{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2288c59f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Generating gw_phase.png...\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Generating GRB bounds table conversions...\n",
      "Dataset \\t\\t\\t\\t lower bound on $E_{QG,2}$ [GeV] \\t implied $\\alpha_{max}$\n",
      "--------------------------------------------------------------------------------\n",
      "LHAASO GRB 221009A (TOF) [LHAASO2024] \\t 7.300e+11 \\t 1.862e+14\n",
      "LHAASO (KM2A+WCDA) [Yang2023] \\t 1.200e+12 \\t 6.891e+13\n",
      "DisCan reanalysis (GRB 221009A) [Xi2025] \\t 1.000e+13 \\t 9.923e+11\n",
      "GRBs (multi-band) [Chen2024] \\t 8.180e+09 \\t 1.483e+18\n",
      "\n",
      "Running SymPy verifications for Appendix...\n",
      "MDR expansion confirms quartic term with alpha=1/12: -DeltaTau**2*E**4/(12*hbar**2) + E**2 - c**4*m**2 - c**2*p**2\n",
      "Symbolic gamma_max: 6145211067.0686/(c**2*m)\n",
      "\n",
      "All figures and verifications complete. Files saved in current directory:\n",
      "- fig2_lorentz_plot_mc288.png\n",
      "- gw_phase.png\n",
      "GRB table printed above.\n",
      "SymPy outputs for appendix verifications printed.\n"
     ]
    }
   ],
   "source": [
    "# Jupyter Notebook to reproduce all figures and simulations from the article\n",
    "# \"Gravity as Resynchronization\" (Spinelli 2025, engrXiv preprint).\n",
    "# Run this in a Jupyter notebook on Windows 11. Files will be saved in the current working directory.\n",
    "# Required libraries: numpy, matplotlib, scipy, sympy (all available in the environment)\n",
    "# %pip install sympy if not yet installed\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.constants import hbar, c, G\n",
    "import sympy as sp\n",
    "import numpy as np, mpmath as mp\n",
    "from math import pi\n",
    "from scipy.constants import hbar, c\n",
    "\n",
    "# ---------------- Inset: x = (v/c - 1) in sci, y = log with 10^n mathtext ----------------\n",
    "from mpl_toolkits.axes_grid1.inset_locator import inset_axes\n",
    "from matplotlib.ticker import FuncFormatter, FixedLocator, LogLocator, LogFormatterMathtext, NullFormatter\n",
    "\n",
    "# --- Canonical mass constants (SI) ---\n",
    "M_U = 1.66053906660e-27    # atomic mass unit (kg)\n",
    "\n",
    "\n",
    "# =============================================================================\n",
    "# Section: Constants (directly aligned with article notation and definitions)\n",
    "# =============================================================================\n",
    "tmin = 5.391_247e-44  # Planck time in s\n",
    "epsilon_q = 1e-86  # Approximate epsilon_q = (t_min / t_0)^2 ~10^{-86}\n",
    "l_p = np.sqrt(hbar * G / c**3)  # Planck length m\n",
    "f_P = c / l_p  # Planck frequency ~10^43 Hz\n",
    "E_pl_gev = 1.22e19  # Planck energy in GeV\n",
    "\n",
    "# For MDR integration (alpha = 1/12 from finite difference)\n",
    "alpha = 1 / 12\n",
    "def alpha_from_EQG2(E_QG2_gev):\n",
    "    return (2 / 3) * (E_pl_gev / E_QG2_gev)**2\n",
    "\n",
    "# High precision for inset\n",
    "mp.mp.dps = 200  \n",
    "\n",
    "# =============================================================================\n",
    "# Functions\n",
    "# =============================================================================\n",
    "def gamma_classical(v):\n",
    "    return 1 / mp.sqrt(1 - v**2)\n",
    "\n",
    "# (removed: redundant early gamma_max precompute; using gamma_max_float from M_CONSTITUENT_KG)\n",
    "# =========================================================================\n",
    "# Article Fig. 2 (Notebook Fig. 1):\n",
    "# Discrete vs Classical Lorentz factor near v/c = 1 (constituent-based MDR)\n",
    "# Constituent: Moscovium (Mc-288) nucleus\n",
    "# =========================================================================\n",
    "\n",
    "\n",
    "# --- Choose the co-moving constituent ---\n",
    "Z, A = 115, 288              # Moscovium-288\n",
    "M_CONSTITUENT_KG = A * M_U  # nuclear mass ≈ A·u\n",
    "NAME = f\"Moscovium Mc-{A} nucleus\"\n",
    "\n",
    "# --- Single source of truth for gamma_max ---\n",
    "E_end_J = pi * hbar / tmin\n",
    "gamma_max_float = float(E_end_J / (M_CONSTITUENT_KG * c**2))\n",
    "gamma_max_mp = mp.mpf(str(gamma_max_float))\n",
    "\n",
    "def gamma_classical_float(v: float) -> float:\n",
    "    return 1.0 / np.sqrt(1.0 - v*v) if v < 1.0 else np.nan\n",
    "\n",
    "def gamma_quantized(v, m):\n",
    "    \"\"\"\n",
    "    Discrete-time Lorentz factor with MDR saturation.\n",
