scbe-entropy-dynamics

name	scbe-entropy-dynamics
description	Monitor and compute entropy, time flow, and quantum state dynamics for the SCBE-AETHERMOORE 7th/8th/9th dimensions. Use when debugging entropy anomalies, time drift, quantum decoherence, or tuning the Ornstein-Uhlenbeck process parameters.

SCBE Entropy Dynamics

Use this skill for reasoning about the three higher-dimensional dynamics (time, entropy, quantum) that govern SCBE-AETHERMOORE system health.

Three Dynamic Dimensions

Dimension 7: Time Flow τ̇(t)

τ̇(t) = 1.0 + DELTA_DRIFT_MAX · sin(OMEGA_TIME · t)

• Normal flow = 1.0
• Oscillates in range [1 - DELTA_DRIFT_MAX, 1 + DELTA_DRIFT_MAX] = [0.5, 1.5]
• Period = 60 seconds (OMEGA_TIME = 2π/60)
• Hard constraint: τ̇ > 0 (causality — time never reverses)
• With current parameters, minimum is 0.5 > 0, so causality is always satisfied under normal operation

Dimension 8: Entropy Flow η̇

η̇ = BETA · (ETA_TARGET - η) + 0.1 · sin(t)

• Ornstein-Uhlenbeck mean-reverting drift toward ETA_TARGET = 4.0
• BETA = 0.1 controls reversion speed
• Periodic perturbation amplitude = 0.1
• Bounds: η must stay within [ETA_MIN=2.0, ETA_MAX=6.0]

Dimension 9: Quantum State q(t)

q(t) = q₀ · e^(-iHt)

• Unitary evolution preserves |q| = |q₀|
• Phase rotates at rate H (Hamiltonian energy)
• Health checks: Fidelity f_q ≥ 0.9, Von Neumann entropy S_q ≤ 0.2

Shannon Entropy Computation

# For the 6D context vector:
magnitudes = [|x| if complex else float(x) for x in context_vector]
histogram = np.histogram(magnitudes, bins=16, density=True)
η = -Σ p · log₂(p + 1e-9)  # over non-zero bins

• Uses 16 bins for granularity
• density=True normalizes to probability distribution
• 1e-9 epsilon prevents log(0)

Key Constants

Constant	Value	Role
DELTA_DRIFT_MAX	0.5	Max time drift amplitude
OMEGA_TIME	2π/60	Time cycle frequency (1/min)
BETA	0.1	Entropy mean-reversion rate
ETA_TARGET	4.0	Entropy attractor
ETA_MIN	2.0	Entropy floor (QUARANTINE below)
ETA_MAX	6.0	Entropy ceiling (QUARANTINE above)
KAPPA_ETA_MAX	0.1	Max entropy curvature
DOT_TAU_MIN	0.0	Causality floor (τ̇ must exceed)

Diagnostic Workflow

1. Entropy anomaly: Check if context vector has degenerate components (all same value → low entropy, or uniform random → high entropy).
2. Time drift: Verify OMEGA_TIME period matches expected system cycle. Check if external clock sync is causing discontinuities.
3. Quantum decoherence: Check if Hamiltonian H is stable. Large H causes fast phase rotation which can reduce fidelity measurements.
4. Curvature spike: Compute numerical second derivative of η(t). If |κ_η| > KAPPA_ETA_MAX, the entropy landscape is too volatile.

Guardrails

1. Entropy computation must handle mixed float/complex arrays gracefully.
2. The O-U process parameters (BETA, ETA_TARGET) are tuned together — changing one requires re-evaluating the other.
3. Quantum evolution must use exact unitary operator, not approximations.
4. Time flow monitoring should raise alerts well before τ̇ approaches 0.