{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "gpuType": "T4"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "source": [
        "!pip -q install numpy matplotlib warp-lang torch"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6nCegUGTE8jg",
        "outputId": "f5a7ce52-8c68-4867-f906-f6a572caf491"
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m136.4/136.4 MB\u001b[0m \u001b[31m8.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OhI3LExdEd0t",
        "outputId": "28967416-10ef-4f44-e3ad-e4743cfdc491"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "==========================================================================\n",
            "  TopoDevPOC — Developing POC Pattern Enumerator\n",
            "  n = 39 candles | 38 transitions | device = cuda\n",
            "  GPU = Tesla T4\n",
            "==========================================================================\n",
            "\n",
            "[THEOREM]  Total unique developing POC patterns for n=39\n",
            "  Bullish (non-increasing) : 2^38 = 274,877,906,944\n",
            "  Bearish (non-decreasing) : 2^38 = 274,877,906,944\n",
            "  Total  (2^39)           : 549,755,813,888\n",
            "\n",
            "[MATRIX]  A = [[1,1],[1,1]] | v_0 = [1,1]^T\n",
            "  A^37 = [[68719476736, 68719476736],\n",
            "             [68719476736, 68719476736]]\n",
            "  B_39 = 1^T · A^37 · v_0 = 274,877,906,944\n",
            "  Expected 2^{n-1}           = 274,877,906,944\n",
            "  [OK] 2 × 274,877,906,944 = 549,755,813,888  ✓\n",
            "\n",
            "[SAMPLE]  100 patterns sampled on GPU (torch.randint)\n",
            "          Sampling time: 276.10 ms\n",
            "\n",
            "==========================================================================\n",
            "  OUTPUT 1 — TERNARY MATRICES  (1×38, values ∈ {-1,0,+1})\n",
            "  Format: [#] Direction | PatternID | M = [m_0 … m_37]\n",
            "==========================================================================\n",
            "  [  1] Bullish | ID=   167790361200 | M=[0,0,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,1,1,1,0,0,1,0]\n",
            "  [  2] Bearish | ID=   112296131307 | M=[-1, 0,-1, 0,-1,-1,-1, 0,-1, 0,-1,-1,-1,-1,-1, 0,-1,-1,-1,-1, 0,-1, 0,-1, 0,-1, 0, 0,-1, 0, 0, 0,-1, 0,-1,-1, 0, 0]\n",
            "  [  3] Bullish | ID=   369064015028 | M=[0,1,0,1,1,0,1,0,0,1,0,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1,1,0,1,1,1,1,0,1,0,1,0,1]\n",
            "  [  4] Bearish | ID=   397679224723 | M=[-1, 0, 0,-1, 0, 0,-1,-1,-1,-1, 0, 0,-1,-1, 0,-1,-1,-1, 0, 0, 0, 0,-1,-1,-1,-1, 0,-1, 0, 0,-1, 0, 0,-1,-1,-1, 0,-1]\n",
            "  [  5] Bullish | ID=    37927295500 | M=[0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,0]\n",
            "  [  6] Bullish | ID=   286312365648 | M=[0,0,0,1,0,1,0,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1]\n",
            "  [  7] Bearish | ID=   299333570369 | M=[ 0, 0, 0, 0, 0,-1, 0,-1,-1,-1,-1, 0, 0,-1,-1,-1,-1, 0,-1, 0,-1, 0,-1,-1, 0, 0, 0,-1,-1, 0,-1,-1, 0,-1, 0, 0, 0,-1]\n",
            "  [  8] Bearish | ID=   180886373753 | M=[ 0, 0,-1,-1,-1,-1, 0,-1, 0,-1, 0, 0, 0, 0, 0,-1,-1, 0,-1, 0,-1, 0,-1,-1, 0,-1,-1,-1, 0, 0, 0, 0,-1, 0,-1, 0,-1, 0]\n",
            "  [  9] Bullish | ID=   367632183586 | M=[1,0,0,0,1,0,0,1,0,0,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,1]\n",
            "  [ 10] Bullish | ID=   524916622536 | M=[0,0,1,0,0,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,1,1]\n",
            "  [ 11] Bullish | ID=    31775345360 | M=[0,0,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]\n",
            "  [ 12] Bullish | ID=   425035078904 | M=[0,0,1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,1]\n",
            "  [ 13] Bullish | ID=   220258295520 | M=[0,0,0,0,1,1,1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,0]\n",
            "  [ 14] Bearish | ID=   369470979075 | M=[-1, 0, 0, 0, 0, 0, 0, 0, 0,-1,-1,-1,-1, 0,-1,-1,-1,-1,-1, 0,-1, 0, 0, 0,-1,-1, 0, 0, 0, 0, 0, 0,-1,-1, 0,-1, 0,-1]\n",
            "  [ 15] Bearish | ID=   318324601329 | M=[ 0, 0, 0,-1,-1,-1,-1,-1, 0, 0, 0,-1,-1,-1,-1,-1,-1,-1,-1,-1, 0, 0,-1,-1, 0,-1,-1,-1, 0, 0, 0, 0,-1, 0,-1, 0, 0,-1]\n",
            "  [ 16] Bearish | ID=   147404907673 | M=[ 0, 0,-1,-1, 0, 0,-1, 0, 0,-1, 0, 0,-1,-1, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0,-1, 0, 0,-1, 0,-1, 0, 0,-1, 0, 0, 0,-1, 0]\n",
            "  [ 17] Bearish | ID=   371069085929 | M=[ 0, 0,-1, 0,-1,-1,-1, 0, 0, 0,-1, 0,-1,-1,-1, 0, 0, 0, 0,-1,-1,-1, 0,-1, 0,-1, 0, 0,-1,-1, 0, 0,-1,-1, 0,-1, 0,-1]\n",
            "  [ 18] Bearish | ID=     2330012161 | M=[ 0, 0, 0, 0, 0, 0, 0, 0,-1, 0,-1, 0,-1, 0, 0,-1, 0, 0, 0, 0,-1,-1,-1, 0,-1, 0,-1, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0]\n",
            "  [ 19] Bearish | ID=   419107634965 | M=[ 0,-1, 0,-1, 0, 0, 0,-1,-1,-1,-1,-1,-1,-1,-1, 0,-1, 0, 0, 0, 0,-1,-1, 0, 0,-1, 0,-1, 0, 0,-1,-1, 0, 0, 0, 0,-1,-1]\n",
            "  [ 20] Bullish | ID=   479318507150 | M=[1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,1,1]\n",
            "  [ 21] Bearish | ID=   319608669591 | M=[-1,-1, 0,-1, 0, 0,-1,-1, 0,-1, 0, 0, 0,-1, 0,-1, 0, 0,-1, 0,-1, 0, 0, 0,-1, 0,-1, 0,-1,-1, 0, 0,-1, 0,-1, 0, 0,-1]\n",
            "  [ 22] Bullish | ID=   534756389730 | M=[1,0,0,0,1,1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,1,1,1,1]\n",
            "  [ 23] Bullish | ID=   234063416010 | M=[1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0,1,1,1,1,1,1,1,0,0,1,1,0,1,1,0]\n",
            "  [ 24] Bullish | ID=   259589951898 | M=[1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,0,0,1,0,0,0,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0]\n",
            "  [ 25] Bullish | ID=    33069957648 | M=[0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0]\n",
            "  [ 26] Bullish | ID=   386376948582 | M=[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,1,1,0,1]\n",
            "  [ 27] Bearish | ID=   137526752343 | M=[-1,-1, 0,-1, 0,-1, 0, 0, 0,-1, 0,-1,-1, 0,-1,-1,-1, 0,-1,-1,-1, 0, 0,-1, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-1, 0]\n",
            "  [ 28] Bearish | ID=   466989440093 | M=[ 0,-1,-1,-1, 0,-1, 0, 0, 0,-1,-1,-1, 0,-1, 0,-1, 0,-1,-1,-1,-1, 0,-1, 0,-1, 0,-1,-1,-1, 0,-1, 0, 0,-1,-1, 0,-1,-1]\n",
            "  [ 29] Bearish | ID=    30541739875 | M=[-1, 0, 0, 0,-1,-1, 0,-1,-1,-1, 0,-1,-1,-1,-1,-1, 0,-1,-1, 0,-1,-1, 0, 0, 0,-1,-1,-1, 0, 0, 0,-1,-1,-1, 0, 0, 0, 0]\n",
            "  [ 30] Bullish | ID=   256289197764 | M=[0,1,0,0,0,1,1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,1,0,1,1,1,0,1,1,1,0]\n",
            "  [ 31] Bullish | ID=   463423679574 | M=[1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0,1,1,0,0,1,1,1,1,1,0,1,0,1,1]\n",
            "  [ 32] Bearish | ID=   269170438337 | M=[ 0, 0, 0, 0, 0,-1,-1, 0, 0, 0, 0,-1,-1,-1,-1, 0,-1,-1,-1, 0, 0,-1,-1,-1,-1, 0,-1, 0,-1, 0,-1, 0,-1,-1,-1,-1,-1, 0]\n",
            "  [ 33] Bearish | ID=   535223428555 | M=[-1, 0,-1, 0, 0,-1,-1,-1, 0,-1, 0, 0,-1,-1, 0,-1, 0,-1,-1, 0, 0,-1,-1,-1, 0,-1,-1,-1, 0, 0,-1, 0, 0,-1,-1,-1,-1,-1]\n",
            "  [ 34] Bearish | ID=   295288782235 | M=[-1, 0,-1,-1, 0, 0,-1,-1, 0,-1,-1,-1,-1, 0, 0,-1, 0,-1, 0,-1, 0, 0,-1, 0, 0, 0, 0, 0, 0,-1,-1, 0, 0,-1, 0, 0, 0,-1]\n",
            "  [ 35] Bearish | ID=   343554777039 | M=[-1,-1,-1, 0, 0,-1,-1,-1,-1,-1,-1,-1, 0,-1,-1,-1, 0,-1, 0,-1,-1,-1, 0,-1, 0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, 0, 0,-1]\n",
            "  [ 36] Bearish | ID=   547418250595 | M=[-1, 0, 0, 0,-1,-1, 0,-1, 0,-1,-1,-1, 0, 0,-1,-1,-1, 0,-1, 0,-1, 0,-1, 0, 0,-1, 0,-1,-1,-1, 0,-1,-1,-1,-1,-1,-1,-1]\n",
            "  [ 37] Bullish | ID=   177868470766 | M=[1,1,1,0,1,1,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]\n",
