scbe-entropy-dynamics

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Atualizado15 de junho de 2026 às 03:36

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.

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issdandavis

issdandavis/SCBE-AETHERMOORE

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Ocupações relacionadasSOC

Baseado na classificação ocupacional SOC

Desenvolvedores de softwareInformática e Matemática·SOC 15-1252

SKILL.md

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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

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

Guardrails

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

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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

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

Guardrails

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