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    "<!--\n",
    "Created: 2026-08-25 UTC\n",
    "Location: /chapters/chapter-23-assets/derivations.ipynb (DimRel site)\n",
    "Purpose: Faithful notebook version of the Chapter 23 frequency derivations, reproducing exactly the math already shown in derivations.html and the Master Frequency Table. Nothing new is asserted.\n",
    "Author: frosty | AI: Claude Opus 4.8\n",
    "TEMPORARY: NO\n",
    "-->\n",
    "\n",
    "# Chapter 23 &mdash; Frequency Derivations\n",
    "\n",
    "**Resonant Field Architectures.** This notebook reproduces the derivations shown in the\n",
    "interactive page `derivations.html` and the Master Frequency Table on the chapter page.\n",
    "It introduces no values beyond those already published on the chapter page.\n",
    "\n",
    "Compactification radii give the base frequencies\n",
    "\n",
    "$$ f_k = \\frac{c}{2\\pi R_k}. $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "c = 299_792_458  # m/s, speed of light\n",
    "phi = (1 + math.sqrt(5)) / 2  # golden ratio\n",
    "print(f\"phi = {phi:.6f}\")\n",
    "\n",
    "def f_k(R_k):\n",
    "    \"\"\"Base frequency from a compactification radius R_k (metres): f = c / (2*pi*R).\"\"\"\n",
    "    return c / (2 * math.pi * R_k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mitochondrial ATP &mdash; golden-ratio series\n",
    "\n",
    "Base frequency **1420.405 MHz**, stepped by $\\varphi^{\\,n}$ (same series exposed by the\n",
    "live slider in `derivations.html`, for $n \\in [-10, 10]$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "f_ATP = 1420.405  # MHz\n",
    "series = [(n, f_ATP * phi**n) for n in range(-10, 11)]\n",
    "for n, f in series:\n",
    "    print(f\"n = {n:+3d}   phi^n = {phi**n:10.4f}   f = {f:14.3f} MHz\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Master Frequency Table\n",
    "\n",
    "The four published systems (identical to `frequency-table.csv` and &sect;23.2 on the page)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "table = [\n",
    "    (\"Mitochondrial ATP\",     \"1420.405 MHz\",            \"x phi^n\",         \"300-500% efficiency\"),\n",
    "    (\"Microtubule Coherence\", \"8.085 THz -> 40.425 kHz\", \"x (phi^-2)^n\",    \"Anesthesia resistance\"),\n",
    "    (\"DNA Resonance\",         \"369.3 Hz\",                \"3-6-9 sequence\",  \"Epigenetic shift\"),\n",
    "    (\"Conscious State\",       \"7.83 Hz x phi^n\",         \"Schumann-Fibonacci\", \"Lucid/OBE states\"),\n",
    "]\n",
    "w = [max(len(str(row[i])) for row in table) for i in range(4)]\n",
    "for row in table:\n",
    "    print(\"  \".join(str(row[i]).ljust(w[i]) for i in range(4)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Microtubule down-conversion check\n",
    "\n",
    "The microtubule coherence line is quoted as **8.085 THz &rarr; 40.425 kHz**. That factor is\n",
    "$\\varphi^{-2}$ applied repeatedly; below we recover the published ratio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "f_micro_hi = 8.085e12   # Hz (8.085 THz)\n",
    "f_micro_lo = 40.425e3   # Hz (40.425 kHz)\n",
    "ratio = f_micro_hi / f_micro_lo\n",
    "print(f\"8.085 THz / 40.425 kHz = {ratio:,.1f}\")\n",
    "# number of phi^-2 steps that spans this ratio:\n",
    "steps = math.log(ratio) / math.log(phi**2)\n",
    "print(f\"equivalent (phi^-2) steps = {steps:.3f}\")"
   ]
  }
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