            "  [ 38] Bullish | ID=   294601994596 | M=[0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1]\n",
            "  [ 39] Bullish | ID=    57969416624 | M=[0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0]\n",
            "  [ 40] Bullish | ID=    27863637690 | M=[1,0,1,1,1,0,1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0]\n",
            "  [ 41] Bullish | ID=   224985691976 | M=[0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,1,0,1,1,0]\n",
            "  [ 42] Bearish | ID=   487090078369 | M=[ 0, 0, 0, 0,-1, 0,-1, 0,-1, 0, 0, 0, 0,-1,-1, 0, 0,-1, 0,-1, 0,-1,-1, 0, 0, 0,-1, 0,-1,-1, 0,-1, 0, 0, 0,-1,-1,-1]\n",
            "  [ 43] Bullish | ID=     4141515848 | M=[0,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]\n",
            "  [ 44] Bullish | ID=   197888556010 | M=[1,0,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0,0,1,1,1,0,1,0]\n",
            "  [ 45] Bearish | ID=   434117278173 | M=[ 0,-1,-1,-1, 0,-1,-1,-1, 0, 0,-1,-1,-1,-1,-1,-1,-1,-1, 0, 0,-1,-1, 0,-1,-1, 0, 0,-1, 0, 0, 0,-1, 0,-1, 0, 0,-1,-1]\n",
            "  [ 46] Bullish | ID=   538864504842 | M=[1,0,1,0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,1,1,1,1]\n",
            "  [ 47] Bullish | ID=    95860229666 | M=[1,0,0,0,1,0,0,0,1,1,0,0,0,0,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0,1,1,0,1,0,0]\n",
            "  [ 48] Bearish | ID=   175140355631 | M=[-1,-1,-1, 0,-1, 0, 0, 0,-1,-1,-1,-1,-1, 0,-1,-1, 0,-1,-1, 0,-1, 0, 0,-1,-1,-1, 0, 0, 0,-1,-1, 0, 0, 0,-1, 0,-1, 0]\n",
            "  [ 49] Bearish | ID=   229634663885 | M=[ 0,-1,-1, 0, 0,-1,-1,-1, 0,-1, 0, 0,-1,-1,-1, 0,-1, 0,-1, 0, 0,-1, 0,-1,-1,-1, 0,-1,-1,-1, 0,-1, 0,-1, 0,-1,-1, 0]\n",
            "  [ 50] Bearish | ID=   215659952263 | M=[-1,-1, 0, 0, 0, 0,-1, 0, 0, 0,-1,-1,-1, 0,-1,-1, 0,-1, 0,-1, 0,-1, 0, 0,-1,-1, 0,-1,-1, 0, 0, 0,-1, 0, 0,-1,-1, 0]\n",
            "  [ 51] Bearish | ID=    88951779299 | M=[-1, 0, 0, 0,-1,-1,-1,-1,-1,-1,-1, 0,-1,-1, 0, 0, 0, 0, 0,-1,-1,-1,-1,-1, 0,-1, 0,-1,-1, 0,-1, 0, 0,-1, 0,-1, 0, 0]\n",
            "  [ 52] Bearish | ID=    93340530549 | M=[ 0,-1, 0,-1,-1,-1, 0,-1,-1,-1, 0,-1,-1,-1, 0,-1,-1,-1, 0, 0, 0, 0,-1,-1,-1, 0,-1,-1,-1, 0,-1,-1, 0,-1, 0,-1, 0, 0]\n",
            "  [ 53] Bearish | ID=   520761088879 | M=[-1,-1,-1, 0,-1,-1, 0,-1,-1, 0,-1,-1, 0, 0,-1,-1,-1,-1, 0, 0, 0,-1,-1,-1,-1,-1,-1,-1,-1, 0, 0,-1, 0, 0,-1,-1,-1,-1]\n",
            "  [ 54] Bullish | ID=   427826220636 | M=[0,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,0,1,1]\n",
            "  [ 55] Bullish | ID=   483254597582 | M=[1,1,1,0,0,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,1,1]\n",
            "  [ 56] Bullish | ID=    99519992790 | M=[1,1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,1,1,0,1,0,0]\n",
            "  [ 57] Bullish | ID=   318036678048 | M=[0,0,0,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0,1,0,0,1]\n",
            "  [ 58] Bullish | ID=   465354264024 | M=[0,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1]\n",
            "  [ 59] Bearish | ID=   257366456073 | M=[ 0, 0,-1, 0, 0, 0, 0,-1,-1,-1, 0,-1,-1,-1, 0, 0, 0,-1,-1,-1,-1, 0, 0, 0, 0,-1,-1, 0,-1,-1,-1,-1,-1, 0,-1,-1,-1, 0]\n",
            "  [ 60] Bearish | ID=   438801001563 | M=[-1, 0,-1,-1, 0,-1, 0, 0, 0,-1,-1, 0,-1,-1,-1,-1,-1, 0, 0,-1, 0, 0,-1, 0,-1, 0,-1, 0,-1, 0, 0, 0,-1,-1, 0, 0,-1,-1]\n",
            "  [ 61] Bullish | ID=   524444180016 | M=[0,0,0,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,1,1,1]\n",
            "  [ 62] Bearish | ID=   326267911843 | M=[-1, 0, 0, 0,-1, 0,-1, 0,-1,-1,-1,-1,-1, 0, 0,-1, 0,-1, 0,-1, 0, 0, 0,-1,-1,-1, 0,-1,-1,-1,-1,-1,-1, 0,-1, 0, 0,-1]\n",
            "  [ 63] Bullish | ID=    79552418304 | M=[0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0,1,0,0]\n",
            "  [ 64] Bearish | ID=    47263338937 | M=[ 0, 0,-1,-1,-1, 0,-1,-1, 0, 0, 0,-1, 0,-1, 0,-1, 0,-1,-1,-1, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0,-1,-1, 0,-1, 0, 0, 0]\n",
            "  [ 65] Bearish | ID=   175808306983 | M=[-1,-1, 0, 0,-1, 0, 0,-1,-1,-1,-1,-1, 0,-1,-1,-1, 0,-1,-1,-1,-1,-1,-1, 0,-1,-1,-1, 0,-1,-1,-1, 0, 0, 0,-1, 0,-1, 0]\n",
            "  [ 66] Bullish | ID=   482859874250 | M=[1,0,1,0,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0,1,1,1]\n",
            "  [ 67] Bullish | ID=   437378623348 | M=[0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,1]\n",
            "  [ 68] Bearish | ID=   400478158341 | M=[ 0,-1, 0, 0, 0, 0, 0, 0,-1,-1,-1,-1,-1, 0,-1,-1,-1, 0,-1,-1, 0,-1, 0, 0,-1,-1,-1,-1,-1, 0, 0,-1, 0,-1,-1,-1, 0,-1]\n",
            "  [ 69] Bearish | ID=   401295312607 | M=[-1,-1,-1,-1, 0,-1,-1, 0,-1,-1, 0, 0, 0, 0,-1, 0, 0, 0, 0,-1, 0, 0, 0,-1,-1,-1,-1, 0,-1,-1, 0,-1, 0,-1,-1,-1, 0,-1]\n",
            "  [ 70] Bullish | ID=   418612558654 | M=[1,1,1,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,1]\n",
            "  [ 71] Bullish | ID=    85827056944 | M=[0,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,1,0,0]\n",
            "  [ 72] Bullish | ID=   128616350616 | M=[0,0,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,1,1,0,0]\n",
            "  [ 73] Bearish | ID=   314776501053 | M=[ 0,-1,-1,-1,-1, 0, 0,-1,-1, 0,-1,-1,-1, 0, 0, 0, 0,-1, 0, 0,-1, 0, 0, 0,-1, 0,-1, 0, 0,-1, 0,-1, 0, 0,-1, 0, 0,-1]\n",
            "  [ 74] Bullish | ID=   210744214082 | M=[1,0,0,0,0,1,0,0,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,1,1,0]\n",
            "  [ 75] Bearish | ID=   231440688619 | M=[-1, 0,-1, 0,-1,-1,-1,-1, 0,-1, 0, 0,-1, 0,-1, 0, 0, 0, 0,-1,-1,-1,-1, 0,-1, 0, 0, 0,-1,-1,-1,-1, 0,-1, 0,-1,-1, 0]\n",
            "  [ 76] Bearish | ID=   266647084447 | M=[-1,-1,-1,-1, 0, 0,-1,-1, 0,-1,-1,-1, 0, 0,-1,-1,-1,-1, 0, 0,-1,-1, 0,-1, 0,-1, 0,-1, 0, 0, 0, 0,-1,-1,-1,-1,-1, 0]\n",
            "  [ 77] Bullish | ID=   198293842838 | M=[1,1,0,1,0,0,1,1,1,0,1,0,1,1,1,1,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0]\n",
            "  [ 78] Bearish | ID=   357662675445 | M=[ 0,-1, 0,-1,-1,-1,-1,-1, 0, 0, 0,-1, 0,-1, 0,-1,-1, 0,-1,-1, 0,-1, 0, 0,-1,-1, 0, 0, 0,-1, 0,-1,-1, 0, 0,-1, 0,-1]\n",
            "  [ 79] Bullish | ID=   273125219496 | M=[0,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,1,1,1,1,0,1,0,0,1,1,1,1,1,1,1,0]\n",
            "  [ 80] Bullish | ID=    75425469868 | M=[0,1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]\n",
            "  [ 81] Bearish | ID=   195189967611 | M=[-1, 0,-1,-1,-1,-1,-1, 0,-1, 0,-1, 0, 0, 0,-1, 0,-1, 0,-1,-1,-1, 0, 0, 0,-1, 0, 0,-1,-1,-1, 0,-1, 0,-1,-1, 0,-1, 0]\n",
            "  [ 82] Bearish | ID=   225512663559 | M=[-1,-1, 0, 0, 0, 0, 0, 0,-1, 0,-1, 0,-1, 0, 0, 0,-1, 0,-1,-1, 0, 0,-1,-1, 0, 0, 0, 0, 0, 0,-1, 0, 0,-1, 0,-1,-1, 0]\n",
            "  [ 83] Bearish | ID=    78254493955 | M=[-1, 0, 0, 0, 0, 0, 0,-1, 0, 0, 0,-1, 0,-1,-1, 0, 0,-1, 0,-1, 0,-1, 0, 0, 0, 0,-1,-1,-1, 0, 0, 0,-1, 0, 0,-1, 0, 0]\n",
            "  [ 84] Bullish | ID=   389605294658 | M=[1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,1,0,1,1,0,1]\n",
            "  [ 85] Bearish | ID=   373561087563 | M=[-1, 0,-1, 0, 0,-1, 0, 0,-1,-1, 0,-1, 0,-1,-1,-1, 0, 0,-1,-1,-1,-1,-1,-1, 0, 0,-1,-1,-1,-1,-1, 0,-1,-1, 0,-1, 0,-1]\n",
            "  [ 86] Bullish | ID=   444857134536 | M=[0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1]\n",
            "  [ 87] Bearish | ID=   490743440237 | M=[ 0,-1,-1, 0,-1,-1, 0,-1,-1, 0, 0, 0,-1, 0,-1, 0,-1,-1, 0,-1, 0, 0,-1, 0,-1, 0, 0, 0, 0,-1, 0, 0,-1, 0, 0,-1,-1,-1]\n",
            "  [ 88] Bearish | ID=   379217567217 | M=[ 0, 0, 0,-1,-1,-1,-1,-1, 0,-1,-1,-1, 0,-1,-1, 0, 0, 0, 0, 0,-1, 0, 0,-1,-1, 0,-1, 0, 0,-1, 0, 0, 0, 0,-1,-1, 0,-1]\n",
            "  [ 89] Bullish | ID=   225620347090 | M=[1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,0]\n",
            "  [ 90] Bearish | ID=   222579730557 | M=[ 0,-1,-1,-1,-1,-1, 0, 0, 0, 0,-1, 0,-1, 0, 0,-1, 0, 0,-1, 0, 0,-1,-1, 0,-1, 0, 0,-1, 0,-1,-1,-1,-1, 0, 0,-1,-1, 0]\n",
