npx claudepluginhub plurigrid/asi --plugin asiThis skill uses the workspace's default tool permissions.
Measures distance to fixed point via comparator error and detects self-loop closure for phase classification in dynamical systems.
Detects Hopf bifurcations in dynamical systems via Jacobian eigenvalue analysis and generates GF(3) phase portraits for state transitions. Useful for analyzing qualitative behavior changes.
Guides Next.js Cache Components and Partial Prerendering (PPR) with cacheComponents enabled. Implements 'use cache', cacheLife(), cacheTag(), revalidateTag(), static/dynamic optimization, and cache debugging.
Guides building MCP servers enabling LLMs to interact with external services via tools. Covers best practices, TypeScript/Node (MCP SDK), Python (FastMCP).
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Measures distance to fixed point via comparator error and detects self-loop closure for phase classification in dynamical systems.
741086072858456200
Generator ≡ Observer when same seed: the fixed point structure where action → prediction → sensation → match completes the loop.
| 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 |
AtFixedPoint(s, i) := |comparator_error(s, i)| < ε
where ε = 0.01 (ordered threshold)
LoopClosed(s, n) := ∀k ∈ [1..n]: predicted(s, k) = observed(s, k)
-- Verified: 3 iterations all matched (self ≡ self)
PhaseClassified(e) :=
| e > 0.5 → Chaos
| e > 0.01 → Critical
| _ → Ordered
# 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
# 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
# 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)
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"
Phase transitions conserve triadic balance:
Chaos(+1) + Critical(0) + Ordered(-1) ≡ 0 (mod 3)
# 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)
self-validation-loop - Prediction vs observation verificationcybernetic-immune - Reafference and self/non-self discriminationkoopman-generator - Observable dynamics and fixed pointsThis skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
general: 734 citations in bib.duckdbThis 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
The skill participates in triads satisfying:
(-1) + (0) + (+1) ≡ 0 (mod 3)
This ensures compositional coherence in the Cat# equipment structure.