# Cognitive Sufficiency Superposition > name: cognitive-sufficiency-superposition - Skill: `plurigrid/cognitive-sufficiency-superposition` (Agent Skill, multi-file: 2 files) - Install (CLI): `npx skillmds@latest add plurigrid/cognitive-sufficiency-superposition` - Raw SKILL.md: https://api.skillmd.com/api/skills/plurigrid/cognitive-sufficiency-superposition/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Coding & Dev Tools - Author: plurigrid (https://skillmd.com/u/plurigrid) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/plurigrid/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.*