            "  [ 91] Bearish | ID=   191729915761 | M=[ 0, 0, 0,-1,-1,-1, 0,-1,-1,-1, 0,-1, 0,-1, 0, 0,-1,-1,-1,-1,-1,-1,-1,-1,-1, 0, 0, 0,-1, 0,-1, 0, 0,-1,-1, 0,-1, 0]\n",
            "  [ 92] Bearish | ID=   119739270581 | M=[ 0,-1, 0,-1,-1, 0,-1,-1, 0,-1, 0, 0, 0,-1, 0, 0, 0,-1, 0, 0, 0, 0, 0,-1, 0, 0, 0, 0,-1,-1,-1,-1,-1, 0,-1,-1, 0, 0]\n",
            "  [ 93] Bullish | ID=   485971249076 | M=[0,1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,0,1,1,0,0,1,0,0,1,0,0,0,1,1,1]\n",
            "  [ 94] Bearish | ID=   216427290349 | M=[ 0,-1,-1, 0,-1,-1,-1, 0,-1,-1,-1,-1, 0,-1, 0, 0,-1, 0, 0,-1, 0, 0, 0, 0, 0,-1, 0, 0,-1,-1, 0, 0,-1, 0, 0,-1,-1, 0]\n",
            "  [ 95] Bearish | ID=   425495675577 | M=[ 0, 0,-1,-1,-1, 0,-1, 0,-1, 0, 0, 0, 0,-1,-1, 0, 0,-1, 0, 0, 0, 0,-1,-1, 0, 0, 0,-1, 0, 0, 0,-1,-1, 0, 0, 0,-1,-1]\n",
            "  [ 96] Bearish | ID=    63855804407 | M=[-1,-1, 0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, 0, 0, 0,-1, 0,-1,-1, 0, 0, 0, 0,-1,-1,-1,-1, 0,-1,-1, 0,-1,-1,-1, 0, 0, 0]\n",
            "  [ 97] Bearish | ID=    69480015969 | M=[ 0, 0, 0, 0,-1,-1, 0, 0, 0, 0,-1, 0,-1,-1,-1, 0, 0,-1, 0,-1, 0,-1, 0,-1, 0,-1,-1, 0,-1, 0, 0, 0, 0, 0, 0,-1, 0, 0]\n",
            "  [ 98] Bearish | ID=   256615250465 | M=[ 0, 0, 0, 0,-1, 0, 0, 0,-1, 0,-1,-1,-1,-1,-1,-1, 0,-1, 0,-1,-1,-1, 0,-1,-1,-1,-1,-1,-1, 0,-1,-1,-1, 0,-1,-1,-1, 0]\n",
            "  [ 99] Bullish | ID=   488221437982 | M=[1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,1,0,1,0,1,1,0,0,0,1,1,1]\n",
            "  [100] Bearish | ID=    89681994059 | M=[-1, 0,-1, 0, 0,-1, 0,-1, 0, 0, 0, 0,-1, 0,-1, 0,-1,-1, 0,-1,-1,-1, 0,-1, 0, 0, 0, 0,-1,-1,-1, 0, 0,-1, 0,-1, 0, 0]\n",
            "\n",
            "==========================================================================\n",
            "  OUTPUT 2 — SYMBOLIC SEQUENCES  (Σ, length 38)\n",
            "  Format: [#] Direction | PatternID | Σ = σ_0 σ_1 … σ_37\n",
            "==========================================================================\n",
            "  [  1] Bullish | ID=   167790361200 | Σ = = = = > > > = = > = > > > = > > = > = > = = = > = = = > = = = > > > = = > =\n",
            "  [  2] Bearish | ID=   112296131307 | Σ = < = < = < < < = < = < < < < < = < < < < = < = < = < = = < = = = < = < < = =\n",
            "  [  3] Bullish | ID=   369064015028 | Σ = = > = > > = > = = > = > > > > > = > > = > > > > = > > = > > > > = > = > = >\n",
            "  [  4] Bearish | ID=   397679224723 | Σ = < = = < = = < < < < = = < < = < < < = = = = < < < < = < = = < = = < < < = <\n",
            "  [  5] Bullish | ID=    37927295500 | Σ = = > > = = = = = > = > > = = > = = > = = > = > = = > = > = > > = = = > = = =\n",
            "  [  6] Bullish | ID=   286312365648 | Σ = = = = > = > = = > > > > > > > > > = > = = = > > = = > = > = > = > = = = = >\n",
            "  [  7] Bearish | ID=   299333570369 | Σ = = = = = = < = < < < < = = < < < < = < = < = < < = = = < < = < < = < = = = <\n",
            "  [  8] Bearish | ID=   180886373753 | Σ = = = < < < < = < = < = = = = = < < = < = < = < < = < < < = = = = < = < = < =\n",
            "  [  9] Bullish | ID=   367632183586 | Σ = > = = = > = = > = = = > > > > > = > = > = = > = = = > > = = > > = > = > = >\n",
            "  [ 10] Bullish | ID=   524916622536 | Σ = = = > = = > > = = > = = = = = = = = > > > > = > > > = > > = = = > = > > > >\n",
            "  [ 11] Bullish | ID=    31775345360 | Σ = = = = > = > > = > = > = = > = > = > = > > > > > = > = = > > = > > > = = = =\n",
            "  [ 12] Bullish | ID=   425035078904 | Σ = = = > > > > > = = > > > = = > = = = = > = = = = > > = > > > > = > = = = > >\n",
            "  [ 13] Bullish | ID=   220258295520 | Σ = = = = = > > > = > > > > = > > = > = > = > > = = = = > = = > = > > = = > > =\n",
            "  [ 14] Bearish | ID=   369470979075 | Σ = < = = = = = = = = < < < < = < < < < < = < = = = < < = = = = = = < < = < = <\n",
            "  [ 15] Bearish | ID=   318324601329 | Σ = = = = < < < < < = = = < < < < < < < < < = = < < = < < < = = = = < = < = = <\n",
            "  [ 16] Bearish | ID=   147404907673 | Σ = = = < < = = < = = < = = < < = = = < = = = = = = < = = < = < = = < = = = < =\n",
            "  [ 17] Bearish | ID=   371069085929 | Σ = = = < = < < < = = = < = < < < = = = = < < < = < = < = = < < = = < < = < = <\n",
            "  [ 18] Bearish | ID=     2330012161 | Σ = = = = = = = = = < = < = < = = < = = = = < < < = < = < = = = < = = = = = = =\n",
            "  [ 19] Bearish | ID=   419107634965 | Σ = = < = < = = = < < < < < < < < = < = = = = < < = = < = < = = < < = = = = < <\n",
            "  [ 20] Bullish | ID=   479318507150 | Σ = > > > = = = > = > > > > > > > > > = > > = = > > = = > > = = > > > > > = > >\n",
            "  [ 21] Bearish | ID=   319608669591 | Σ = < < = < = = < < = < = = = < = < = = < = < = = = < = < = < < = = < = < = = <\n",
            "  [ 22] Bullish | ID=   534756389730 | Σ = > = = = > > = > > = = > > > > = > > = > > > > > = = = = = = > = = > > > > >\n",
            "  [ 23] Bullish | ID=   234063416010 | Σ = > = > = = > > = > = > = = > = = = > = = = > = > > > > > > > = = > > = > > =\n",
            "  [ 24] Bullish | ID=   259589951898 | Σ = > = > > = = > > = = = > = > = = = > = = = > > = = = = > > > = = = > > > > =\n",
            "  [ 25] Bullish | ID=    33069957648 | Σ = = = = > = = = = > = = = = = > > > > > > = = = > > = = > > = > > > > = = = =\n",
            "  [ 26] Bullish | ID=   386376948582 | Σ = > > = = > > = > > = > > = > = = = > > > = > > > = > = > > > > > = = > > = >\n",
            "  [ 27] Bearish | ID=   137526752343 | Σ = < < = < = < = = = < = < < = < < < = < < < = = < = < = = = = = = = = = = < =\n",
            "  [ 28] Bearish | ID=   466989440093 | Σ = = < < < = < = = = < < < = < = < = < < < < = < = < = < < < = < = = < < = < <\n",
            "  [ 29] Bearish | ID=    30541739875 | Σ = < = = = < < = < < < = < < < < < = < < = < < = = = < < < = = = < < < = = = =\n",
            "  [ 30] Bullish | ID=   256289197764 | Σ = = > = = = > > = > > > = = > > = > > = = = = = = = > > = > = > > > = > > > =\n",
            "  [ 31] Bullish | ID=   463423679574 | Σ = > > = > = > = = = > > = > = = = = > = > > = = = > > = = > > > > > = > = > >\n",
            "  [ 32] Bearish | ID=   269170438337 | Σ = = = = = = < < = = = = < < < < = < < < = = < < < < = < = < = < = < < < < < =\n",
            "  [ 33] Bearish | ID=   535223428555 | Σ = < = < = = < < < = < = = < < = < = < < = = < < < = < < < = = < = = < < < < <\n",
            "  [ 34] Bearish | ID=   295288782235 | Σ = < = < < = = < < = < < < < = = < = < = < = = < = = = = = = < < = = < = = = <\n",
            "  [ 35] Bearish | ID=   343554777039 | Σ = < < < = = < < < < < < < = < < < = < = < < < = < = < < < < < < < < < < = = <\n",
            "  [ 36] Bearish | ID=   547418250595 | Σ = < = = = < < = < = < < < = = < < < = < = < = < = = < = < < < = < < < < < < <\n",
            "  [ 37] Bullish | ID=   177868470766 | Σ = > > > = > > > > = = > > > > = > = = > = = > > > = = > = > > = > = = > = > =\n",
            "  [ 38] Bullish | ID=   294601994596 | Σ = = > = = > > = > = = = > > = > > = > = = > = > > > > = > = = > = = > = = = >\n",
            "  [ 39] Bullish | ID=    57969416624 | Σ = = = = > > = > > = = > > = = = > > > > > > = = > > > > > > > = > = > > = = =\n",
            "  [ 40] Bullish | ID=    27863637690 | Σ = > = > > > = > = > > > > = > = > = > > = = > > = = > > > > > = = > > = = = =\n",
            "  [ 41] Bullish | ID=   224985691976 | Σ = = = > = = > = > > > = > > = = > = = = > > = = = > = = = > > = = = > = > > =\n",
            "  [ 42] Bearish | ID=   487090078369 | Σ = = = = = < = < = < = = = = < < = = < = < = < < = = = < = < < = < = = = < < <\n",
            "  [ 43] Bullish | ID=     4141515848 | Σ = = = > = = > = = = > = = = = > = > = > > = > > = > > = > > > > = = = = = = =\n",
