ENTRO-PULSE

💓 Overview

From continuous suppression to rhythmic oscillatory control

"A system that pulses does not merely survive its entropy dynamics; it dances with them." — Samir Baladi, April 2026

ENTRO-PULSE introduces Periodic Entropy Pulsing (PEP) — a control paradigm that transforms entropy flow management from continuous suppression into a rhythmically-managed oscillatory regime. Drawing on analogies with cardiac dynamics, PWM in power electronics, and the Kuramoto model of coupled oscillator synchronization.

38.7%

Throughput Gain

vs continuous baseline

0%

Collapse Rate

Under burst overload

86.1%

Peak Load Reduction

With RRL anti-phase sync

100%

Burst Survival

Rate under overload

EPWM

Entropy Pulse Width Modulation

// Entropic Pulse Function (Equation 3.1) S_pulse(t; ω, δ) = H(δ - frac(ω·t/2π)) // EPWM Adaptive Duty Cycle Law (Equation 4.1) δ(t) = δ_max · exp(-Ψ(t) / (θ_crit - Ψ(t))) // EPWM Pulsed Control Law (Equation 4.2) u_EPWM(t) = S_pulse(t; ω, δ(t)) · u_base(t) // Python implementation from entro_pulse import EntropyPulseController epwm = EntropyPulseController(omega=0.8, delta_max=0.7) result = epwm.step(psi=0.85, u_base=0.1)

Parameter	Description	Default
omega	Entropic frequency [rad/cycle]	0.8
delta_max	Maximum duty cycle	0.7
theta_crit	Critical stability threshold	0.85
beta_s	Sigmoid sharpness (soft pulse)	10.0

RRL

Rhythmic Resonance Law

// Modified Kuramoto Equation (Equation 5.1) dφ_i/dt = ω_i - (K/N)·Σ_j sin(φ_i - φ_j - Δφ_target_ij) // Target Phase Distribution (Equation 5.2) Δφ_target_ij = 2π(i - j)/N // Kuramoto Order Parameter (Equation 5.3) r = |(1/N)·Σ_j exp(i·(φ_j - φ_target_j))| // Python implementation from entro_pulse import RhythmicResonanceController rrl = RhythmicResonanceController(n_agents=8, K=0.5) rrl.step(100) r = rrl.order_parameter() # r → 0 for anti-phase

PGC

Pulse-Ghost Controller

// Pulse-Ghost Control Law (Equation 6.1) u_PGC(t) = S_pulse·[u_base + ζ·(Ψ* - Γ)] + (1-S_pulse)·u_cooldown // Phase-Aware Ghost Recall Factor (Equation 6.2) ζ_phase(t) = ζ · (1 + ρ·(1 - frac/δ)) // Continuous Ghost Trace Update (Equation 6.3) Γ[k] = exp(-α·Δt)·Γ[k-1] + (1 - exp(-α·Δt))·Ψ[k] // Python implementation from entro_pulse import PulseGhostController pgc = PulseGhostController(omega=0.8, zeta=0.65, rho=0.4) result = pgc.step(psi=0.85, u_base=0.1)

📐 Hopf

Hopf Bifurcation Analysis

// Hopf Bifurcation Condition (Equation 5.4) μ(ω*, δ) = 0 → ω* = (k_p·α) / (δ·θ_crit) // Supercritical Hopf Condition // For default parameters: ω* ≈ 0.24 rad/cycle // Default ω = 0.8 > ω* → supercritical regime → stable pulsing // Complex Normal Form dz/dt = (μ + iω)z - c|z|^2 z

🎲 Simulator

Monte Carlo Simulation

// Run complete simulation from entro_pulse import run_simulation, print_simulation_results results = run_simulation( steps=1000, omega=0.8, delta_max=0.7, use_ghost=True ) print_simulation_results(results)

📦 Installation

Quick setup

# Install from PyPI pip install entro-pulse # Clone repository git clone https://github.com/gitdeeper10/ENTRO-PULSE.git cd ENTRO-PULSE # Install with pip pip install -e . # Verify installation python -c "from entro_pulse import __version__; print(__version__)"

🔧 API Reference

Python interface

EntropyPulseController

EPWM adaptive duty cycle controller

from entro_pulse import EntropyPulseController epwm = EntropyPulseController(omega=0.8, delta_max=0.7) result = epwm.step(psi=0.85, u_base=0.1)

RhythmicResonanceController

Modified Kuramoto for anti-phase synchronization

from entro_pulse import RhythmicResonanceController rrl = RhythmicResonanceController(n_agents=8, K=0.5) phases = rrl.step(100)

PulseGhostController

Integration with ENTRO-GHOST (E-LAB-08)

from entro_pulse import PulseGhostController pgc = PulseGhostController(omega=0.8, zeta=0.65, rho=0.4) result = pgc.step(psi=0.85, u_base=0.1)

🧩 Core Modules

ENTRO-PULSE architecture

epwm.py

EPWM

Entropy Pulse Width Modulation

rrl.py

RRL

Rhythmic Resonance Law

pgc.py

PGC

Pulse-Ghost Controller

utils.py

Utils

Simulation & metrics

👤 Author

Principal investigator

💓

Samir Baladi

Interdisciplinary AI Researcher — Theoretical Physics, Statistical Mechanics & Information Theory

Ronin Institute / Rite of Renaissance

Samir Baladi is an independent researcher affiliated with the Ronin Institute, developing the Rite of Renaissance interdisciplinary research program. ENTRO-PULSE is the ninth project (E-LAB-09) in a ten-project research program, building directly on ENTROPIA (E-LAB-01) through ENTRO-GHOST (E-LAB-08).

No conflicts of interest declared. All code and data are open-source under MIT License.

📧 gitdeeper@gmail.com 🔗 ORCID: 0009-0003-8903-0029 🐙 GitHub 🦊 GitLab

📝 Citation

How to cite

@software{baladi2026entropulse, author = {Samir Baladi}, title = {ENTRO-PULSE: Periodic Entropy Pulsing and Informational Wave Management in High-Velocity AI Systems}, year = {2026}, version = {1.0.0}, publisher = {Zenodo}, doi = {10.5281/zenodo.19547863}, url = {https://doi.org/10.5281/zenodo.19547863}, note = {E-LAB-09. Builds on E-LAB-01 through E-LAB-08} }

"A system that pulses does not merely survive its entropy dynamics; it dances with them. The heart does not beat continuously — and neither should an intelligence that wishes to endure."

From continuous suppression to rhythmic oscillatory control

Entropy Pulse Width Modulation

Rhythmic Resonance Law

Pulse-Ghost Controller

Hopf Bifurcation Analysis

Monte Carlo Simulation

Quick setup

Python interface

ENTRO-PULSE architecture

Principal investigator

Samir Baladi

How to cite

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