    "    v : speed in units of c (mpmath.mpf or float)\n",
    "    m : constituent mass (kg)\n",
    "    returns (gamma_q, gamma_max)\n",
    "    \"\"\"\n",
    "    # mp-safe copies of globals\n",
    "    Delta_mp = mp.mpf(str(tmin))      # tmin defined earlier in the cell\n",
    "    hbar_mp  = mp.mpf(str(hbar))      # from scipy.constants import hbar\n",
    "    c_mp     = mp.mpf(str(c))         # from scipy.constants import c\n",
    "\n",
    "    # MDR endpoint energy and plateau\n",
    "    E_end    = mp.pi * hbar_mp / Delta_mp\n",
    "    gamma_max = E_end / (m * c_mp**2)\n",
    "\n",
    "    # gamma_q with analytic continuation for v>1\n",
    "    v_mp = mp.mpf(v)\n",
    "    if v_mp < 1:\n",
    "        E = m * c_mp**2 / mp.sqrt(1 - v_mp**2)\n",
    "    else:\n",
    "        E = m * c_mp**2 / mp.sqrt(v_mp**2 - 1)\n",
    "\n",
    "    return min(E / (m * c_mp**2), gamma_max), gamma_max\n",
    "\n",
    "\n",
    "# --- Main panel around v/c=1, omit tiny gap around the pole ---\n",
    "v_main = np.linspace(0.95, 1.05, 4000)\n",
    "mask = (v_main < 0.9999) | (v_main > 1.0001)\n",
    "v_main_masked = v_main[mask]\n",
    "\n",
    "gamma_class = [1/np.sqrt(1.0 - v*v) if v < 1.0 else np.nan for v in v_main_masked]\n",
    "gamma_q     = [gamma_quantized(v, M_CONSTITUENT_KG)[0] for v in v_main_masked]\n",
    "\n",
    "# >>> Use constrained layout to avoid tight_layout hang <<<\n",
    "fig1, ax = plt.subplots(figsize=(8, 6), layout='constrained')\n",
    "\n",
    "ax.semilogy(v_main_masked, gamma_q, 'b:', lw=1.8, label=r'Discrete $\\gamma_q$ (MDR)')\n",
    "ax.semilogy(v_main_masked, gamma_class, 'r-', lw=1.0, label=r'Classical $\\gamma$')\n",
    "ax.axvline(x=1.0, color='gray', ls='--')\n",
    "ax.axvspan(0.9999, 1.0001, color='gray', alpha=0.15)\n",
    "\n",
    "ax.set_xlim(0.95, 1.05)\n",
    "ax.set_ylim(1, 2e3)\n",
    "ax.set_xlabel(\"v/c\")\n",
    "ax.set_ylabel(\"γ\")\n",
    "ax.set_title(\"Fig. 2 — Discrete-time Lorentz factor near $v/c=1$ (constituent-based MDR)\")\n",
    "ax.grid(True, which='both', alpha=0.3)\n",
    "ax.legend(loc='upper left')\n",
    "\n",
    "\n",
    "axins = ax.inset_axes([0.58, 0.50, 0.32, 0.32])\n",
    "\n",
    "# Half-width from physics: 1 - v/c ≈ 1/(2 γ_max^2) (widen ×2 for visibility)\n",
    "delta_phys = 1.0 / (2.0 * gamma_max_float**2)\n",
    "delta = float(2.0 * delta_phys)\n",
    "\n",
    "# Geometric sampling in |x| ∈ [delta/100, delta]\n",
    "N = 1200  # trimmed for speed; visually equivalent\n",
    "delta_mp = mp.mpf(str(delta))\n",
    "emin = delta_mp / mp.mpf('100')\n",
    "elog_min = mp.log10(emin)\n",
    "elog_max = mp.log10(delta_mp)\n",
    "elog_grid = [elog_min + (elog_max - elog_min)*i/(N-1) for i in range(N)]\n",
    "eps = [mp.power(10, e) for e in elog_grid]  # |v/c - 1|\n",
    "\n",
    "# Build v on each side (mpmath), then gammas\n",
    "v_left_mp  = [1 - e for e in eps]     # v < 1\n",
    "v_right_mp = [1 + e for e in eps]     # v > 1\n",
    "\n",
    "gcl_left   = [float(1/mp.sqrt(1 - v*v)) for v in v_left_mp]\n",
    "gq_left    = [float(min(1/mp.sqrt(1 - v*v), gamma_max_mp)) for v in v_left_mp]\n",
    "gq_right   = [float(min(1/mp.sqrt(v*v - 1),   gamma_max_mp)) for v in v_right_mp]\n",
    "\n",
    "# X = v/c - 1 (signed offsets, as floats)\n",
    "x_left  = [float(v - 1) for v in v_left_mp]     # negative\n",
    "x_right = [float(v - 1) for v in v_right_mp]    # positive\n",
    "\n",
    "# Plot the inset curves\n",
    "axins.semilogy(x_left,  gcl_left, 'r-',  lw=0.9, label='Classical')\n",
    "axins.semilogy(x_left,  gq_left,  'b:',  lw=1.2, label='Discrete')\n",
    "axins.semilogy(x_right, gq_right, 'b:',  lw=1.2)\n",
    "axins.axhline(gamma_max_float, color='k', ls=':', lw=1)\n",
    "\n",
    "# Mark the saturation point on the left side (x_crit < 0)\n",
    "v_crit_mp = mp.sqrt(1 - 1/(gamma_max_mp**2))\n",
    "x_crit = float(v_crit_mp - 1)\n",
    "axins.plot(x_crit, float(gamma_max_mp), 'bs', ms=6, markeredgecolor='k')\n",
    "\n",
    "# Inset X axis: symmetric window and ONLY 3 tick labels (-Δ, 0, +Δ), mathtext formatter\n",
    "axins.set_xlim(-delta, delta)\n",
    "x_ticks = [-delta, 0.0, delta]\n",
    "axins.xaxis.set_major_locator(FixedLocator(x_ticks))\n",
    "\n",
    "def fmt_x_mathtext(x, pos):\n",
    "    if abs(x) < 1e-300:\n",
    "        return r\"$0$\"\n",
    "    exp  = int(np.floor(np.log10(abs(x))))\n",
    "    mant = x / (10.0**exp)\n",
    "    sign = \"-\" if x < 0 else \"\"\n",
    "    return rf\"$ {sign}{abs(mant):.2f}\\times 10^{{{exp}}} $\"\n",
    "\n",
    "axins.xaxis.set_major_formatter(FuncFormatter(fmt_x_mathtext))\n",