            "  [ 44] Bullish | ID=   197888556010 | Σ = > = > = > > > > > = > > > = > > > = = > = = = > > = = > = = = = > > > = > =\n",
            "  [ 45] Bearish | ID=   434117278173 | Σ = = < < < = < < < = = < < < < < < < < = = < < = < < = = < = = = < = < = = < <\n",
            "  [ 46] Bullish | ID=   538864504842 | Σ = > = > = = = = = = = = > = > > > > = = > = > > = > > = > > > = > = > > > > >\n",
            "  [ 47] Bullish | ID=    95860229666 | Σ = > = = = > = = = > > = = = = = > > > = > > = > > = = = > = > = = > > = > = =\n",
            "  [ 48] Bearish | ID=   175140355631 | Σ = < < < = < = = = < < < < < = < < = < < = < = = < < < = = = < < = = = < = < =\n",
            "  [ 49] Bearish | ID=   229634663885 | Σ = = < < = = < < < = < = = < < < = < = < = = < = < < < = < < < = < = < = < < =\n",
            "  [ 50] Bearish | ID=   215659952263 | Σ = < < = = = = < = = = < < < = < < = < = < = < = = < < = < < = = = < = = < < =\n",
            "  [ 51] Bearish | ID=    88951779299 | Σ = < = = = < < < < < < < = < < = = = = = < < < < < = < = < < = < = = < = < = =\n",
            "  [ 52] Bearish | ID=    93340530549 | Σ = = < = < < < = < < < = < < < = < < < = = = = < < < = < < < = < < = < = < = =\n",
            "  [ 53] Bearish | ID=   520761088879 | Σ = < < < = < < = < < = < < = = < < < < = = = < < < < < < < < = = < = = < < < <\n",
            "  [ 54] Bullish | ID=   427826220636 | Σ = = > > > = > = = > > > = = = = = > > > = > > = = = > > > = = > > > = = = > >\n",
            "  [ 55] Bullish | ID=   483254597582 | Σ = > > > = = > > > > > = > > > > > > > = > > = = = = > = = = = > = = = = > > >\n",
            "  [ 56] Bullish | ID=    99519992790 | Σ = > > = > = > > > > = = > = = > = > = > > = > > > > = > = > = = > > > = > = =\n",
            "  [ 57] Bullish | ID=   318036678048 | Σ = = = = = > = > > = > = > = = > = > > = > > > = = = > > = = = = = > = > = = >\n",
            "  [ 58] Bullish | ID=   465354264024 | Σ = = = > > = > > > = > > = = = > = > > = = = > = > = = > > = > = = = > > = > >\n",
            "  [ 59] Bearish | ID=   257366456073 | Σ = = = < = = = = < < < = < < < = = = < < < < = = = = < < = < < < < < = < < < =\n",
            "  [ 60] Bearish | ID=   438801001563 | Σ = < = < < = < = = = < < = < < < < < = = < = = < = < = < = < = = = < < = = < <\n",
            "  [ 61] Bullish | ID=   524444180016 | Σ = = = = > > = = = > > > > = = = > > > > = = > = > > = > > = = = = > = > > > >\n",
            "  [ 62] Bearish | ID=   326267911843 | Σ = < = = = < = < = < < < < < = = < = < = < = = = < < < = < < < < < < = < = = <\n",
            "  [ 63] Bullish | ID=    79552418304 | Σ = = = = = = = = = > = = > = = > > = = = > > = > > = > = = = = > = > = = > = =\n",
            "  [ 64] Bearish | ID=    47263338937 | Σ = = = < < < = < < = = = < = < = < = < < < = = = < = = = = = = = < < = < = = =\n",
            "  [ 65] Bearish | ID=   175808306983 | Σ = < < = = < = = < < < < < = < < < = < < < < < < = < < < = < < < = = = < = < =\n",
            "  [ 66] Bullish | ID=   482859874250 | Σ = > = > = = > > > > > = > > > > = = = = > > = > = = > > = > > = = = = = > > >\n",
            "  [ 67] Bullish | ID=   437378623348 | Σ = = > = > > > = > > > = = > = = = = > > = = > > > = > = > = > > > = > = = > >\n",
            "  [ 68] Bearish | ID=   400478158341 | Σ = = < = = = = = = < < < < < = < < < = < < = < = = < < < < < = = < = < < < = <\n",
            "  [ 69] Bearish | ID=   401295312607 | Σ = < < < < = < < = < < = = = = < = = = = < = = = < < < < = < < = < = < < < = <\n",
            "  [ 70] Bullish | ID=   418612558654 | Σ = > > > > > = = > > = > > > = > = = = = = = > = > > > = > > > = > = = = = > >\n",
            "  [ 71] Bullish | ID=    85827056944 | Σ = = = = > > = = > = > = > > > > = = = = > > = > > > = > > > > > > > = = > = =\n",
            "  [ 72] Bullish | ID=   128616350616 | Σ = = = > > = = > > > = = = = > > > = = = = > = = = > = = > > > > > = > > > = =\n",
            "  [ 73] Bearish | ID=   314776501053 | Σ = = < < < < = = < < = < < < = = = = < = = < = = = < = < = = < = < = = < = = <\n",
            "  [ 74] Bullish | ID=   210744214082 | Σ = > = = = = > = = > = = = = = > > = > = > = > = > = = = > = = = > = = = > > =\n",
            "  [ 75] Bearish | ID=   231440688619 | Σ = < = < = < < < < = < = = < = < = = = = < < < < = < = = = < < < < = < = < < =\n",
            "  [ 76] Bearish | ID=   266647084447 | Σ = < < < < = = < < = < < < = = < < < < = = < < = < = < = < = = = = < < < < < =\n",
            "  [ 77] Bullish | ID=   198293842838 | Σ = > > = > = = > > > = > = > > > > > = > > > = = > > = > = > = = = > > > = > =\n",
            "  [ 78] Bearish | ID=   357662675445 | Σ = = < = < < < < < = = = < = < = < < = < < = < = = < < = = = < = < < = = < = <\n",
            "  [ 79] Bullish | ID=   273125219496 | Σ = = = > = > = > = = > > > = = = = = = > = = = > > > > = > = = > > > > > > > =\n",
            "  [ 80] Bullish | ID=    75425469868 | Σ = = > > = > = > > = > = > = > = > = > = > > = > > > > > = = = > > = = = > = =\n",
            "  [ 81] Bearish | ID=   195189967611 | Σ = < = < < < < < = < = < = = = < = < = < < < = = = < = = < < < = < = < < = < =\n",
            "  [ 82] Bearish | ID=   225512663559 | Σ = < < = = = = = = < = < = < = = = < = < < = = < < = = = = = = < = = < = < < =\n",
            "  [ 83] Bearish | ID=    78254493955 | Σ = < = = = = = = < = = = < = < < = = < = < = < = = = = < < < = = = < = = < = =\n",
            "  [ 84] Bullish | ID=   389605294658 | Σ = > = = = = > = = > = = = = = = > = = > = = > = = > > = > > = > = > = > > = >\n",
            "  [ 85] Bearish | ID=   373561087563 | Σ = < = < = = < = = < < = < = < < < = = < < < < < < = = < < < < < = < < = < = <\n",
            "  [ 86] Bullish | ID=   444857134536 | Σ = = = > = = > > > = > > = > = = > = > > = = = > > > = = > = = > > > > = = > >\n",
            "  [ 87] Bearish | ID=   490743440237 | Σ = = < < = < < = < < = = = < = < = < < = < = = < = < = = = = < = = < = = < < <\n",
            "  [ 88] Bearish | ID=   379217567217 | Σ = = = = < < < < < = < < < = < < = = = = = < = = < < = < = = < = = = = < < = <\n",
            "  [ 89] Bullish | ID=   225620347090 | Σ = > = = > = > > = = = > = = > = > = > = = = = = = = = > = = = > = = > = > > =\n",
            "  [ 90] Bearish | ID=   222579730557 | Σ = = < < < < < = = = = < = < = = < = = < = = < < = < = = < = < < < < = = < < =\n",
            "  [ 91] Bearish | ID=   191729915761 | Σ = = = = < < < = < < < = < = < = = < < < < < < < < < = = = < = < = = < < = < =\n",
            "  [ 92] Bearish | ID=   119739270581 | Σ = = < = < < = < < = < = = = < = = = < = = = = = < = = = = < < < < < = < < = =\n",
            "  [ 93] Bullish | ID=   485971249076 | Σ = = > = > > = > > > > = = = > > = = > = = > = = = > > = = > = = > = = = > > >\n",
            "  [ 94] Bearish | ID=   216427290349 | Σ = = < < = < < < = < < < < = < = = < = = < = = = = = < = = < < = = < = = < < =\n",
            "  [ 95] Bearish | ID=   425495675577 | Σ = = = < < < = < = < = = = = < < = = < = = = = < < = = = < = = = < < = = = < <\n",
            "  [ 96] Bearish | ID=    63855804407 | Σ = < < = < < < < < < < < < < = = = < = < < = = = = < < < < = < < = < < < = = =\n",
            "  [ 97] Bearish | ID=    69480015969 | Σ = = = = = < < = = = = < = < < < = = < = < = < = < = < < = < = = = = = = < = =\n",
            "  [ 98] Bearish | ID=   256615250465 | Σ = = = = = < = = = < = < < < < < < = < = < < < = < < < < < < = < < < = < < < =\n",
            "  [ 99] Bullish | ID=   488221437982 | Σ = > > > > = = = = = = = > > > > > > = = = = > = = = > > = > = > > = = = > > >\n",
            "  [100] Bearish | ID=    89681994059 | Σ = < = < = = < = < = = = = < = < = < < = < < < = < = = = = < < < = = < = < = =\n",
            "\n",
            "==========================================================================\n",
