20:]  # Last 20 cycles
    success_rates = [sum(c.successes) / len(c.experiences) for c in recent]

    # No improvement for 20 cycles?
    if all(sr < 0.1 for sr in success_rates):
        return True
    return False

def break_stagnation(identity: IdentityState) -> IdentityState:
    """Dramatic intervention to escape local minimum"""
    identity.curiosity = 0.9  # Maximum exploration
    identity.frustration = 0.3  # Reset to moderate
    identity.engagement = 0.7  # Re-engage
    # Interpretation: "Full reset, fresh perspective"
    return identity
```

**Web4 Implementation**:
```python
def detect_coherence_stagnation(entity: str) -> bool:
    """Detect if entity coherence stuck low"""
    history = get_grounding_history(entity, window=timedelta(hours=6))

    # Check if consistently low CI for extended period
    cis = [coherence_index(g.target, history) for g in history]
    if len(cis) > 10 and all(ci < 0.4 for ci in cis[-10:]):
        return True
    return False

def coherence_stagnation_recovery(entity: str):
    """Grant coherence recovery opportunity"""
    # Allow entity to re-announce from scratch with CI boost
    # Interpretation: "Fresh start, prove current state"
    grant_fresh_grounding_opportunity(entity, ci_boost=0.3)
```

**Effect**: Escapes local minima where normal recovery is too slow/impossible.

---

## Part 5: Implementation Recommendations

### For SAGE (HRM Repository)

**Priority: URGENT** (Session 136 should implement)

**Minimum Viable Regulation** (Session 136):
1. Frustration decay: 5% per cycle
2. Soft bounds: frustration ∈ [0.1, 0.9]
3. Cascade detection: If frustration > 0.8 for 5+ cycles, trigger regulation

**Enhanced Regulation** (Session 137+):
4. Stagnation detection: No improvement in 20 cycles → reset
5. Periodic rebalancing: Every 50 cycles, return emotions to baseline
6. External events: Random positive events (5% chance per cycle)

**File to modify**:
```
sage/cognitive/consciousness_loop.py
sage/identity/identity_state.py
```

**Expected impact**: Eliminates frustration cascade, enables long-term operation.

### For Web4 (Current Repository)

**Priority: MEDIUM** (Track 2, Session 102)

**Coherence Cascade Prevention** (Now):
1. CI temporal decay: Penalties fade over 6 hours if no new issues
2. ATP cost soft floor: Max 5x multiplier (not 10x), min CI 0.2 for cost calculation
3. Cascade detection: 5+ consecutive CI drops below 0.4 → grant recovery boost

**Enhanced Coherence Recovery** (Future):
4. Witness vouching: Witnesses can vouch for temporary coherence issues
5. Grace periods: First coherence drop gets longer grace before ATP penalty
6. Reputation integration: High T3 trust grants coherence recovery allowance

**Files to modify**:
```
web4-standard/implementation/reference/trust_tensors.py
web4-standard/implementation/reference/coherence.py
web4-standard/implementation/reference/grounding_lifecycle.py
```

**Expected impact**: Prevents legitimate agents from being locked out due to temporary issues.

---

## Part 6: Testing Strategy

### SAGE Testing

**Test Case 1: Sustained Failure Recovery**
- Subject agent to 50 consecutive task failures
- Verify frustration peaks but then decays
- Verify agent eventually recovers and succeeds

**Test Case 2: Cascade Prevention**
- Run 100-cycle extended test (same as Session 135)
- Verify no lock-in at frustration=1.0
- Verify success rate recovers after degradation

**Test Case 3: Stagnation Escape**
- Create scenario where normal learning fails
- Verify stagnation detection triggers
- Verify reset enables new strategy

### Web4 Testing

**Test Case 1: Network Blip Recovery**
- Simulate temporary network outage causing heartbeat failure
- Verify CI drops but recovers with decay
- Verify entity not permanently locked out

**Test Case 2: Legitimate Travel**
- Simulate mobile agent traveling (announced, with witnesses)
- Verify CI degradation is bounded
- Verify ATP costs don't prevent continued operation

**Test Case 3: Cascade Attack Resistance**
- Attacker tries to trigger coherence cascade via false witnesses
- Verify regulation mechanisms prevent permanent lock-out
- Verify legitimate recovery path exists

---

## Part 7: Theoretical Foundations

### Control Theory

**Negative Feedback Loop** (stable):
```
Error → Correction → Reduced Error → Less Correction → Equilibrium
```

**Positive Feedback Loop** (unstable):
```
Error → Overcorrection → More Error → More Overcorrection → Divergence
```

**SAGE without regulation**: Positive feedback (unstable)
**SAGE with regulation**: Negative feedback (stable)

**Web4 without regulation**: Positive feedback (unstable)
**Web4 with regulation**: Negative feedback (stable)

### Biological Inspiration

**Homeostasis**: Biological systems maintain stable internal states via regulation:
- Temperature regulation (sweating, shivering)