    "axins.set_xlabel(r'$v/c - 1$', fontsize=8, labelpad=1)\n",
    "\n",
    "# Inset Y axis: log scale with major 10^n ticks, and 2/5/9 minor gridlines (no labels)\n",
    "axins.yaxis.set_major_locator(LogLocator(base=10.0, numticks=4))\n",
    "axins.yaxis.set_major_formatter(LogFormatterMathtext(base=10.0))\n",
    "axins.yaxis.set_minor_locator(LogLocator(base=10.0, subs=(2, 5, 9)))\n",
    "axins.yaxis.set_minor_formatter(NullFormatter())\n",
    "\n",
    "# Subtle y-grid styling: majors light, minors dotted (2/5/9)\n",
    "axins.grid(which='major', axis='y', linestyle='-',  alpha=0.25)\n",
    "axins.grid(which='minor', axis='y', linestyle=':',  alpha=0.30)\n",
    "axins.tick_params(axis='both', which='major', labelsize=8, direction=\"out\")\n",
    "axins.axvline(x_crit, color='k', ls=':', lw=0.6, alpha=0.5)\n",
    "\n",
    "\n",
    "# Annotation with true newlines (join strings)\n",
    "t_P = tmin # alias for clarirty in the annotation only\n",
    "legend_lines = [\n",
    "    rf\"Constituent: Mc-{A} ($m={M_CONSTITUENT_KG:.2e}$ kg)\",\n",
    "    rf\"$\\gamma_{{\\max}}=\\dfrac{{\\pi\\hbar}}{{t_P\\,m\\,c^2}}\\approx {gamma_max_float:.2e}$\",\n",
    "    r\"$|v/c-1|\\sim 1/(2\\gamma_{\\max}^2)$\",\n",
    "]\n",
    "ax.text(\n",
    "    0.60, 0.965, \"\\n\".join(legend_lines),\n",
    "    transform=ax.transAxes, fontsize=8, ha='left', va='top',\n",
    "    bbox=dict(facecolor='white', alpha=0.9, edgecolor='gray')\n",
    ")\n",
    "\n",
    "\n",
    "# No tight_layout() needed when layout='constrained'\n",
    "plt.savefig(\"fig2_lorentz_plot_mc288.png\", dpi=600, bbox_inches='tight')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# =============================================================================\n",
    "# Figure 2: Predicted GW phase shift δφ vs. frequency f\n",
    "# Formula: δφ ≈ (f/f_P)^2 ε_q^{-1/2}, with shaded LIGO O4 band (10–1000 Hz)\n",
    "# =============================================================================\n",
    "print('\\nGenerating gw_phase.png...')\n",
    "f = np.logspace(-1, 4, 1000)  # Hz, from 0.1 to 10 kHz covering LIGO\n",
    "delta_phi = (f / f_P)**2 / np.sqrt(epsilon_q)  # From paper formula\n",
    "\n",
    "fig2, ax2 = plt.subplots(figsize=(6, 4))\n",
    "ax2.loglog(f, delta_phi, 'g-', label=r'Predicted $\\delta \\phi$')\n",
    "# Shade LIGO O4 band approx 10-1000 Hz\n",
    "ax2.axvspan(10, 1000, alpha=0.3, color='gray', label='LIGO O4 band')\n",
    "ax2.set_xlabel('Frequency $f$ (Hz)')\n",
    "ax2.set_ylabel(r'Phase shift $\\delta \\phi$')\n",
    "ax2.set_title(r'Fig. 3 — Predicted GW phase shift $\\delta \\phi$ vs. $f$')\n",
    "ax2.legend()\n",
    "ax2.grid(True, which='both', alpha=0.3)\n",
    "plt.tight_layout()\n",
    "plt.savefig('gw_phase.png', dpi=300, bbox_inches='tight')\n",
    "plt.show()\n",
    "plt.close()\n",
    "\n",
    "# =============================================================================\n",
    "# Table 1: GRB constraints — implied α_max\n",
    "# Converts published E_QG2 bounds into quartic MDR coefficients (article Table~\\ref{tab:GRB_bounds})\n",
    "# =============================================================================\n",
    "print('\\nGenerating GRB bounds table conversions...')\n",
    "bounds = {\n",
    "    'LHAASO GRB 221009A (TOF) [LHAASO2024]': 7.3e11,\n",
    "    'LHAASO (KM2A+WCDA) [Yang2023]': 1.2e12,\n",
    "    'DisCan reanalysis (GRB 221009A) [Xi2025]': 1.0e13,\n",
    "    'GRBs (multi-band) [Chen2024]': 8.18e9\n",
    "}\n",
    "\n",
    "print('Dataset \\\\t\\\\t\\\\t\\\\t lower bound on $E_{QG,2}$ [GeV] \\\\t implied $\\\\alpha_{max}$')\n",
    "print('-' * 80)\n",
    "for name, eqg in bounds.items():\n",
    "    alpha_max = alpha_from_EQG2(eqg)\n",
    "    print(f'{name} \\\\t {eqg:.3e} \\\\t {alpha_max:.3e}')\n",
    "\n",
    "# =============================================================================\n",
    "# Appendix: SymPy checks of MDR expansion\n",
    "# Confirms quartic correction term with α=1/12 and symbolic γ_max scaling\n",
    "# =============================================================================\n",
    "print('\\nRunning SymPy verifications for Appendix...')\n",
    "E, DeltaTau, hbar_sym, p, c_sym, m = sp.symbols('E DeltaTau hbar p c m')\n",
    "mdr = (4 * hbar_sym**2 / DeltaTau**2) * sp.sin(E * DeltaTau / (2 * hbar_sym))**2 - p**2 * c_sym**2 - m**2 * c_sym**4\n",
    "expansion = sp.series(mdr.series(E, 0, 5).removeO(), x=E, x0=0, n=5).removeO()\n",
    "print('MDR expansion confirms quartic term with alpha=1/12:', expansion)\n",
    "\n",
    "# Numerical gamma_max for protons\n",