            "  OUTPUT 3 — DEVELOPING POC CHARTS  (100 patterns)\n",
            "==========================================================================\n",
            "  [SAVED] TopoDevPOC_n39_100samples.png\n",
            "\n",
            "  ASCII CLI Charts — first 10 samples (right side = C_0 = newest)\n",
            "\n",
            "  [ 1] Bullish | ID=167790361200 | strict_moves=17/38\n",
            "       POC range: oldest=50  →  newest=67\n",
            "       ┌───────────────────────────────────────┐\n",
            "       │                                  ●····│\n",
            "       │                            ·●··●●     │\n",
            "       │                        ·●●●           │\n",
            "       │                     ·●●               │\n",
            "       │           ···●···●·●                  │\n",
            "       │     ●●···●                            │\n",
            "       │·●··●                                  │\n",
            "       └───────────────────────────────────────┘\n",
            "       Σ (first 12): = = = > > > = = > = > > …\n",
            "\n",
            "  [ 2] Bearish | ID=112296131307 | strict_moves=22/38\n",
            "       POC range: oldest=50  →  newest=28\n",
            "       ┌───────────────────────────────────────┐\n",
            "       │··●●                                   │\n",
            "       │    ·●···●··●·●                        │\n",
            "       │               ·●·●●●                  │\n",
            "       │                     ●·●●              │\n",
            "       │                         ●●●·●         │\n",
            "       │                              ·●●●·●   │\n",
            "       │                                    ·●·│\n",
            "       └───────────────────────────────────────┘\n",
            "       Σ (first 12): < = < = < < < = < = < < …\n",
            "\n",
            "  [ 3] Bullish | ID=369064015028 | strict_moves=25/38\n",
            "       POC range: oldest=50  →  newest=75\n",
            "       ┌───────────────────────────────────────┐\n",
            "       │                                  ●·●··│\n",
            "       │                          ●·●··●·●     │\n",
            "       │                     ·●●●●             │\n",
            "       │                ●●·●●                  │\n",
            "       │          ·●●·●●                       │\n",
            "       │     ·●●●●                             │\n",
            "       │●·●·●                                  │\n",
            "       └───────────────────────────────────────┘\n",
            "       Σ (first 12): = > = > > = > = = > = > …\n",
            "\n",
            "  [ 4] Bearish | ID=397679224723 | strict_moves=21/38\n",
            "       POC range: oldest=50  →  newest=29\n",
            "       ┌───────────────────────────────────────┐\n",
            "       │●·●                                    │\n",
            "       │   ●●··●··●                            │\n",
            "       │           ·●●●                        │\n",
            "       │               ●····●●●                │\n",
            "       │                       ·●●··●          │\n",
            "       │                             ●●●··●    │\n",
            "       │                                   ··●·│\n",
            "       └───────────────────────────────────────┘\n",
            "       Σ (first 12): < = = < = = < < < < = = …\n",
            "\n",
            "  [ 5] Bullish | ID=37927295500 | strict_moves=14/38\n",
            "       POC range: oldest=50  →  newest=64\n",
            "       ┌───────────────────────────────────────┐\n",
            "       │                                    ●··│\n",
            "       │                            ·●·····●   │\n",
            "       │                        ··●●           │\n",
            "       │                ·●··●··●               │\n",
            "       │           ·●··●                       │\n",
            "       │        ●·●                            │\n",
            "       │···●···●                               │\n",
            "       └───────────────────────────────────────┘\n",
            "       Σ (first 12): = > > = = = = = > = > > …\n",
            "\n",
            "  [ 6] Bullish | ID=286312365648 | strict_moves=19/38\n",
            "       POC range: oldest=50  →  newest=69\n",
            "       ┌───────────────────────────────────────┐\n",
            "       │                                 ·●····│\n",
            "       │                            ●●··●      │\n",
            "       │                         ●●●           │\n",
            "       │                    ·●●●●              │\n",
            "       │            ··●●···●                   │\n",
            "       │      ·●·●·●                           │\n",
            "       │●····●                                 │\n",
            "       └───────────────────────────────────────┘\n",
            "       Σ (first 12): = = = > = > = = > > > > …\n",
            "\n",
            "  [ 7] Bearish | ID=299333570369 | strict_moves=19/38\n",
            "       POC range: oldest=50  →  newest=31\n",
            "       ┌───────────────────────────────────────┐\n",
            "       │●···●                                  │\n",
            "       │     ·●●·●                             │\n",
            "       │          ●···●●                       │\n",
            "       │                ·●·●·●●                │\n",
            "       │                       ●●··●           │\n",
            "       │                            ●●●        │\n",
            "       │                               ·●······│\n",
            "       └───────────────────────────────────────┘\n",
            "       Σ (first 12): = = = = = < = < < < < = …\n",
            "\n",
            "  [ 8] Bearish | ID=180886373753 | strict_moves=18/38\n",
            "       POC range: oldest=50  →  newest=32\n",
            "       ┌───────────────────────────────────────┐\n",
            "       │·●·●                                   │\n",
            "       │    ·●····●●                           │\n",
            "       │            ●·●●                       │\n",
            "       │                ·●·●·●                 │\n",
            "       │                      ●·····●·●        │\n",
            "       │                               ·●●●    │\n",
            "       │                                   ●···│\n",
            "       └───────────────────────────────────────┘\n",
            "       Σ (first 12): = = < < < < = < = < = = …\n",
            "\n",
            "  [ 9] Bullish | ID=367632183586 | strict_moves=18/38\n",
            "       POC range: oldest=50  →  newest=68\n",
            "       ┌───────────────────────────────────────┐\n",
            "       │                                  ···●·│\n",
            "       │                          ●···●··●     │\n",
            "       │                       ●●●             │\n",
            "       │                ··●·●·●                │\n",
            "       │        ··●●···●                       │\n",
            "       │   ·●·●●                               │\n",
            "       │●·●                                    │\n",
            "       └───────────────────────────────────────┘\n",
            "       Σ (first 12): > = = = > = = > = = = > …\n",
            "\n",
            "  [10] Bullish | ID=524916622536 | strict_moves=18/38\n",
            "       POC range: oldest=50  →  newest=68\n",
            "       ┌───────────────────────────────────────┐\n",
            "       │                                 ··●···│\n",
            "       │                    ········●··●●      │\n",
