Cognitive Sufficiency Superposition

---
name: cognitive-sufficiency-superposition
description: 'name: cognitive-sufficiency-superposition'
---
# Cognitive Sufficiency Superposition

---
name: cognitive-sufficiency-superposition
description: Four ASI perspectives (Riehl, Sutskever, Schmidhuber, Bengio) in superposition on the ε-machine gating problem. Collapse to specific strategy based on task measurement.
trit: 0
color: "#77DEB1"
parents: [cognitive-superposition, dynamic-sufficiency]
---

## Overview

**Cognitive Sufficiency Superposition** applies the four-pillar ASI framework to the ε-machine sufficiency gate:

```
|ψ_sufficiency⟩ = α|Riehl⟩ + β|Sutskever⟩ + γ|Schmidhuber⟩ + δ|Bengio⟩
```

The gate holds ALL perspectives until measurement collapses it.

## The Four Perspectives on ε-Machine Gating

### Riehl: Segal Type View

```rzk
#lang rzk-1

-- ε-machine as Segal type
#define EpsilonMachine : U := Segal-type

-- Causal states as objects
#define CausalState : EpsilonMachine → U := object

-- Skill requirements as morphisms
#define SkillReq (S : EpsilonMachine) (s1 s2 : CausalState S) : U
  := hom S s1 s2

-- Sufficiency = composite exists
#define sufficient (S : EpsilonMachine)
                   (current required : CausalState S) : U
  := Σ (path : hom S current required), is-contr path
```

**Key insight**: Test sufficiency at identity (directed Yoneda).

### Sutskever: Compression View

```python
class SutskeverSufficiency:
    """ε-machine = minimal sufficient statistic."""

    def compression_sufficient(self, loaded: Set[Skill], required: Set[Skill]) -> bool:
        """
        Sufficient if loaded skills can be compressed to program
        that generates required skills.

        K(required | loaded) < K(required) → sufficient
        """
        program = self.compress(loaded)
        generated = self.decompress(program)
        return required <= generated

    def gating_intelligence(self) -> float:
        """Compression ratio = intelligence of gate."""
        return self.bits_saved / self.total_bits
```

**Key insight**: Compression ratio measures gating intelligence.

### Schmidhuber: Curiosity View

```python
class SchmidhuberSufficiency:
    """Insufficient coverage = exploration opportunity."""

    def curiosity_reward(self, action: Action, coverage: float) -> float:
        """
        Low coverage → high curiosity → learning opportunity.

        Reward = compression progress on ε-machine after seeing failure.
        """
        if coverage >= 0.95:
            return 0  # Already sufficient, no learning

        # Expected learnability from this failure
        return self.expected_compression_progress(action)

    def explore_skills(self, missing: List[Skill]) -> Skill:
        """Load skill that maximizes expected learnability."""
        return max(missing, key=self.expected_learnability)
```

**Key insight**: Failures are learning opportunities for ε-machine.

### Bengio: GFlowNet View

```python
class BengioSufficiency:
    """Sample sufficient skill sets proportional to success."""

    def sample_sufficient_skills(self, action: Action) -> Set[Skill]:
        """
        GFlowNet: P(skills | action) ∝ P(success | skills, action)

        Don't just maximize - sample DIVERSE sufficient sets.
        """
        # Trajectory balance for skill loading
        trajectory = []
        state = self.initial_skills()

        while not self.is_sufficient(state, action):
            skill = self.P_F.sample(state, action)
            state = state | {skill}
            trajectory.append(skill)

        return state

    def diversity_bonus(self, skill_set: Set[Skill]) -> float:
        """Reward novel skill combinations."""
        return self.novelty(skill_set) * self.success_prob(skill_set)
```

**Key insight**: Multiple sufficient sets exist - sample their diversity.

## Measurement Collapse

| Measurement | Collapses To | ε-Machine Operation |
|-------------|--------------|---------------------|
| `verify` | Riehl | Check hom-space non-empty |
| `compress` | Sutskever | Minimize description length |
| `explore` | Schmidhuber | Seek compressible failures |
| `sample` | Bengio | GFlowNet sample sufficient sets |
| `integrate` | ALL FOUR | Weighted superposition |

