282 lines
8.8 KiB
Plaintext
282 lines
8.8 KiB
Plaintext
{
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"cells": [
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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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"# N-Dimensional Ellipsoid Bonding Surface\n",
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"\n",
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"Deep dive into the generalized N-asset bonding surface — the core pricing primitive for MYCO."
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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 mpl_toolkits.mplot3d import Axes3D\n",
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"from matplotlib import cm\n",
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"\n",
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"%matplotlib inline\n",
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"plt.rcParams['figure.figsize'] = (12, 8)\n",
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"plt.rcParams['figure.dpi'] = 100"
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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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"from src.primitives.n_dimensional_surface import (\n",
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" NDSurfaceParams, NDSurfaceState,\n",
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" create_params, compute_invariant, compute_virtual_offsets,\n",
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" mint, redeem, spot_prices,\n",
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")"
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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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"## 2D Surface Visualization\n",
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"\n",
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"Start with 2 assets to visualize the invariant curve."
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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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"# Create 2D surface with different lambda values\n",
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"fig, axes = plt.subplots(1, 3, figsize=(18, 5))\n",
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"\n",
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"for ax, lambdas, title in [\n",
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" (axes[0], np.array([1.0, 1.0]), 'λ = [1, 1] (circular)'),\n",
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" (axes[1], np.array([3.0, 1.0]), 'λ = [3, 1] (elliptical)'),\n",
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" (axes[2], np.array([5.0, 5.0]), 'λ = [5, 5] (concentrated)'),\n",
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"]:\n",
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" params = create_params(2, lambdas=lambdas)\n",
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" \n",
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" # Compute invariant at a reference point\n",
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" ref_balances = np.array([1000.0, 1000.0])\n",
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" r = compute_invariant(ref_balances, params)\n",
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" offsets = compute_virtual_offsets(r, params)\n",
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" \n",
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" # Trace the invariant curve\n",
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" b0_range = np.linspace(100, 2000, 500)\n",
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" b1_values = []\n",
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" for b0 in b0_range:\n",
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" # Find b1 such that invariant = r\n",
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" v0 = b0 + offsets[0]\n",
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" A = params.A\n",
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" # Quadratic in v1: sum of (A @ v)^2 terms involving v1\n",
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" # Use numerical search\n",
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" from scipy.optimize import brentq\n",
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" def f(b1):\n",
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" v = np.array([b0 + offsets[0], b1 + offsets[1]])\n",
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" return np.sum((A @ v)**2) - r**2\n",
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" try:\n",
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" b1 = brentq(f, 1, 5000)\n",
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" b1_values.append(b1)\n",
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" except:\n",
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" b1_values.append(np.nan)\n",
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" \n",
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" ax.plot(b0_range, b1_values, 'b-', linewidth=2)\n",
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" ax.plot(1000, 1000, 'ro', markersize=8, label='Reference point')\n",
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" ax.set_xlabel('Balance 0')\n",
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" ax.set_ylabel('Balance 1')\n",
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" ax.set_title(title)\n",
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" ax.set_aspect('equal')\n",
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" ax.legend()\n",
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" ax.grid(True, alpha=0.3)\n",
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"\n",
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"plt.tight_layout()\n",
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"plt.show()"
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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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"## Minting Dynamics\n",
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"\n",
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"How token supply grows with deposits."
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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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"# Simulate sequential deposits\n",
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"params = create_params(3, lambdas=np.array([2.0, 2.0, 2.0]))\n",
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"state = NDSurfaceState(\n",
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" balances=np.array([1000.0, 1000.0, 1000.0]),\n",
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" invariant=0.0,\n",
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" supply=0.0,\n",
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")\n",
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"state.invariant = compute_invariant(state.balances, params)\n",
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"state.supply = state.invariant\n",
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"\n",
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"deposits = []\n",
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"supplies = [state.supply]\n",
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"invariants = [state.invariant]\n",
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"prices_history = [spot_prices(state, params)]\n",
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"\n",
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"for i in range(20):\n",
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" # Deposit into different assets to create imbalance\n",
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" deposit = np.zeros(3)\n",
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" deposit[i % 3] = 200.0 # Rotate deposits\n",
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" state, minted = mint(state, params, deposit)\n",
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" deposits.append(deposit)\n",
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" supplies.append(state.supply)\n",
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" invariants.append(state.invariant)\n",
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" prices_history.append(spot_prices(state, params))\n",
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"\n",
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"fig, axes = plt.subplots(1, 3, figsize=(18, 5))\n",
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"\n",
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"axes[0].plot(supplies, 'b-o', markersize=4)\n",
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"axes[0].set_xlabel('Deposit #')\n",
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"axes[0].set_ylabel('Total supply')\n",
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"axes[0].set_title('Supply Growth')\n",
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"\n",
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"axes[1].plot(invariants, 'r-o', markersize=4)\n",
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"axes[1].set_xlabel('Deposit #')\n",
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"axes[1].set_ylabel('Invariant r')\n",
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"axes[1].set_title('Invariant Growth')\n",
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"\n",
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"prices_arr = np.array(prices_history)\n",
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"for j in range(3):\n",
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" axes[2].plot(prices_arr[:, j], '-o', markersize=4, label=f'Asset {j}')\n",
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"axes[2].set_xlabel('Deposit #')\n",
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"axes[2].set_ylabel('Spot price')\n",
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"axes[2].set_title('Spot Prices (rotating deposits)')\n",
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"axes[2].legend()\n",
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"\n",
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"plt.tight_layout()\n",
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"plt.show()"
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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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"## 3D Invariant Surface\n",
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"\n",
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"For 3 assets, the invariant defines an ellipsoidal surface in balance space."
