Cybernetic Immune Skill

"The immune system is a cognitive system: it learns, remembers, and discriminates self from non-self." — Francisco Varela, Principles of Biological Autonomy (1979)

bmorphism Contributions

"Autopoietic Ergodicity combines the principles of autopoiesis and ergodicity. Autopoiesis refers to the self-maintenance of a system, where the system is capable of reproducing and maintaining itself." — vibes.lol gist

"Active Inference in String Diagrams: A Categorical Account of Predictive Processing and Free Energy" — ACT 2023, Tull, Kleiner, Smithe

Categorical Cybernetics Connection: The immune system's self/non-self discrimination maps directly to:

• Reafference (self-caused) → SELF trit (-1)
• Exafference (externally-caused) → NON-SELF trit (+1)
• Markov blanket → boundary of selfhood

Key Papers (from bmorphism's Plurigrid references):

• Towards Foundations of Categorical Cybernetics - parametrised optics for agency
• Active Inference in String Diagrams - free energy via category theory
• Categorical Cybernetics Manifesto - control theory of complex systems

Related to bmorphism's work on:

• plurigrid/act - active inference + ACT + enacted cognition
• Autopoietic ergodicity and embodied gradualism

1. Core Concept

Self/Non-Self Discrimination via reafference vs exafference:

• Reafference: Self-caused sensations (predicted = observed) → tolerate
• Exafference: Externally-caused sensations (predicted ≠ observed) → inspect/attack

GF(3) Trit Encoding:

Autoimmune = GF(3) Conservation Violation: Σ(trits) ≢ 0 mod 3

2. Information Geometry

The immune state manifold is a probability simplex with Fisher-Rao metric:

// Fisher information: I(θ) = E[(∂log p/∂θ)²]
computeFisherInformation() {
  const probs = Array.from(this.stateDistribution.values());
  // For categorical: I_ij = δ_ij/p_i - 1
  return probs.map((p, i) => 1 / Math.max(p, 0.001));
}

// Fisher-Rao geodesic distance: d(p,q)² = 4 Σ (√p_i - √q_i)²
fisherRaoDistance(dist1, dist2) {
  let sum = 0;
  for (const k of keys) {
    const p = dist1.get(k) || 0;
    const q = dist2.get(k) || 0;
    sum += (Math.sqrt(p) - Math.sqrt(q)) ** 2;
  }
  return 2 * Math.sqrt(sum); // = 2 × Hellinger distance
}

Natural Gradient: F⁻¹ · ∇L for efficient belief updating in curved space.

Parallel Transport: Cytokine signals transported along geodesics preserve information content.

3. Immune States

const IMMUNE_STATES = {
  NAIVE: 'naive',       // Not yet encountered antigen
  TOLERANT: 'tolerant', // Self-recognized, suppress response (-1)
  ACTIVATED: 'activated', // Response engaged (+1)
  MEMORY: 'memory',     // Prior encounter, fast recall
  ANERGIC: 'anergic'    // Exhausted, non-responsive (0)
};

4. Collision → Immune Response

// Recognition via color signature (antigenic epitope)
colorSignature(color) {
  const hueBin = Math.floor(color.H / 30); // 12 bins
  return `H${hueBin}T${color.trit}`;
}

// Response classification
recognize(antigenColor) {
  const signature = this.colorSignature(antigenColor);
  
  // Self-tolerance check
  if (this.toleranceList.has(signature)) {
    return { classification: 'self', trit: -1, action: 'tolerate' };
  }
  
  // Adaptive memory
  if (this.memory.has(signature)) {
    const mem = this.memory.get(signature);
    return { trit: mem.trit, action: mem.hostile ? 'attack' : 'tolerate' };
  }
  
  // Novel: inspect via Markov blanket
  return { classification: 'novel', trit: 0, action: 'inspect' };
}

5. Cognitive Firewall

System-level immune coordination:

class CognitiveFirewall {
  constructor(immuneAgents) {
    this.agents = immuneAgents;
    this.threatLevel = 0;
    this.autoimmuneCrisis = false;
  }
  