## Integrated Gate

```python
class CognitiveSufficiencyGate:
    """Superposition of four gating strategies."""

    def __init__(self):
        self.riehl = RiehlSufficiency()      # Segal type check
        self.sutskever = SutskeverSufficiency()  # Compression
        self.schmidhuber = SchmidhuberSufficiency()  # Curiosity
        self.bengio = BengioSufficiency()    # GFlowNet

        # Amplitude weights (learned or fixed)
        self.amplitudes = {
            'riehl': 0.25,
            'sutskever': 0.25,
            'schmidhuber': 0.25,
            'bengio': 0.25
        }

    def gate(self, action: Action, loaded: Set[Skill],
             measurement: str = 'integrate') -> Verdict:
        """
        Apply superposition gate with measurement collapse.
        """
        if measurement == 'verify':
            return self.riehl.gate(action, loaded)
        elif measurement == 'compress':
            return self.sutskever.gate(action, loaded)
        elif measurement == 'explore':
            return self.schmidhuber.gate(action, loaded)
        elif measurement == 'sample':
            return self.bengio.gate(action, loaded)
        else:
            # Integrate: weighted vote
            verdicts = {
                'riehl': self.riehl.gate(action, loaded),
                'sutskever': self.sutskever.gate(action, loaded),
                'schmidhuber': self.schmidhuber.gate(action, loaded),
                'bengio': self.bengio.gate(action, loaded),
            }
            return self.weighted_vote(verdicts)

    def weighted_vote(self, verdicts: Dict[str, Verdict]) -> Verdict:
        """Amplitude-weighted voting."""
        scores = {'PROCEED': 0, 'LOAD_MORE': 0, 'ABORT': 0}

        for perspective, verdict in verdicts.items():
            weight = self.amplitudes[perspective] ** 2  # Born rule
            scores[verdict.name] += weight

        return Verdict[max(scores, key=scores.get)]
```

## Narya Bridge Types

```narya
-- Superposition as sigma type over perspectives
def SufficiencySuperposition : Type := sig (
  riehl_amplitude : ℝ,
  sutskever_amplitude : ℝ,
  schmidhuber_amplitude : ℝ,
  bengio_amplitude : ℝ,
  normalized : riehl² + sutskever² + schmidhuber² + bengio² ≡ 1
)

-- Collapse as projection
def collapse (measurement : Measurement) (ψ : SufficiencySuperposition)
  : Perspective :=
  match measurement with
  | verify → Riehl
  | compress → Sutskever
  | explore → Schmidhuber
  | sample → Bengio
  | integrate → Integrated ψ

-- ε-machine as Segal type
def EpsilonMachineSegal (S : Category) : Type := sig (
  causal_states : Obj S,
  skill_morphisms : (s1 s2 : causal_states) → Hom S s1 s2,
  segal_composite : (s1 s2 s3 : causal_states) →
    Hom S s1 s2 → Hom S s2 s3 → Hom S s1 s3,
  segal_unique : IsContr (segal_composite ...)
)
```

## GF(3) Conservation

```
dynamic-sufficiency (-1) ⊗ cognitive-superposition (0) ⊗ gay-mcp (+1) = 0 ✓

The gate (MINUS) observes
The superposition (ERGODIC) coordinates
The color generator (PLUS) produces witnesses
```

### Perspective Trits

| Perspective | Trit | Role in Gate |
|-------------|------|--------------|
| Riehl | -1 | Validate (hom-space check) |
| Sutskever | +1 | Generate (compressed program) |
| Schmidhuber | +1 | Explore (curiosity-driven) |
| Bengio | 0 | Coordinate (GFlowNet sampling) |

**Sum**: -1 + 1 + 1 + 0 = +1 → Needs MINUS to balance → `dynamic-sufficiency (-1)`

## Free Energy Analysis

```
Free Energy = Prediction Error + Complexity
            = 1.237 (measured between sufficiency and superposition)

High free energy → rich synthesis opportunity
Minimize by: updating beliefs (perceptual inference)
           OR acting to change world (active inference)
```

## Commands

```bash
# Apply superposition gate
just cognitive-sufficiency action="code:julia:acset"

# Collapse to specific perspective
just cognitive-sufficiency --collapse=verify
just cognitive-sufficiency --collapse=compress
just cognitive-sufficiency --collapse=explore
just cognitive-sufficiency --collapse=sample

# Full integration (maintain superposition)
just cognitive-sufficiency --collapse=integrate

# Show perspective weights
just cognitive-sufficiency --amplitudes
```

## Related Skills

| Skill | Trit | Connection |
|-------|------|------------|
| `cognitive-superposition` | 0 | Parent: four-pillar framework |
| `dynamic-sufficiency` | -1 | Parent: ε-machine gating |
| `curiosity-driven` | +1 | Schmidhuber perspective |
| `gflownet` | 0 | Bengio perspective |
| `segal-types` | -1 | Riehl perspective |
| `kolmogorov-compression` | +1 | Sutskever perspective |

---

**Skill Name**: cognitive-sufficiency-superposition
**Type**: Meta-Skill / Gating / Superposition
**Trit**: 0 (ERGODIC - coordinates perspectives)
**Free Energy**: 1.237 (high tension → rich synthesis)
**Collapse**: Measurement-dependent
**GF(3)**: Conserved with dynamic-sufficiency + gay-mcp


---

## 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.*