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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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"params = create_params(3, lambdas=np.array([2.0, 1.5, 1.0]))\n",
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"ref = np.array([1000.0, 1000.0, 1000.0])\n",
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"r = compute_invariant(ref, params)\n",
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"offsets = compute_virtual_offsets(r, params)\n",
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"\n",
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"# Sample points on the ellipsoid using parametric form\n",
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"fig = plt.figure(figsize=(10, 8))\n",
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"ax = fig.add_subplot(111, projection='3d')\n",
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"\n",
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"# Use spherical coordinates to trace the surface\n",
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"theta = np.linspace(0.1, np.pi/2 - 0.1, 30)\n",
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"phi = np.linspace(0.1, np.pi/2 - 0.1, 30)\n",
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"THETA, PHI = np.meshgrid(theta, phi)\n",
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"\n",
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"# Direction vectors on the positive octant\n",
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"d0 = np.sin(THETA) * np.cos(PHI)\n",
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"d1 = np.sin(THETA) * np.sin(PHI)\n",
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"d2 = np.cos(THETA)\n",
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"\n",
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"A = params.A\n",
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"B0 = np.zeros_like(THETA)\n",
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"B1 = np.zeros_like(THETA)\n",
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"B2 = np.zeros_like(THETA)\n",
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"\n",
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"for i in range(THETA.shape[0]):\n",
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" for j in range(THETA.shape[1]):\n",
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" d = np.array([d0[i,j], d1[i,j], d2[i,j]])\n",
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" # Scale d so that |A @ (scale*d)|^2 = r^2\n",
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" Ad = A @ d\n",
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" scale = r / np.linalg.norm(Ad)\n",
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" v = scale * d\n",
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" b = v - offsets\n",
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" B0[i,j] = max(b[0], 0)\n",
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" B1[i,j] = max(b[1], 0)\n",
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" B2[i,j] = max(b[2], 0)\n",
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"\n",
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"ax.plot_surface(B0, B1, B2, cmap=cm.viridis, alpha=0.6)\n",
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"ax.scatter([1000], [1000], [1000], color='red', s=100, label='Reference')\n",
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"ax.set_xlabel('Balance 0')\n",
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"ax.set_ylabel('Balance 1')\n",
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"ax.set_zlabel('Balance 2')\n",
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"ax.set_title(f'3-Asset Ellipsoid Surface (λ = {list(params.lambdas)})')\n",
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"ax.legend()\n",
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"plt.tight_layout()\n",
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"plt.show()"
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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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"## Mint/Redeem Symmetry\n",
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"\n",
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"Verify that minting then redeeming the same amount returns approximately the original state."
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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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"params = create_params(3)\n",
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"initial_balances = np.array([1000.0, 1000.0, 1000.0])\n",
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"state = NDSurfaceState(\n",
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" balances=initial_balances.copy(),\n",
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" invariant=compute_invariant(initial_balances, params),\n",
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" supply=0.0,\n",
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")\n",
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"state.supply = state.invariant\n",
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"\n",
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"# Mint\n",
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"deposit = np.array([100.0, 50.0, 75.0])\n",
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"state_after_mint, minted = mint(state, params, deposit)\n",
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"print(f'Minted: {minted:.4f} MYCO')\n",
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"print(f'Balances after mint: {state_after_mint.balances}')\n",
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"\n",
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"# Redeem exactly what was minted\n",
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"state_after_redeem, amounts_out = redeem(state_after_mint, params, minted)\n",
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"print(f'\\nAmounts out: {amounts_out}')\n",
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"print(f'Balances after redeem: {state_after_redeem.balances}')\n",
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"print(f'\\nBalance difference from original: {state_after_redeem.balances - initial_balances}')\n",
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"print(f'Supply difference: {state_after_redeem.supply - state.supply:.6f}')"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"name": "python",
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"version": "3.11.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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