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Update quark_zbw_mixing.ipynb
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‎standard_model_emergence_in_the_600-cell_lattice/cpp-zbw-mixing-fractions/notebooks/quark_zbw_mixing.ipynb‎

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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Quark Orbital ZBW DP Mixing Fractions (Up Quark + N_k Sensitivity)\n\n",
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"This notebook reproduces the quark orbital ZBW composition (~74% qDP) for up quark (N_k=1) and shows N_k dependence."
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"# Lepton Orbital ZBW DP Mixing Fractions (Muon Example)\n\n",
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"This notebook reproduces the lepton orbital ZBW composition (~68.5% eDP, 13% qDP, 18.5% hDP) for muon-like cages (N_k=4)."
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]
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},
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{
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from scipy.optimize import minimize\n\n",
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"phi = (1 + np.sqrt(5)) / 2\n",
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"phi = (1 + np.sqrt(5)) / 2 # ≈1.618\n",
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"base_gradient = 1.0\n",
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"gradients = {\n",
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" 'qDP': (phi - 1) * base_gradient, # favorable for quarks\n",
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" 'eDP': (phi - 1) * base_gradient, # Favorable for leptons\n",
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" 'hDP': base_gradient,\n",
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" 'eDP': phi * base_gradient # least favorable\n",
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"}"
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],
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"execution_count": null,
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"outputs": []
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" 'qDP': phi * base_gradient\n",
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"}\n\n",
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"N_k = 4 # muon tetra cage\n",
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"T = N_k # thermal scale T ∝ N_k (normalized)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 2. Function Definitions (same as lepton notebook)"
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"## 2. Energy Function"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"def energy(f):\n",
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" f_q, f_h, f_e = f\n",
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" E = f_q * gradients['qDP'] + f_h * gradients['hDP'] + f_e * gradients['eDP']\n",
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" return E\n\n",
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" f_e, f_h, f_q = f\n",
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" E = f_e * gradients['eDP'] + f_h * gradients['hDP'] + f_q * gradients['qDP']\n",
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" return E # minimize total energy"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 3. Constraints and Bounds"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"cons = ({'type': 'eq', 'fun': lambda f: np.sum(f) - 1})\n",
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"bounds = [(0, 1)] * 3"
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],
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"execution_count": null,
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"outputs": []
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 3. Single Calculation (Up Quark, N_k=1)"
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"## 4. Minimize Energy"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"N_k = 1\n",
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"T = N_k\n",
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"res = minimize(energy, [1/3, 1/3, 1/3], method='SLSQP', bounds=bounds, constraints=cons)\n",
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"min_fractions = res.x\n",
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"probs = np.exp(-np.array([gradients['qDP'], gradients['hDP'], gradients['eDP']]) / T)\n",
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"probs /= np.sum(probs)\n",
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"min_fractions = res.x"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 5. Thermal Probabilities"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"probs = np.exp(-np.array([gradients['eDP'], gradients['hDP'], gradients['qDP']]) / T)\n",
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"probs /= np.sum(probs)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 6. Equilibrium Fractions (average min + thermal)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"equil = 0.5 * min_fractions + 0.5 * probs\n",
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"equil /= np.sum(equil)\n\n",
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"print(\"Up quark (N_k=1) equilibrium fractions:\", equil)"
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],
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"execution_count": null,
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"outputs": []
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"print(\"Optimized minimum fractions:\", min_fractions)\n",
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"print(\"Thermal probabilities:\", probs)\n",
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"print(\"Equilibrium fractions:\", equil)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 4. N_k Sensitivity Sweep"
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"## 7. Visualization"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"N_k_values = [1, 4, 12, 20, 60, 30000] # up → top\n",
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"qDP_fracs = []\n",
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"for nk in N_k_values:\n",
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" T = nk\n",
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" probs = np.exp(-np.array([gradients['qDP'], gradients['hDP'], gradients['eDP']]) / T)\n",
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" probs /= np.sum(probs)\n",
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" # Simplified: use thermal only for sweep (min is always qDP-heavy)\n",
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" qDP_fracs.append(probs[0])\n\n",
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"plt.plot(N_k_values, qDP_fracs, marker='o')\n",
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"plt.xscale('log')\n",
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"plt.xlabel('N_k (cage occupancy)')\n",
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"plt.ylabel('qDP fraction in orbital ZBW')\n",
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"plt.title('Quark Orbital ZBW: qDP Dominance vs. Cage Size')\n",
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"plt.grid(True, which=\"both\", ls=\"--\")\n",
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"plt.savefig('../figures/sensitivity_plot.png')\n",
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"labels = ['eDP', 'hDP', 'qDP']\n",
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"plt.pie(equil, labels=labels, autopct='%1.1f%%', colors=['#1f77b4', '#ff7f0e', '#2ca02c'])\n",
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"plt.title('Lepton Orbital ZBW DP Composition (Muon, N_k=4)')\n",
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"plt.savefig('../figures/lepton_pie_chart.png')\n",
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"plt.show()"
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],
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"execution_count": null,
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"outputs": []
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]
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}
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],
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"metadata": {

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