    "eV_to_J = 1.602176634e-19\n",
    "proton_mass_gev = 0.9382720813  # Proton rest mass energy in GeV\n",
    "\n",
    "proton_mc2_j = proton_mass_gev * 1e9 * eV_to_J\n",
    "\n",
    "# Define endpoint energy consistent with earlier derivations\n",
    "E_end = sp.pi * hbar / tmin  # Joules\n",
    "\n",
    "gamma_max_sym = E_end / (m * c_sym**2)\n",
    "print('Symbolic gamma_max:', gamma_max_sym)\n",
    "\n",
    "print('\\nAll figures and verifications complete. Files saved in current directory:')\n",
    "print('- fig2_lorentz_plot_mc288.png')\n",
    "print('- gw_phase.png')\n",
    "print('GRB table printed above.')\n",
    "print('SymPy outputs for appendix verifications printed.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "cc512fde",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Precision] Calibration: mpmath with 80 digits\n",
      "[Precision] Production : float64 on NumPy CPU\n",
      "[1/200] phase=calibration, elapsed=0.07 min, resid_mu~-3.912e-52\n",
      "[50/200] phase=calibration, elapsed=3.19 min, resid_mu~-3.973e-52\n",
      "[100/200] phase=calibration, elapsed=6.69 min, resid_mu~-3.996e-52\n",
      "[150/200] phase=calibration, elapsed=10.37 min, resid_mu~-3.991e-52\n",
      "[200/200] phase=calibration, elapsed=14.12 min, resid_mu~-3.986e-52\n",
      "\n",
      "=== Simulation Report ===\n",
      "Mode: PRODUCTION\n",
      "Calibration precision : mpmath @ 80 digits\n",
      "Production precision  : float64 on NumPy CPU\n",
      "\n",
      "[Calibration] a4 convergence:\n",
      "  theory a4              = 2.177935e-20\n",
      "  mean(a4_resid)         = 2.177935e-20\n",
      "  mean/theory            = 1.000e+00\n",
      "  relative std           = 2.763e-16\n",
      "  flatness span (max-min)= 0.000e+00\n",
      "  ✅ Convergence OK. Flatness expected: tiny-y series → ratio ≈ 1/3 across samples.\n",
      "\n",
      "Model summary:\n",
      "  mean MDR residual   = -3.986e-52\n",
      "  ⟨Tq⟩                 = 4.153e+24\n",
      "  ⟨Q⟩                  = 5.155e+85\n",
      "  gamma_max           = 4.088e+19\n",
      "  runtime (s)         = 847.33\n",
      "\n",
      "Saved:\n",
      "  CSV   -> mdr_outputs\\timeseries.csv\n",
      "  JSON  -> mdr_outputs\\summary.json\n"
     ]
    }
   ],
   "source": [
    "# === Simulation configuration: calibration vs production runs (article Section III) ===\n",
    "# Toggle precision and backend choices to reproduce article figures.\n",
    "\n",
    "DEV_MODE = False   # set False for full production runs\n",
    "\n",
    "import os, time, math, json, csv\n",
    "from datetime import datetime\n",
    "import numpy as np\n",
    "import mpmath as mp\n",
    "try:\n",
    "    tmin\n",
    "except NameError:\n",
    "    tmin = 5.391_247e-44  # Planck time (s), fallback if cell 1 wasn't run\n",
    "\n",
    "# -------- Backend selection (NumPy/CuPy; article results use NumPy float64) --------\n",
    "xp = np\n",
    "USE_CUPY = False  # you can wire this later if you want CuPy for production\n",
    "\n",
    "# -------- Precision setup (mpmath for calibration, float64 for production) --------\n",
    "# # High-precision (mpmath) for calibration, float64 for reproducibility.\n",
    "# Calibration uses mpmath high precision; production uses float64 for throughput\n",
    "mp.dps = 80\n",
    "xp_float = np.float64\n",
    "\n",
    "print(f\"[Precision] Calibration: mpmath with {mp.dps} digits\")\n",
    "print(f\"[Precision] Production : float64 on {'CuPy GPU' if USE_CUPY else 'NumPy CPU'}\")\n",
    "\n",
    "# -------- Physical constants (SI units; identical to article definitions) --------\n",
    "# ħ, c, t_min, m_p are the foundational parameters for all derived results.\n",
    "hbar = 1.054_571_817e-34\n",
    "c    = 2.997_924_58e8\n",
    "m_p  = 1.672_621_92369e-27  # kg (proton mass, SI; used to build nuclear mass A * M_U)\n",
    "\n",
    "# -------- Config --------\n",
    "CFG = {\n",
    "    \"batches\"       : 200,\n",
    "    \"batch_size\"    : 200_000,\n",
    "    \"report_every\"  : 50,\n",
    "    \"seed\"          : 42,\n",
    "\n",
    "    # production (massive) settings\n",
    "    \"m_choice\"      : m_p,\n",
    "    \"prod_E_min_GeV\": 1e-3,       # 1 MeV\n",
    "    \"prod_E_max_GeV\": 1e4,        # 10 TeV\n",
    "\n",
    "    # calibration (massless) settings (small y, in Joules)\n",
    "    \"cal_E_min_J\"   : 1e-20,\n",
    "    \"cal_E_max_J\"   : 1e-17,\n",
    "\n",
    "    # Toy tensor model knobs\n",
    "    \"Tq_strength\"   : 1.0,\n",
    "    \"Q_strength\"    : 1.0,\n",
    "\n",
