README/(love_os_core_v3.py at main · TN-Holdings-LLC/README · GitHub

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import numpy as np

import matplotlib.pyplot as plt

class LoveOS_Kernel:

    def __init__(self, N=50, seed=42):

        self.rng = np.random.default_rng(seed)

        self.N = N

        self.dt = 0.05


        # 1. Field Geometry Setup (Circular Manifold)

        angles = np.linspace(0, 2*np.pi, N, endpoint=False)

        self.X = np.c_[np.cos(angles), np.sin(angles)]

        self.W = self._build_initial_geometry()


        # 2. State Initialization: W = R * exp(i*theta)

        self.state = 0.1 * (self.rng.normal(size=N) + 1j*self.rng.normal(size=N))

        self.omega = self.rng.normal(1.0, 0.1, size=N) # Natural rhythms


        # 3. Parameters

        self.mu0, self.c2 = 0.2, 1.5

        self.K_base = 0.1

        self.Q_accum = 0.0

    def _build_initial_geometry(self):

        dist = np.sqrt(((self.X[:, None] - self.X[None, :])**2).sum(axis=-1))

        W = np.exp(-(dist**2) / (2 * 0.7**2))

        np.fill_diagonal(W, 0)

        return W

    def ricci_flow_smoothing(self, eta=0.05):

        """Geometric smoothing: Strengthens weak links in the manifold."""

        degrees = self.W.sum(axis=1)

        # Simple Forman-Ricci heuristic: F = 4 - d1 - d2

        for i in range(self.N):

            for j in range(i+1, self.N):

                if self.W[i, j] > 0:

                    F = 4 - degrees[i] - degrees[j]

                    self.W[i, j] *= np.exp(-eta * F)

        self.W = self.W / (self.W.max() + 1e-12)

    def step(self, Y=1.0, Z=1.0, chi=1.0):

        # mu: Linear Gain (Ordering force)

        mu = (Y + Z * chi) * 0.5


        # Cubic Non-linearity (Self-regulation)

        nonlin = (1 + 1j*self.c2) * (np.abs(self.state)**2) * self.state


        # Coupling through Geometry

        coupling = (self.K_base * self.W) @ self.state


        # Update Equation (Stuart-Landau)

        dW = (mu + 1j*self.omega)*self.state - nonlin + coupling

        self.state += dW * self.dt


        # Entropy/Dissipation Calculation

        resistance = np.exp(-0.5 * np.abs(self.state).mean())

        self.Q_accum += (resistance * self.dt)


        return np.abs(self.state).mean(), self.Q_accum

# --- Simulation Demo ---

kernel = LoveOS_Kernel()

r_baseline, q_baseline = [], []

r_optimized, q_optimized = [], []

# Phase 1: Baseline

for _ in range(200):

    r, q = kernel.step(Y=0.5, Z=0.5)

    r_baseline.append(r)

    q_baseline.append(q)

# Intervention: /phase-shift + Ricci Flow

kernel.ricci_flow_smoothing()

for _ in range(200):

    r, q = kernel.step(Y=1.5, Z=1.2, chi=0.9) # Higher alignment

    r_optimized.append(r)

    q_optimized.append(q)

# Visualization

plt.figure(figsize=(12, 5))

plt.subplot(1, 2, 1)

plt.plot(r_baseline + r_optimized, color='purple', lw=2)

plt.axvline(200, color='red', ls='--', label='/phase-shift')

plt.title("Order Parameter (Coherence)")

plt.legend()

plt.subplot(1, 2, 2)

plt.plot(q_baseline + q_optimized, color='red', lw=2)

plt.title("Accumulated Dissipation (Q)")

plt.tight_layout()

plt.show()