            "       │                 ●●●                   │\n",
            "       │             ●●·●                      │\n",
            "       │      ···●●·●                          │\n",
            "       │  ●●·●                                 │\n",
            "       │●●                                     │\n",
            "       └───────────────────────────────────────┘\n",
            "       Σ (first 12): = = > = = > > = = > = = …\n",
            "\n",
            "==========================================================================\n",
            "  SUMMARY\n",
            "==========================================================================\n",
            "  n (candles)                = 39\n",
            "  Transitions per pattern    = 38\n",
            "  Total patterns  [2^39]    = 549,755,813,888\n",
            "  Bullish         [2^38]  = 274,877,906,944\n",
            "  Bearish         [2^38]  = 274,877,906,944\n",
            "  Matrix B_n validated       = 274,877,906,944  ✓\n",
            "  Samples generated          = 100\n",
            "  Chart file                 = TopoDevPOC_n39_100samples.png\n",
            "  Compute device             = cuda\n",
            "  Wall-clock (sample+decode) = 13032.35 ms\n",
            "==========================================================================\n",
            "\n",
            "  CONVERSION FORMULAS  (tex Sec. V)\n",
            "  Symbolic → Ternary:\n",
            "    Bullish: '>' → +1,  '=' →  0\n",
            "    Bearish: '<' → -1,  '=' →  0\n",
            "  Ternary → Symbolic:\n",
            "    +1 → '>',  0 → '=',  -1 → '<'\n",
            "\n",
            "  TEMPORAL CONVENTION:\n",
            "    Chart x-axis: left = C_{-38} (oldest) → right = C_0 (newest)\n",
            "    Bullish pattern: POC non-increasing toward right (higher on left)\n",
            "    Bearish pattern: POC non-decreasing toward right (lower on left)\n",
            "==========================================================================\n"
          ]
        }
      ],
      "source": [
        "#!/usr/bin/env python3\n",
        "\"\"\"\n",
        "TopoDevPOC_n39.py\n",
        "Topologically Unique Developing Point of Control Patterns\n",
        "Pre-market K-Lines, n = 39 three-minute candlesticks\n",
        "\n",
        "Paper : TopoDevPOC.tex  (ConQ Research Team, Continual Quasars)\n",
        "Compute: Vectorized NumPy + GPU Torch (T4) + Warp branchless ops\n",
        "         Architectural patterns from core_engine_v11.py (Hyper-Warp Edition)\n",
        "\n",
        "Outputs (CLI):\n",
        "  1. Total combination count for n=39\n",
        "  2. Matrix state-transition validation\n",
        "  3. 100 random ternary matrices  (1×38 each)\n",
        "  4. 100 random symbolic sequences (length-38 strings)\n",
        "  5. 100 developing_poc charts saved as PNG + ASCII CLI preview\n",
        "\n",
        "Run on Google Colab T4:\n",
        "    !python TopoDevPOC_n39.py\n",
        "\"\"\"\n",
        "\n",
        "# ── stdlib ────────────────────────────────────────────────────────────────────\n",
        "import os, sys, time, math\n",
        "import numpy as np\n",
        "\n",
        "# ── matplotlib (non-interactive for Colab CLI) ────────────────────────────────\n",
        "import matplotlib\n",
        "matplotlib.use('Agg')\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.ticker as mticker\n",
        "\n",
        "# ── GPU setup (T4 Colab) ─────────────────────────────────────────────────────\n",
        "try:\n",
        "    import torch\n",
        "    HAS_CUDA = torch.cuda.is_available()\n",
        "    DEVICE   = 'cuda' if HAS_CUDA else 'cpu'\n",
        "except ImportError:\n",
        "    HAS_CUDA = False\n",
        "    DEVICE   = 'cpu'\n",
        "    torch    = None\n",
        "\n",
        "# Optional Warp (core_engine_v11.py pattern) ─────────────────────────────────\n",
        "HAS_WARP = False\n",
        "try:\n",
        "    import warp as wp\n",
        "    wp.init()\n",
        "    wp.set_module_options({\"enable_backward\": False, \"fast_math\": True, \"max_unroll\": 8})\n",
        "    HAS_WARP = bool(wp.get_cuda_devices())\n",
        "except Exception:\n",
        "    pass\n",
        "\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "# CONSTANTS  (tex Section II)\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "N         = 39          # pre-market 3-min candles  (C_0 … C_{-(n-1)})\n",
        "N_TRANS   = N - 1       # 38 adjacent-pair relations\n",
        "N_SAMPLES = 100\n",
        "SEED      = int(time.time() * 1000) & 0x7FFFFFFF\n",
        "\n",
        "SEP = \"=\" * 74\n",
        "\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "# 0. HEADER\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "print(SEP)\n",
        "print(\"  TopoDevPOC — Developing POC Pattern Enumerator\")\n",
        "print(f\"  n = {N} candles | {N_TRANS} transitions | device = {DEVICE}\")\n",
        "if HAS_CUDA and torch:\n",
        "    print(f\"  GPU = {torch.cuda.get_device_name(0)}\")\n",
        "if HAS_WARP:\n",
        "    print(f\"  Warp = enabled (branchless kernel path)\")\n",
        "print(SEP)\n",
        "\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "# SECTION 1 — COMBINATORIAL ENUMERATION  (tex Theorem, Sec. III)\n",
        "#\n",
        "#   Bullish:  each of (n-1) transitions ∈ {>, =}  → 2^(n-1) patterns\n",
        "#   Bearish:  each of (n-1) transitions ∈ {<, =}  → 2^(n-1) patterns\n",
        "#   Total   : 2^(n-1) + 2^(n-1) = 2^n  (disjoint families)\n",
        "#   n=39    : 2^39 = 549,755,813,888\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "TOTAL = 1 << N          # exact Python int (arbitrary precision)\n",
        "HALF  = 1 << (N - 1)\n",
        "\n",
        "print(f\"\\n[THEOREM]  Total unique developing POC patterns for n={N}\")\n",
        "print(f\"  Bullish (non-increasing) : 2^{N-1} = {HALF:,}\")\n",
        "print(f\"  Bearish (non-decreasing) : 2^{N-1} = {HALF:,}\")\n",
        "print(f\"  Total  (2^{N})           : {TOTAL:,}\")\n",
        "\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "# SECTION 2 — MATRIX STATE-TRANSITION VALIDATION  (tex Sec. IV)\n",
        "#\n",
        "#   States  : S_0 (equality), S_± (strict move)\n",
        "#   A = [[1,1],[1,1]]   (fully-connected 2-state digraph)\n",
        "#   v_0 = [1,1]^T       (both states reachable initially)\n",
        "#\n",
        "#   B_n = 1^T · A^(n-2) · v_0\n",
        "#       = 2^(n-3) · 1^T · A · 1     (using A^k = 2^(k-1)·A for k≥1)\n",
        "#       = 2^(n-3) · 4  =  2^(n-1)   per direction\n",
        "#\n",
        "#   Implementation: exact Python-int matrix exponentiation (no float rounding)\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "\n",
        "def _mm2(A, B):\n",
        "    \"\"\"Exact 2×2 matrix multiply with Python arbitrary-precision ints.\"\"\"\n",
        "    return [\n",
        "        [A[0][0]*B[0][0] + A[0][1]*B[1][0],  A[0][0]*B[0][1] + A[0][1]*B[1][1]],\n",
        "        [A[1][0]*B[0][0] + A[1][1]*B[1][0],  A[1][0]*B[0][1] + A[1][1]*B[1][1]],\n",
        "    ]\n",
        "\n",
        "def _mpow2(M, k):\n",
        "    \"\"\"Fast 2×2 matrix power, exact ints, O(log k).\"\"\"\n",
        "    if k == 0: return [[1,0],[0,1]]\n",
        "    if k == 1: return M\n",
        "    h = _mpow2(M, k >> 1)\n",
        "    s = _mm2(h, h)\n",
        "    return s if (k & 1) == 0 else _mm2(s, M)\n",
        "\n",
        "A_mat  = [[1,1],[1,1]]\n",
        "v0     = [1, 1]\n",
        "A_pow  = _mpow2(A_mat, N - 2)\n",
        "# 1^T · A^(n-2) · v0\n",
        "Av0_0  = A_pow[0][0]*v0[0] + A_pow[0][1]*v0[1]\n",
        "Av0_1  = A_pow[1][0]*v0[0] + A_pow[1][1]*v0[1]\n",
        "B_n    = Av0_0 + Av0_1          # = 1^T · (A^(n-2)·v0)\n",