    "    # diagnostics knobs (currently unused in this cell, but kept for consistency)\n",
    "    \"diag_y_scale\"  : 1.0,\n",
    "    \"diag_mode\"     : False,\n",
    "\n",
    "    # I/O\n",
    "    \"outdir\"        : \"mdr_outputs\",\n",
    "    \"save_csv\"      : True,\n",
    "\n",
    "    # NEW: high-precision subset size per calibration batch\n",
    "    \"calib_highprec_samples\": 50_000\n",
    "}\n",
    "\n",
    "if DEV_MODE:\n",
    "    CFG[\"batches\"]                 = 5\n",
    "    CFG[\"batch_size\"]              = 50_000\n",
    "    CFG[\"report_every\"]            = 5\n",
    "    CFG[\"diag_mode\"]               = True\n",
    "    CFG[\"calib_highprec_samples\"]  = 500\n",
    "    print(\"⚠️ DEV mode: reduced batches, diag_mode on, fewer high-precision samples\")\n",
    "\n",
    "# -------- Reproducibility --------\n",
    "np.random.seed(CFG[\"seed\"])\n",
    "\n",
    "# -------- Derived constants --------\n",
    "m     = CFG[\"m_choice\"]\n",
    "Delta = tmin\n",
    "E_end = math.pi * hbar / Delta\n",
    "gamma_max = E_end / (m * c**2)\n",
    "\n",
    "# a4 (theory)\n",
    "a4_theory = float((Delta*Delta) / (12.0*hbar*hbar))\n",
    "\n",
    "# I/O prep\n",
    "os.makedirs(CFG[\"outdir\"], exist_ok=True)\n",
    "\n",
    "# -------- Core MDR residual (production math) --------\n",
    "def mdr_residual(E, p, mass):\n",
    "    E = E.astype(xp_float)\n",
    "    p = p.astype(xp_float)\n",
    "    mass = xp.asarray(mass, dtype=xp_float)\n",
    "    coef = xp.asarray(4.0*hbar*hbar/(Delta*Delta), dtype=xp_float)\n",
    "    arg  = E * xp.asarray(Delta/(2.0*hbar), dtype=xp_float)\n",
    "    lhs  = coef * xp.sin(arg).astype(xp_float)**2\n",
    "    rhs  = (p * xp.asarray(c, dtype=xp_float))**2 + (mass * xp.asarray(c*c, dtype=xp_float))**2\n",
    "    return (lhs - rhs).astype(xp_float)\n",
    "\n",
    "# -------- a4 estimators --------\n",
    "def a4_est_from_residual_highprec(E):\n",
    "    \"\"\"\n",
    "    High-precision calibration of a4 using mpmath on a subset of samples.\n",
    "    Uses small-y series for |y|<1e-3 and the exact ratio elsewhere.\n",
    "    Returns a float64 number (converted at the end).\n",
    "    \"\"\"\n",
    "    vals = []\n",
    "    for Ei in E:\n",
    "        Ei = mp.mpf(Ei)\n",
    "        y  = Ei * Delta / (2*mp.mpf(hbar))\n",
    "        if abs(y) < mp.mpf(\"1e-3\"):\n",
    "            z = y*y\n",
    "            ratio = (mp.mpf(1)/3) - (mp.mpf(2)/45)*z + (mp.mpf(1)/315)*z**2 - (mp.mpf(2)/2835)*z**3\n",
    "        else:\n",
    "            ratio = -(mp.sin(y)**2 - y**2) / (y**4)\n",
    "        vals.append(ratio)\n",
    "    mean_ratio = mp.fsum(vals) / len(vals)\n",
    "    a4_th_mp = (Delta*Delta) / (12* hbar*hbar)\n",
    "    return float(a4_th_mp * (mean_ratio / (mp.mpf(1)/3)))\n",
    "\n",
    "# -------- Toy T_q and Q tensors (diagnostic model; see article Sec. IV) --------\n",
    "lP = math.sqrt(hbar * 6.67430e-11 / c**3)\n",
    "def toy_Tq_Q(batch_size, Tq_strength=1.0, Q_strength=1.0):\n",
    "    scale_T = (hbar / (c**3 * Delta**2)) * Tq_strength\n",
    "    scale_Q = (hbar / (c * lP**4)) * Q_strength\n",
    "    M = 4\n",
    "    dT = xp.random.normal(loc=0.0, scale=1e-3, size=(batch_size, M, M))\n",
    "    dG = xp.random.normal(loc=0.0, scale=1e-6, size=(batch_size, M, M))\n",
    "    dT = 0.5 * (dT + xp.swapaxes(dT, -1, -2))\n",
    "    dG = 0.5 * (dG + xp.swapaxes(dG, -1, -2))\n",
    "    T_norms = xp.linalg.norm(dT, axis=(1,2))\n",
    "    Q_norms = xp.linalg.norm(dG, axis=(1,2))\n",
    "    Tq_batch = scale_T * xp.mean(T_norms)\n",
    "    Q_batch  = scale_Q * xp.mean(Q_norms**2)\n",
    "    return Tq_batch, Q_batch\n",
    "\n",
    "# -------- Energy-momentum samplers (massless/massive cases; calibration vs production) --------\n",
    "def sample_massless(n, Emin_J, Emax_J):\n",
    "    u  = xp.random.uniform(0.0, 1.0, size=n).astype(xp_float)\n",
    "    Emin_J = xp.asarray(Emin_J, dtype=xp_float)\n",
    "    Emax_J = xp.asarray(Emax_J, dtype=xp_float)\n",
    "    E  = xp.exp(xp.log(Emin_J) + u * (xp.log(Emax_J) - xp.log(Emin_J))).astype(xp_float)\n",
    "    noise = xp.random.normal(loc=0.0, scale=1e-30, size=n).astype(xp_float)\n",
    "    E = xp.maximum(E + noise, xp.asarray(1e-40, dtype=xp_float))\n",
    "    p  = (E / c).astype(xp_float)\n",
    "    return E, p\n",
    "\n",
    "def sample_massive_on_shell(n, Emin_J, Emax_J, mass):\n",
    "    u  = xp.random.uniform(0.0, 1.0, size=n).astype(xp_float)\n",
    "    Emin_J = xp.asarray(Emin_J, dtype=xp_float)\n",
    "    Emax_J = xp.asarray(Emax_J, dtype=xp_float)\n",
