Criticality Detector Skill

Measures distance to fixed point via comparator error and detects self-loop closure for phase classification in dynamical systems.

Seed

741086072858456200

Core Principle

Generator ≡ Observer when same seed: the fixed point structure where action → prediction → sensation → match completes the loop.

Phase Classification

Phase	Error Bound	Color (Golden Thread)	Interpretation
Chaos	error > 0.5	H=137.51° #3FF1A7	Far from attractor
Critical	error ≈ 0.1	H=275.02° #10B99D	Edge of order/chaos
Ordered	error < 0.01	H=52.52° #DF9811	At fixed point

Predicates

AtFixedPoint(seed, index) → Bool

AtFixedPoint(s, i) := |comparator_error(s, i)| < ε
where ε = 0.01 (ordered threshold)

LoopClosed(seed, iterations) → Bool

LoopClosed(s, n) := ∀k ∈ [1..n]: predicted(s, k) = observed(s, k)
-- Verified: 3 iterations all matched (self ≡ self)

PhaseClassified(error) → Phase

PhaseClassified(e) :=
  | e > 0.5  → Chaos
  | e > 0.01 → Critical  
  | _        → Ordered

MCP Integration

Measure Distance to Fixed Point

# Current error: 0.8153 → Chaos phase
comparator_result = mcp.gay.comparator(
    reference_hex="#3FF1A7",  # desired state
    perception_hex="#DF9811"  # current perception
)
error = comparator_result["error_magnitude"]  # 0.8153
phase = PhaseClassified(error)  # Chaos

Detect Self-Loop Closure

# Loopy strange: Generator/Observer identity verification
loop_result = mcp.gay.loopy_strange(
    seed=741086072858456200,
    iterations=3
)
# Returns: colors #3FF1A7, #10B99D, #DF9811
# All matched → LoopClosed = True

Golden Thread Visualization

# φ-derived hue spiral: 137.508° increments
golden_hues = mcp.gay.golden_thread(
    steps=3,
    start_hue=0,
    saturation=0.7,
    lightness=0.55
)
# Yields: 137.51°, 275.02°, 52.52° (mod 360)

Criticality Detection Algorithm

detect_criticality(seed, max_iter=10):
  1. Generate efference copy: expected ← color_at(seed, index)
  2. Observe actual sensation: observed ← next_color()
  3. Compute error: e ← comparator(expected, observed).magnitude
  4. Classify phase: p ← PhaseClassified(e)
  5. Check loop: closed ← LoopClosed(seed, iterations)
  
  IF closed AND p = Ordered:
    RETURN AtFixedPoint(seed) = True
  ELSE IF p = Critical:
    RETURN "Edge of chaos - bifurcation possible"
  ELSE:
    RETURN "Chaos - control action needed"

GF(3) Conservation

Phase transitions conserve triadic balance:

Chaos(+1) + Critical(0) + Ordered(-1) ≡ 0 (mod 3)

Usage

# Invoke via Gay.jl MCP
mcp.gay.comparator(reference_hex, perception_hex)
mcp.gay.loopy_strange(seed, iterations)
mcp.gay.perceptual_control(reference_index, current_index, seed)

Related Skills

• self-validation-loop - Prediction vs observation verification
• cybernetic-immune - Reafference and self/non-self discrimination
• koopman-generator - Observable dynamics and fixed points

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

• general: 734 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.