        "\n",
        "print(f\"\\n[MATRIX]  A = [[1,1],[1,1]] | v_0 = [1,1]^T\")\n",
        "print(f\"  A^{N-2} = [[{A_pow[0][0]}, {A_pow[0][1]}],\")\n",
        "print(f\"             [{A_pow[1][0]}, {A_pow[1][1]}]]\")\n",
        "print(f\"  B_{N} = 1^T · A^{N-2} · v_0 = {B_n:,}\")\n",
        "print(f\"  Expected 2^{{n-1}}           = {HALF:,}\")\n",
        "assert B_n == HALF,          f\"Matrix B_n mismatch: {B_n} ≠ {HALF}\"\n",
        "assert 2 * B_n == TOTAL,     f\"Total mismatch: {2*B_n} ≠ {TOTAL}\"\n",
        "print(f\"  [OK] 2 × {B_n:,} = {TOTAL:,}  ✓\")\n",
        "\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "# SECTION 3 — PATTERN ENCODING SCHEME\n",
        "#\n",
        "#   Each of the 2^39 patterns maps bijectively to a 39-bit integer:\n",
        "#     bit  0          : direction   (0 = Bullish, 1 = Bearish)\n",
        "#     bits 1 … N-1   : transitions  (1 = strict move, 0 = equality)\n",
        "#\n",
        "#   pattern_id ∈ [0, 2^39)   uniquely identifies every valid pattern.\n",
        "#\n",
        "#   Ternary matrix m ∈ {+1,0}^(n-1) for bullish,\n",
        "#                  m ∈ {-1,0}^(n-1) for bearish.\n",
        "#   Bijection: m_k = sign(direction) × trans_bit_k\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "# SECTION 4 — GPU-ACCELERATED RANDOM SAMPLING\n",
        "#   Generate (N_SAMPLES × N) binary matrix at once on T4 GPU.\n",
        "#   Inspired by core_engine_v11.py XOR-shift PRNG kernel design.\n",
        "#   bits[:,0]  = direction flags\n",
        "#   bits[:,1:] = N_TRANS transition flags per pattern\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "\n",
        "t_sample = time.perf_counter()\n",
        "\n",
        "if HAS_WARP:\n",
        "    # ── Warp branchless path (core_engine_v11.py style) ─────────────────────\n",
        "    # Launch one thread per sample; XOR-shift fills N bits per thread.\n",
        "    _seed_wp = SEED\n",
        "\n",
        "    @wp.kernel\n",
        "    def k_rng_bits(seed: int, N_cols: int,\n",
        "                   out: wp.array(dtype=wp.int8)):\n",
        "        tid = wp.tid()\n",
        "        rng = wp.uint32(seed) ^ wp.uint32(tid)\n",
        "        if rng == wp.uint32(0):\n",
        "            rng = wp.uint32(123456789)\n",
        "        base = tid * N_cols\n",
        "        for col in range(N_cols):\n",
        "            rng = rng ^ (rng << wp.uint32(13))\n",
        "            rng = rng ^ (rng >> wp.uint32(17))\n",
        "            rng = rng ^ (rng << wp.uint32(5))\n",
        "            out[base + col] = wp.int8(int(rng) & 1)\n",
        "\n",
        "    out_wp  = wp.zeros(N_SAMPLES * N, dtype=wp.int8, device='cuda')\n",
        "    wp.launch(k_rng_bits, dim=N_SAMPLES, block_dim=128,\n",
        "              inputs=[_seed_wp, N, out_wp], device='cuda')\n",
        "    wp.synchronize()\n",
        "    bits_np = out_wp.numpy().reshape(N_SAMPLES, N)\n",
        "    print(f\"\\n[SAMPLE]  {N_SAMPLES} patterns sampled via Warp XOR-shift kernel\")\n",
        "\n",
        "elif HAS_CUDA and torch is not None:\n",
        "    # ── Torch GPU path ───────────────────────────────────────────────────────\n",
        "    gen = torch.Generator(device='cuda')\n",
        "    gen.manual_seed(SEED)\n",
        "    bits_t  = torch.randint(0, 2, (N_SAMPLES, N), device='cuda',\n",
        "                            generator=gen, dtype=torch.int8)\n",
        "    bits_np = bits_t.cpu().numpy()\n",
        "    print(f\"\\n[SAMPLE]  {N_SAMPLES} patterns sampled on GPU (torch.randint)\")\n",
        "\n",
        "else:\n",
        "    # ── CPU NumPy fallback ────────────────────────────────────────────────────\n",
        "    rng_cpu = np.random.default_rng(SEED)\n",
        "    bits_np = rng_cpu.integers(0, 2, size=(N_SAMPLES, N), dtype=np.int8)\n",
        "    print(f\"\\n[SAMPLE]  {N_SAMPLES} patterns sampled on CPU (NumPy)\")\n",
        "\n",
        "sample_ms = (time.perf_counter() - t_sample) * 1e3\n",
        "print(f\"          Sampling time: {sample_ms:.2f} ms\")\n",
        "\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "# SECTION 5 — VECTORISED DECODING  (NumPy, no Python loops over patterns)\n",
        "#\n",
        "#   bits[:,0]   → direction array  (0=Bullish, 1=Bearish), shape (100,)\n",
        "#   bits[:,1:]  → trans array,     shape (100, 38)\n",
        "#   ternary_mat: +trans if Bullish, -trans if Bearish  → shape (100, 38)\n",
        "#   sign: Bullish→+1, Bearish→-1, broadcast multiply\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "\n",
        "dir_bits  = bits_np[:, 0].astype(np.int8)      # 0 or 1\n",
        "trans     = bits_np[:, 1:].astype(np.int8)      # (100,38), values 0 or 1\n",
        "signs     = 1 - 2 * dir_bits                    # 0→+1 (bull), 1→-1 (bear)\n",
        "ternary   = (signs[:, None] * trans).astype(np.int8)  # (100,38): +1/0/-1\n",
        "\n",
        "# Compact 39-bit pattern IDs\n",
        "pows64    = (np.uint64(1) << np.arange(N, dtype=np.uint64))\n",
        "pat_ids   = (bits_np.astype(np.uint64) * pows64[None, :]).sum(axis=1)\n",
        "\n",
        "# Symbolic sequences: vectorised char lookup\n",
        "#   Bullish (sign=+1): trans=1 → '>', trans=0 → '='\n",
        "#   Bearish (sign=-1): trans=1 → '<', trans=0 → '='\n",
        "SYM_BULL = np.array(['=', '>'], dtype='<U1')   # index by trans bit\n",
        "SYM_BEAR = np.array(['=', '<'], dtype='<U1')\n",
        "sym_matrix = np.where(dir_bits[:, None] == 0,\n",
        "                      SYM_BULL[trans],\n",
        "                      SYM_BEAR[trans])          # (100, 38)\n",
        "\n",
        "# POC price sequence (right-to-left: p[0]=C_0=newest, p[N-1]=C_{-(N-1)}=oldest)\n",
        "#   p_raw[i, k] = POC of candle C_{-k} for sample i\n",
        "#   Transition k: p[k] = p[k+1] + ternary[k]\n",
        "#   Build by cumsum from oldest→newest: p_raw[:, N-1] = 50, then forward\n",
        "BASE    = 50.0\n",
        "step    = 1.0\n",
        "p_raw   = np.zeros((N_SAMPLES, N), dtype=np.float32)\n",
        "p_raw[:, N-1] = BASE\n",
        "# Vectorised: cumulative sum of ternary (columns N-2 down to 0)\n",
        "for k in range(N-2, -1, -1):\n",
        "    p_raw[:, k] = p_raw[:, k+1] + ternary[:, k].astype(np.float32) * step\n",
        "\n",
        "# Display order: oldest(left) → newest(right)\n",
        "# poc_disp[:, j] = p_raw[:, N-1-j]\n",
        "poc_disp = p_raw[:, ::-1].copy()   # (100, 39), column 0=oldest, col N-1=newest\n",
        "\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "# OUTPUT 1 — TERNARY MATRICES  (100 × 38)\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "print(f\"\\n{SEP}\")\n",
        "print(f\"  OUTPUT 1 — TERNARY MATRICES  (1×{N_TRANS}, values ∈ {{-1,0,+1}})\")\n",
        "print(f\"  Format: [#] Direction | PatternID | M = [m_0 … m_37]\")\n",
        "print(SEP)\n",
        "\n",
        "for i in range(N_SAMPLES):\n",
        "    d_label = \"Bullish\" if dir_bits[i] == 0 else \"Bearish\"\n",
        "    pid     = int(pat_ids[i])\n",
        "    row_str = np.array2string(ternary[i], separator=',',\n",
        "                              max_line_width=400).replace('\\n','')\n",
        "    print(f\"  [{i+1:3d}] {d_label:7s} | ID={pid:>15d} | M={row_str}\")\n",
        "\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "# OUTPUT 2 — SYMBOLIC SEQUENCES  (length 38)\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "print(f\"\\n{SEP}\")\n",
        "print(f\"  OUTPUT 2 — SYMBOLIC SEQUENCES  (Σ, length {N_TRANS})\")\n",
        "print(f\"  Format: [#] Direction | PatternID | Σ = σ_0 σ_1 … σ_37\")\n",
        "print(SEP)\n",
        "\n",
        "for i in range(N_SAMPLES):\n",
        "    d_label = \"Bullish\" if dir_bits[i] == 0 else \"Bearish\"\n",