    "    E  = xp.exp(xp.log(Emin_J) + u * (xp.log(Emax_J) - xp.log(Emin_J))).astype(xp_float)\n",
    "    Ec = (E / c).astype(xp_float)\n",
    "    mc = xp.asarray(mass * c, dtype=xp_float)\n",
    "    arg = Ec*Ec - mc*mc\n",
    "    arg = xp.clip(arg, 0.0, None).astype(xp_float)\n",
    "    p   = xp.sqrt(arg)\n",
    "    return E, p\n",
    "\n",
    "# -------- Main simulation loop (produces timeseries for Figures 3–4) --------\n",
    "# Phase sizes (DEV vs PRODUCTION)\n",
    "if DEV_MODE:\n",
    "    CALIB_BATCHES = min(CFG[\"batches\"], 5)   # small, quick calibration\n",
    "    PROD_BATCHES  = 0\n",
    "else:\n",
    "    CALIB_BATCHES = min(CFG[\"batches\"], 200) # cap calibration at 200\n",
    "    PROD_BATCHES  = max(0, CFG[\"batches\"] - CALIB_BATCHES)\n",
    "\n",
    "TOTAL_BATCHES = CALIB_BATCHES + PROD_BATCHES\n",
    "\n",
    "PHASES = [\n",
    "    {\"name\": \"calibration\", \"batches\": CALIB_BATCHES,\n",
    "     \"E_min_J\": CFG[\"cal_E_min_J\"], \"E_max_J\": CFG[\"cal_E_max_J\"]},\n",
    "    {\"name\": \"production\",  \"batches\": PROD_BATCHES,\n",
    "     \"E_min_GeV\": CFG[\"prod_E_min_GeV\"], \"E_max_GeV\": CFG[\"prod_E_max_GeV\"]},\n",
    "]\n",
    "\n",
    "start = time.time()\n",
    "\n",
    "# Time series (for plotting cell)\n",
    "residual_means, a4_fits, a4_resid_vals, Tq_vals, Q_vals, phase_names = [], [], [], [], [], []\n",
    "\n",
    "# CSV setup\n",
    "csv_path = os.path.join(CFG[\"outdir\"], \"timeseries.csv\")\n",
    "csv_f = open(csv_path, \"w\", newline=\"\")\n",
    "csv_w = csv.writer(csv_f)\n",
    "csv_w.writerow([\"batch\", \"phase\", \"residual_mean\", \"a4_analytic\", \"a4_resid\", \"Tq\", \"Q\"])\n",
    "\n",
    "batch_idx = 0\n",
    "for phase in PHASES:\n",
    "    for _ in range(phase[\"batches\"]):\n",
    "        batch_idx += 1\n",
    "        if phase[\"name\"] == \"calibration\":\n",
    "            E, p = sample_massless(CFG[\"batch_size\"], phase[\"E_min_J\"], phase[\"E_max_J\"])\n",
    "            r = mdr_residual(E, p, mass=0.0)\n",
    "            a4 = a4_theory\n",
    "            n_highprec = min(CFG[\"calib_highprec_samples\"], E.shape[0])\n",
    "            a4_resid = a4_est_from_residual_highprec(E[:n_highprec])\n",
    "\n",
    "        else:\n",
    "            Emin_J = phase[\"E_min_GeV\"] * 1.602176634e-10\n",
    "            Emax_J = phase[\"E_max_GeV\"] * 1.602176634e-10\n",
    "            E, p   = sample_massive_on_shell(CFG[\"batch_size\"], Emin_J, Emax_J, mass=m)\n",
    "            r = mdr_residual(E, p, mass=m)\n",
    "            a4 = float(\"nan\")\n",
    "            a4_resid = float(\"nan\")\n",
    "\n",
    "        rm  = float(np.mean(r))\n",
    "        Tq_batch, Q_batch = toy_Tq_Q(CFG[\"batch_size\"], CFG[\"Tq_strength\"], CFG[\"Q_strength\"])\n",
    "        tq = float(Tq_batch); qv = float(Q_batch)\n",
    "\n",
    "        residual_means.append(rm)\n",
    "        a4_fits.append(a4)\n",
    "        a4_resid_vals.append(a4_resid)\n",
    "        Tq_vals.append(tq)\n",
    "        Q_vals.append(qv)\n",
    "        phase_names.append(phase[\"name\"])\n",
    "\n",
    "        # Stream to CSV\n",
    "        csv_w.writerow([batch_idx, phase[\"name\"], rm, a4, a4_resid, tq, qv])\n",
    "\n",
    "        # Progress\n",
    "        if (batch_idx % CFG[\"report_every\"]) == 0 or batch_idx == 1:\n",
    "            elapsed = (time.time() - start)/60\n",
    "            print(f\"[{batch_idx}/{TOTAL_BATCHES}] phase={phase['name']}, elapsed={elapsed:.2f} min, \"\n",
    "                  f\"resid_mu~{np.mean(residual_means):.3e}\")\n",
    "\n",
    "csv_f.close()\n",
    "\n",
    "# -------- Save summary.json (runtime metrics, averages; cited in text for reproducibility) --------\n",
    "summary = {\n",
    "    \"runtime_s\"    : time.time() - start,\n",
    "    \"gamma_max\"    : gamma_max,\n",
    "    \"a4_mean\"      : float(np.nanmean(np.array(a4_fits, dtype=float))),\n",
    "    \"a4_resid_mean\": float(np.nanmean(np.array(a4_resid_vals, dtype=float))),\n",
    "    \"a4_theory\"    : a4_theory,\n",
    "    \"residual_mu\"  : float(np.mean(residual_means)),\n",
    "    \"Tq_mean\"      : float(np.mean(Tq_vals)),\n",
    "    \"Q_mean\"       : float(np.mean(Q_vals)),\n",
    "    \"dev_mode\"     : DEV_MODE,\n",
    "    \"calib_highprec_samples\": CFG[\"calib_highprec_samples\"],\n",
    "}\n",
    "with open(os.path.join(CFG[\"outdir\"], \"summary.json\"), \"w\") as f:\n",
    "    json.dump({\"summary\": summary}, f, indent=2)\n",
    "\n",
    "# -------- Human-readable report (calibration convergence, model metrics) --------\n",