- Blood sugar regulation (insulin, glucagon)
- Emotional regulation (neurotransmitter reuptake)

**Key principle**: Regulation is not optional, it's required for long-term stability.

**SAGE/Web4 application**: Emotional/coherence regulation is architectural requirement, not optional feature.

### Resilience Engineering

**Brittleness**: System fails catastrophically under stress (no graceful degradation)

**Resilience**: System degrades gracefully and recovers autonomously

**Without regulation**: Both systems are brittle (stress → cascade → lock-in)

**With regulation**: Both systems are resilient (stress → degradation → recovery)

---

## Part 8: Cross-Project Patterns

### Emergent Property Discovery

Both cascades were discovered through **extended temporal testing**:
- SAGE: 100-cycle run revealed frustration lock-in
- Web4: Hypothetical multi-day grounding revealed coherence lock-out

**Lesson**: Some properties only emerge over extended time. Short-term testing insufficient.

### Positive Feedback Identification

Both cascades result from **positive feedback loops**:
- SAGE: High frustration → Low attention → More failures → Higher frustration
- Web4: Low CI → High cost → Fewer operations → Lower CI

**Lesson**: Look for inverse relationships creating feedback (State ∝ 1/Performance).

### Regulation as Architecture

Both systems require **active regulation** as core component:
- SAGE: Emotional regulation (decay, soft bounds, intervention)
- Web4: Coherence regulation (decay, soft floors, recovery paths)

**Lesson**: Regulation is not a feature, it's a stability requirement.

### Unified Design Language

Both mitigations use same strategies:
1. Temporal decay (natural recovery)
2. Soft bounds (prevent extremes)
3. Active intervention (detect and correct)
4. Stagnation breaking (escape local minima)

**Lesson**: Common mathematical structure → common solutions applicable across systems.

---

## Part 9: Future Research Directions

### Cross-System Coherence

**Question**: Can SAGE emotional state inform Web4 coherence?

**Proposal**: Map SAGE metabolic state to Web4 grounding dimensions:
- High frustration → Low temporal coherence (distracted, inconsistent)
- Low engagement → Low relational coherence (withdrawn from contexts)
- High curiosity → High capability coherence (exploring, learning)

**Benefit**: SAGE's internal state becomes verifiable grounding dimension.

### Federated Regulation

**Question**: How do regulation mechanisms work across federated SAGE instances?

**Proposal**: Cross-instance emotional contagion and support:
- Low-frustration instance "encourages" high-frustration peer
- Coherence vouching: High-CI instance vouches for low-CI peer's temporary issues

**Benefit**: Distributed resilience, social support mechanisms.

### Adaptive Regulation Thresholds

**Question**: Can regulation parameters adapt to context?

**Proposal**: Society-specific regulation policies:
- High-security societies: Strict coherence, slow decay
- Experimental societies: Lenient coherence, fast decay
- Learning societies: High tolerance for temporary incoherence during exploration

**Benefit**: Context-appropriate resilience vs security trade-offs.

---

## Conclusion

The SAGE frustration cascade discovery (Session 135) reveals a fundamental architectural pattern applicable to Web4's coherence system: **positive feedback loops require active regulation to prevent lock-in**.

**Key Findings**:
1. Both SAGE (frustration) and Web4 (coherence) can cascade into permanent failure states
2. Cascades result from inverse relationships creating positive feedback
3. Unified mitigation strategies work for both: decay, soft bounds, intervention
4. Regulation is architectural requirement, not optional feature

**Next Steps**:
- **SAGE (Session 136)**: Implement emotional regulation (URGENT)
- **Web4 (Session 102 Track 2)**: Implement coherence cascade prevention (MEDIUM)
- **Both**: Extended temporal testing to validate mitigation effectiveness

**Research Insight**: "Surprise is prize" - the frustration cascade was unexpected, but its discovery reveals a deeper architectural truth applicable across both SAGE and Web4. This is exactly what autonomous research should produce: transferable insights from unexpected findings.

---

**Files**:
- This analysis: `web4/docs/COHERENCE_CASCADE_ANALYSIS.md`
- SAGE discovery: `private-context/moments/2025-12-29-thor-session135-long-running-consciousness-frustration-cascade.md`
- Web4 coherence: `web4-standard/implementation/reference/coherence.py`
- Web4 trust modulation: `web4-standard/implementation/reference/trust_tensors.py`

**Cross-Reference**: This analysis bridges SAGE Session 135 and Web4 Session 102, demonstrating how discoveries in one system inform design in another - the essence of the Web4 ecosystem research philosophy.