        "    pid     = int(pat_ids[i])\n",
        "    seq_str = ' '.join(sym_matrix[i])\n",
        "    print(f\"  [{i+1:3d}] {d_label:7s} | ID={pid:>15d} | Σ = {seq_str}\")\n",
        "\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "# OUTPUT 3 — CHARTS\n",
        "#   (a) Full matplotlib figure: 10×10 grid, saved to PNG\n",
        "#   (b) ASCII CLI preview for first 10 patterns\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "print(f\"\\n{SEP}\")\n",
        "print(f\"  OUTPUT 3 — DEVELOPING POC CHARTS  (100 patterns)\")\n",
        "print(SEP)\n",
        "\n",
        "# ── x-axis: position 0=oldest C_{-(N-1)}, N-1=newest C_0 ──────────────────\n",
        "x_pos  = np.arange(N, dtype=np.float32)\n",
        "x_tick_pos = [0, 9, 19, 29, N-1]\n",
        "x_tick_lbl = [f'C_{{-{N-1}}}', f'C_{{-29}}', f'C_{{-19}}', f'C_{{-9}}', 'C_0']\n",
        "\n",
        "ROWS, COLS = 10, 10\n",
        "fig = plt.figure(figsize=(COLS * 3.2, ROWS * 2.0))\n",
        "fig.suptitle(\n",
        "    f\"TopoDevPOC — 100 Random Developing POC Patterns   \"\n",
        "    f\"n={N} pre-market 3-min K-lines\\n\"\n",
        "    f\"Total pattern space: 2^{N} = {TOTAL:,}   \"\n",
        "    f\"(Bullish: {HALF:,}  |  Bearish: {HALF:,})\",\n",
        "    fontsize=10, y=1.005\n",
        ")\n",
        "\n",
        "for i in range(N_SAMPLES):\n",
        "    ax  = fig.add_subplot(ROWS, COLS, i + 1)\n",
        "    poc = poc_disp[i]\n",
        "    is_bull = (dir_bits[i] == 0)\n",
        "    color   = '#1a6eb5' if is_bull else '#c0392b'\n",
        "    label   = 'B↑' if is_bull else 'B↓'\n",
        "\n",
        "    # Background shade\n",
        "    ax.set_facecolor('#f7f9fc' if is_bull else '#fdf4f4')\n",
        "\n",
        "    # POC line\n",
        "    ax.plot(x_pos, poc, color=color, linewidth=1.2, zorder=3)\n",
        "\n",
        "    # Mark strict-move positions (non-zero ternary in display coords)\n",
        "    # Transition k corresponds to display segment [N-2-k, N-1-k]\n",
        "    # Highlight the newer-side node at display index N-1-k = N-1-k\n",
        "    strict_k   = np.where(ternary[i] != 0)[0]          # transition indices\n",
        "    strict_disp = (N - 1 - strict_k).astype(int)        # display x-positions\n",
        "    if strict_disp.size > 0:\n",
        "        ax.scatter(strict_disp, poc[strict_disp],\n",
        "                   color=color, s=5, zorder=5, linewidths=0)\n",
        "\n",
        "    # Flat segments (equality)\n",
        "    flat_k     = np.where(ternary[i] == 0)[0]\n",
        "    flat_disp  = (N - 1 - flat_k).astype(int)\n",
        "    if flat_disp.size > 0:\n",
        "        ax.scatter(flat_disp, poc[flat_disp],\n",
        "                   color='gray', s=3, zorder=4, linewidths=0, alpha=0.5)\n",
        "\n",
        "    n_strict = int(np.abs(ternary[i]).sum())\n",
        "    pid_short = int(pat_ids[i]) % 10**9      # last 9 digits for readability\n",
        "    ax.set_title(f\"#{i+1} {label}  mv={n_strict}  …{pid_short:09d}\",\n",
        "                 fontsize=5.5, pad=2, color=color)\n",
        "\n",
        "    ax.set_xlim(-0.5, N - 0.5)\n",
        "    ax.set_xticks(x_tick_pos)\n",
        "    ax.set_xticklabels(['←old', '', '', '', 'new→'], fontsize=3.5)\n",
        "    ax.tick_params(axis='y', labelsize=3.5)\n",
        "    ax.yaxis.set_major_locator(mticker.MaxNLocator(4))\n",
        "    for sp in ('top', 'right'):\n",
        "        ax.spines[sp].set_visible(False)\n",
        "    ax.spines['left'].set_color(color)\n",
        "    ax.spines['left'].set_linewidth(1.5)\n",
        "    ax.spines['bottom'].set_color('#cccccc')\n",
        "\n",
        "plt.tight_layout(rect=[0, 0, 1, 1])\n",
        "chart_path = \"TopoDevPOC_n39_100samples.png\"\n",
        "plt.savefig(chart_path, dpi=110, bbox_inches='tight')\n",
        "plt.close(fig)\n",
        "print(f\"  [SAVED] {chart_path}\")\n",
        "\n",
        "# ── ASCII CLI chart for first 10 patterns ────────────────────────────────────\n",
        "H  = 7          # chart height in rows\n",
        "W  = 39         # chart width  = N\n",
        "\n",
        "print(f\"\\n  ASCII CLI Charts — first 10 samples (right side = C_0 = newest)\\n\")\n",
        "for i in range(10):\n",
        "    poc    = poc_disp[i]\n",
        "    d_lbl  = \"Bullish\" if dir_bits[i] == 0 else \"Bearish\"\n",
        "    pid    = int(pat_ids[i])\n",
        "    n_mv   = int(np.abs(ternary[i]).sum())\n",
        "    pmin, pmax = poc.min(), poc.max()\n",
        "    span   = pmax - pmin if pmax != pmin else 1.0\n",
        "\n",
        "    # Map each x-position to a row\n",
        "    rows   = (H - 1 - ((poc - pmin) / span * (H - 1))).round().astype(int)\n",
        "    rows   = np.clip(rows, 0, H - 1)\n",
        "\n",
        "    grid   = [[' '] * W for _ in range(H)]\n",
        "    for j in range(W):\n",
        "        r = rows[j]\n",
        "        # Strict-move node in the pair ending at display j:\n",
        "        # transition index k = N-1-j  (if j < N-1)\n",
        "        is_strict = (j < N - 1) and (ternary[i, N - 2 - j] != 0)\n",
        "        grid[r][j] = '●' if is_strict else '·'\n",
        "    # Connect with horizontal dash where poc is flat\n",
        "    for row_idx in range(H):\n",
        "        line = grid[row_idx]\n",
        "        for j in range(1, W):\n",
        "            if line[j] == ' ' and rows[j] == row_idx:\n",
        "                line[j] = '-'\n",
        "\n",
        "    print(f\"  [{i+1:2d}] {d_lbl:7s} | ID={pid} | strict_moves={n_mv}/{N_TRANS}\")\n",
        "    poc_hi = poc[N-1]; poc_lo = poc[0]\n",
        "    print(f\"       POC range: oldest={poc_lo:.0f}  →  newest={poc_hi:.0f}\")\n",
        "    print(f\"       ┌{'─'*W}┐\")\n",
        "    for row_idx in range(H):\n",
        "        print(f\"       │{''.join(grid[row_idx])}│\")\n",
        "    print(f\"       └{'─'*W}┘\")\n",
        "    sym_preview = ' '.join(sym_matrix[i, :12]) + ' …'\n",
        "    print(f\"       Σ (first 12): {sym_preview}\\n\")\n",
        "\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "# FINAL SUMMARY\n",
        "# ─────────────────────────────────────────────────────────────────────────────\n",
        "total_ms = (time.perf_counter() - t_sample) * 1e3\n",
        "print(SEP)\n",
        "print(\"  SUMMARY\")\n",
        "print(SEP)\n",
        "print(f\"  n (candles)                = {N}\")\n",
        "print(f\"  Transitions per pattern    = {N_TRANS}\")\n",
        "print(f\"  Total patterns  [2^{N}]    = {TOTAL:,}\")\n",
        "print(f\"  Bullish         [2^{N-1}]  = {HALF:,}\")\n",
        "print(f\"  Bearish         [2^{N-1}]  = {HALF:,}\")\n",
        "print(f\"  Matrix B_n validated       = {B_n:,}  ✓\")\n",
        "print(f\"  Samples generated          = {N_SAMPLES}\")\n",
        "print(f\"  Chart file                 = {chart_path}\")\n",
        "print(f\"  Compute device             = {DEVICE}\")\n",
        "print(f\"  Wall-clock (sample+decode) = {total_ms:.2f} ms\")\n",
        "print(SEP)\n",
        "print()\n",
        "print(\"  CONVERSION FORMULAS  (tex Sec. V)\")\n",
        "print(\"  Symbolic → Ternary:\")\n",
        "print(\"    Bullish: '>' → +1,  '=' →  0\")\n",
        "print(\"    Bearish: '<' → -1,  '=' →  0\")\n",
        "print(\"  Ternary → Symbolic:\")\n",
        "print(\"    +1 → '>',  0 → '=',  -1 → '<'\")\n",
        "print()\n",
        "print(\"  TEMPORAL CONVENTION:\")\n",
        "print(f\"    Chart x-axis: left = C_{{-{N-1}}} (oldest) → right = C_0 (newest)\")\n",
        "print(\"    Bullish pattern: POC non-increasing toward right (higher on left)\")\n",
        "print(\"    Bearish pattern: POC non-decreasing toward right (lower on left)\")\n",
        "print(SEP)"
      ]
    }
  ]
}