    "print(\"\\n=== Simulation Report ===\")\n",
    "print(f\"Mode: {'DEV' if DEV_MODE else 'PRODUCTION'}\")\n",
    "print(f\"Calibration precision : mpmath @ {mp.dps} digits\")\n",
    "print(f\"Production precision  : {xp_float.__name__} on {'CuPy GPU' if USE_CUPY else 'NumPy CPU'}\")\n",
    "\n",
    "# Convergence diagnostics\n",
    "a4_resid_arr = np.array([v for v in a4_resid_vals if not np.isnan(v)], dtype=float)\n",
    "if a4_resid_arr.size > 1:\n",
    "    mean_ratio = np.mean(a4_resid_arr) / a4_theory\n",
    "    spread_rel = np.std(a4_resid_arr) / abs(a4_theory)\n",
    "    flat_span  = (np.max(a4_resid_arr) - np.min(a4_resid_arr)) / abs(a4_theory)\n",
    "    print(\"\\n[Calibration] a4 convergence:\")\n",
    "    print(f\"  theory a4              = {a4_theory:.6e}\")\n",
    "    print(f\"  mean(a4_resid)         = {np.mean(a4_resid_arr):.6e}\")\n",
    "    print(f\"  mean/theory            = {mean_ratio:.3e}\")\n",
    "    print(f\"  relative std           = {spread_rel:.3e}\")\n",
    "    print(f\"  flatness span (max-min)= {flat_span:.3e}\")\n",
    "    # Interpretation\n",
    "    if abs(mean_ratio - 1.0) < 1e-12 and flat_span < 1e-12:\n",
    "        print(\"  ✅ Convergence OK. Flatness expected: tiny-y series → ratio ≈ 1/3 across samples.\")\n",
    "    elif spread_rel < 1e-3:\n",
    "        print(\"  ✅ Convergence stable (low scatter).\")\n",
    "    else:\n",
    "        print(\"  ⚠️ Convergence looks noisy — inspect plots and CSV.\")\n",
    "else:\n",
    "    print(\"\\n[Calibration] Insufficient samples for convergence stats.\")\n",
    "\n",
    "# Model metrics\n",
    "print(\"\\nModel summary:\")\n",
    "print(f\"  mean MDR residual   = {summary['residual_mu']:.3e}\")\n",
    "print(f\"  ⟨Tq⟩                 = {summary['Tq_mean']:.3e}\")\n",
    "print(f\"  ⟨Q⟩                  = {summary['Q_mean']:.3e}\")\n",
    "print(f\"  gamma_max           = {summary['gamma_max']:.3e}\")\n",
    "print(f\"  runtime (s)         = {summary['runtime_s']:.2f}\")\n",
    "\n",
    "print(\"\\nSaved:\")\n",
    "print(f\"  CSV   -> {csv_path}\")\n",
    "print(f\"  JSON  -> {os.path.join(CFG['outdir'], 'summary.json')}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "5fb45caf",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== figure environments ===\n",
      "\n",
      "\\begin{figure}[h]\n",
      "    \\centering\n",
      "    \\includegraphics[width=0.48\\textwidth]{a4_estimates.png}\n",
      "    \\caption{Calibration of the quartic MDR coefficient. Residual-based estimates of $\\alpha_4$ compared with the analytic theory value.}\n",
      "    \\label{fig:a4_estimates}\n",
      "\\end{figure}\n",
      "\n",
      "\n",
      "\\begin{figure}[h]\n",
      "    \\centering\n",
      "    \\includegraphics[width=0.48\\textwidth]{a4_convergence.png}\n",
      "    \\caption{Convergence of residual-based estimates of $\\alpha_4$ to the theoretical value. Fractional error per batch and rolling mean with window $w=25$.}\n",
      "    \\label{fig:a4_convergence}\n",
      "\\end{figure}\n",
      "\n",
      "\n",
      "\\begin{figure}[h]\n",
      "    \\centering\n",
      "    \\includegraphics[width=0.48\\textwidth]{tensors.png}\n",
      "    \\caption{Toy tensor averages $T_q$ and $Q$ computed across batches. Diagnostics for higher-order tensor fluctuations in the discrete framework.}\n",
      "    \\label{fig:tensors}\n",
      "\\end{figure}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# === Unified plotting cell: Figures 3, 3c, and 4 ===\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import os\n",
    "\n",
    "# Fallback so this cell can run even if Cell 2 hasn't been executed yet\n",
    "if \"CFG\" not in globals() or not isinstance(CFG, dict) or \"outdir\" not in CFG:\n",
    "    CFG = {\"outdir\": \"mdr_outputs\"}\n",
    "\n",
    "# Safety: ensure output dir exists even if Cell 2 wasn't run just before\n",
    "os.makedirs(CFG[\"outdir\"], exist_ok=True)\n",
    "\n",
    "# Convert to numpy arrays from Cell 2 results\n",
    "ts_r   = np.array(residual_means, dtype=float)\n",
    "# ts_a4a = np.array(a4_fits,        dtype=float)   # <- unused; safe to remove\n",
    "ts_a4r = np.array(a4_resid_vals,  dtype=float)\n",
    "ts_Tq  = np.array(Tq_vals,        dtype=float)\n",
    "ts_Q   = np.array(Q_vals,         dtype=float)\n",
    "\n",
    "latex_snippets = []  # store figure environments for later printing\n",
    "\n",
    "# Clip to what we actually have from calibration\n",
    "n_cal = min(CALIB_BATCHES, ts_a4r.size)\n",
    "a4r_cal = ts_a4r[:n_cal]\n",
    "finite = np.isfinite(a4r_cal)\n",