  // Coordinated response
  coordinatedResponse() {
    if (this.autoimmuneCrisis) {
      // Emergency T_reg activation
      return { action: 'tolerance_induction' };
    }
    
    if (this.threatLevel > 0.5) {
      // Germinal center reaction
      return { action: 'coordinated_attack' };
    }
    
    return { action: 'homeostasis' };
  }
}

6. Parallel Processing (GF(3) Aligned)

parallelProcess(allTiles) {
  // Partition agents by trit for parallel streams
  const partitions = {
    minus: agents.filter(a => a.trit === -1),   // Validators
    ergodic: agents.filter(a => a.trit === 0),  // Coordinators
    plus: agents.filter(a => a.trit === 1)      // Generators
  };
  
  // Process each partition independently
  for (const [trit, batch] of Object.entries(partitions)) {
    for (const agent of batch) {
      // Collision detection and response
    }
  }
  
  // Synchronize: ensure GF(3) conservation
  const tritBalance = results.minus.length * -1 + results.plus.length * 1;
  return { conserved: tritBalance % 3 === 0 };
}

7. Cytokine Cascade with Parallel Transport

Signals propagate along Fisher-Rao geodesics:

parallelTransport(signal, fromAgent, toAgent) {
  const geodesicDist = this.fisherRaoDistance(
    new Map([[fromAgent.state, 1]]),
    new Map([[toAgent.state, 1]])
  );
  
  // Decay proportional to geodesic distance
  const transported = signal.level * Math.exp(-geodesicDist * 0.5);
  
  return { level: transported, geodesicLoss: signal.level - transported };
}

8. GF(3) Triads

# Core Immune Triads
three-match (-1) ⊗ cybernetic-immune (0) ⊗ gay-mcp (+1) = 0 ✓  [Self/Non-Self]
temporal-coalgebra (-1) ⊗ cybernetic-immune (0) ⊗ agent-o-rama (+1) = 0 ✓  [Immune Response]
sheaf-cohomology (-1) ⊗ cybernetic-immune (0) ⊗ koopman-generator (+1) = 0 ✓  [Cytokine Cascade]
shadow-goblin (-1) ⊗ cybernetic-immune (0) ⊗ gay-mcp (+1) = 0 ✓  [T_reg Surveillance]
polyglot-spi (-1) ⊗ cybernetic-immune (0) ⊗ gay-mcp (+1) = 0 ✓  [Cross-Species]

9. Visualization

• Immune overlays: Red (activated), Green (tolerant), Yellow (memory), Gray (anergic)
• Cytokine network: Orange edges with opacity ∝ signal level
• Fisher-Rao manifold inset: 2D projection of immune state space

10. Diagnostics

getDiagnostics() {
  return {
    entropy: H(stateDistribution),      // Uncertainty
    curvature: trace(FisherMatrix) / n, // Manifold curvature
    threatLevel: activatedCount / total,
    autoimmune: tritSum % 3 !== 0
  };
}

11. References

1. Varela — Principles of Biological Autonomy (1979)
2. Friston — The Free-Energy Principle (2010)
3. Powers — Behavior: The Control of Perception (1973)
4. Amari — Information Geometry and Its Applications (2016)
5. Maturana & Varela — Autopoiesis and Cognition (1980)

12. See Also

• `autopoiesis` — Self-production and operational closure
• `gay-mcp` — Deterministic color generation
• `shadow-goblin` — Observer agent tracing
• `koopman-generator` — Dynamics from observables

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

Graph Theory

• networkx [○] via bicomodule
  • Universal graph hub

Bibliography References

• game-theory: 21 citations in bib.duckdb

Cat# Integration

This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:

Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826

GF(3) Naturality

The skill participates in triads satisfying:

(-1) + (0) + (+1) ≡ 0 (mod 3)

This ensures compositional coherence in the Cat# equipment structure.