    "a4r_cal = a4r_cal[finite]\n",
    "\n",
    "# --- Figure 3: α4 calibration (residual-based) ---\n",
    "made_fig3 = a4r_cal.size > 0\n",
    "if not made_fig3:\n",
    "    print(\"[Fig 3] No finite calibration points to plot.\")\n",
    "else:\n",
    "    plt.figure(figsize=(6,4))\n",
    "    plt.axhline(y=a4_theory, color=\"red\", linestyle=\"--\", label=r\"Theory $\\alpha_4$\")\n",
    "    plt.plot(a4r_cal, \"o\", markersize=2, alpha=0.6, label=r\"Residual-based $\\alpha_4$\")\n",
    "    plt.title(\"Calibration of the quartic MDR coefficient\")\n",
    "    plt.xlabel(\"Batch\")\n",
    "    plt.ylabel(r\"$\\alpha_4$ [SI]\")\n",
    "    plt.legend()\n",
    "    plt.tight_layout()\n",
    "    f3_path = os.path.join(CFG[\"outdir\"], \"a4_estimates.png\")\n",
    "    plt.savefig(f3_path, dpi=160)\n",
    "    plt.show()\n",
    "\n",
    "    latex_snippets.append(r\"\"\"\n",
    "\\begin{figure}[h]\n",
    "    \\centering\n",
    "    \\includegraphics[width=0.48\\textwidth]{a4_estimates.png}\n",
    "    \\caption{Calibration of the quartic MDR coefficient. Residual-based estimates of $\\alpha_4$ compared with the analytic theory value.}\n",
    "    \\label{fig:a4_estimates}\n",
    "\\end{figure}\n",
    "\"\"\")\n",
    "\n",
    "# --- Figure 3c: Convergence (fractional error + rolling mean) ---\n",
    "def rolling_mean(x, w):\n",
    "    x = np.asarray(x, dtype=float)\n",
    "    if len(x) < w:\n",
    "        return x\n",
    "    c = np.cumsum(np.insert(x, 0, 0.0))\n",
    "    return (c[w:] - c[:-w]) / w\n",
    "\n",
    "win = 25\n",
    "made_fig3c = False\n",
    "if not made_fig3:\n",
    "    print(\"[Fig 3c] Skipping: no finite calibration points.\")\n",
    "else:\n",
    "    frac_err = (a4r_cal - a4_theory) / a4_theory\n",
    "    frac_err = frac_err[np.isfinite(frac_err)]\n",
    "\n",
    "    if frac_err.size == 0:\n",
    "        print(\"[Fig 3c] Skipping: fractional errors are empty after NaN filtering.\")\n",
    "    else:\n",
    "        plt.figure(figsize=(6,4))\n",
    "        plt.plot(frac_err, alpha=0.3, label=\"per-batch fractional error\")\n",
    "\n",
    "        if frac_err.size >= win:\n",
    "            frac_err_roll = rolling_mean(frac_err, win)\n",
    "            plt.plot(np.arange(win-1, len(frac_err)), frac_err_roll,\n",
    "                     label=f\"rolling mean (w={win})\")\n",
    "\n",
    "        plt.axhline(0.0, ls=\"--\", color=\"k\", lw=1)\n",
    "        plt.xlabel(\"Batch (calibration)\")\n",
    "        plt.ylabel(r\"$(a_{4,\\mathrm{resid}}-a_{4,\\mathrm{theory}})/a_{4,\\mathrm{theory}}$\")\n",
    "        plt.title(\"a4 convergence (fractional error)\")\n",
    "        plt.legend()\n",
    "        plt.tight_layout()\n",
    "        f3c_path = os.path.join(CFG[\"outdir\"], \"a4_convergence.png\")\n",
    "        plt.savefig(f3c_path, dpi=160)\n",
    "        plt.show()\n",
    "\n",
    "        latex_snippets.append(r\"\"\"\n",
    "\\begin{figure}[h]\n",
    "    \\centering\n",
    "    \\includegraphics[width=0.48\\textwidth]{a4_convergence.png}\n",
    "    \\caption{Convergence of residual-based estimates of $\\alpha_4$ to the theoretical value. Fractional error per batch and rolling mean with window $w=25$.}\n",
    "    \\label{fig:a4_convergence}\n",
    "\\end{figure}\n",
    "\"\"\")\n",
    "\n",
    "# --- Figure 4: Toy tensor averages ---\n",
    "plt.figure(figsize=(6,4))\n",
    "finite_T = np.isfinite(ts_Tq)\n",
    "finite_Q = np.isfinite(ts_Q)\n",
    "finite_idx = finite_T & finite_Q\n",
    "plt.plot(np.where(finite_idx)[0], ts_Tq[finite_idx], label=r\"$T_q$\")\n",
    "plt.plot(np.where(finite_idx)[0], ts_Q[finite_idx],  label=r\"$Q$\")\n",
    "plt.title(\"Toy tensor averages over batches\")\n",
    "plt.xlabel(\"Batch\")\n",
    "plt.ylabel(\"Magnitude (SI, scaled)\")\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "f4_path = os.path.join(CFG[\"outdir\"], \"tensors.png\")\n",
    "plt.savefig(f4_path, dpi=160)\n",
    "plt.show()\n",
    "\n",
    "latex_snippets.append(r\"\"\"\n",
    "\\begin{figure}[h]\n",
    "    \\centering\n",
    "    \\includegraphics[width=0.48\\textwidth]{tensors.png}\n",
    "    \\caption{Toy tensor averages $T_q$ and $Q$ computed across batches. Diagnostics for higher-order tensor fluctuations in the discrete framework.}\n",
    "    \\label{fig:tensors}\n",
    "\\end{figure}\n",
    "\"\"\")\n",
    "\n",
    "# --- Print all LaTeX snippets ---\n",
    "print(\"\\n=== figure environments ===\")\n",
    "for s in latex_snippets:\n",
    "    print(s)\n",
    "\n",
    "\n"
   ]
  }
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