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+version https://git-lfs.github.com/spec/v1
+oid sha256:437427eded07d75c64f043eef75d4431cb783c8fd66385da3fe66cb2f5f2696b
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TopoDevPOC.tex

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+\documentclass[conference]{IEEEtran}
+\usepackage{amsmath, amssymb, amsthm}
+\usepackage{graphicx}
+\usepackage{array}
+\usepackage{booktabs}
+\usepackage{cite}
+\usepackage{tikz}
+\usepackage{xcolor}
+
+% Theorem environments
+\newtheorem{theorem}{Theorem}
+\newtheorem{lemma}{Lemma}
+\newtheorem{corollary}{Corollary}
+\newtheorem{definition}{Definition}
+\newtheorem{proposition}{Proposition}
+
+\begin{document}
+
+\title{TopoDevPOC: Topologically Unique Developing Poin of Control Patterns on Pre-market K-Lines}
+
+\author{\IEEEauthorblockN{ConQ Research Team}\\
+\IEEEauthorblockA{\textit{Continual Quasars}\\
+\today}
+}
+
+\maketitle
+
+\begin{abstract}
+This paper establishes the exact combinatorial enumeration of all possible unique developing Point of Control (POC) line patterns observed during the pre-market session consisting of $n = 39$ three-minute candlesticks. Under the constraint of continuous directional movement (bullish: non-increasing; bearish: non-decreasing), we prove that the total number of distinct patterns is $2^n$. The derivation employs elementary combinatorics and a state-transition matrix formulation. Additionally, we provide explicit formulas for converting between symbolic sequence representations and ternary matrix encodings using values $+1$, $0$, and $-1$. Ten illustrative random patterns are presented in both symbolic and matrix formats, with a visual chart emphasizing the right-to-left temporal ordering. The results are purely theoretical and require no empirical simulation.
+\end{abstract}
+
+\begin{IEEEkeywords}
+developing POC, combinatorial enumeration, candlestick patterns, monotonic sequences, transition matrix, pre-market analysis
+\end{IEEEkeywords}
+
+\section{Introduction}
+
+The Point of Control (POC) is the price level at which the maximum volume is traded during a given time interval. In pre-market trading, where volume is often thin and directional conviction emerges gradually, the evolving POC exhibits a tendency toward monotonicity: it either trends upward (bullish) or downward (bearish) with possible flat segments, but seldom oscillates. This observation motivates the following combinatorial question: Given a sequence of $n$ consecutive pre-market candles, each associated with a developing POC value, how many distinct patterns of directional movement (strict or flat) exist under the constraint that the sequence is non-increasing (bullish) or non-decreasing (bearish)?
+
+The present work provides a definitive answer to this question, with the following main contributions:
+
+\begin{enumerate}
+    \item A closed-form enumeration showing that for $n$ candles there are exactly $2^n$ unique developing POC line patterns.
+    \item A matrix-based state-transition formulation that validates the combinatorial result.
+    \item Explicit formulas for converting a pattern between its symbolic sequence representation and a ternary matrix encoding using values $+1$ (strict up), $-1$ (strict down), and $0$ (equality).
+    \item A set of ten randomly generated pattern examples, displayed in both symbolic and ternary matrix forms, with a visual chart aligned to the correct right-to-left temporal order.
+\end{enumerate}
+
+The analysis is purely theoretical; no simulations, empirical data, or numerical approximations are employed.
+
+\section{Problem Definition and Notation}
+
+Let $n \in \mathbb{N}$ denote the number of candles. For the conventional pre-market session, $n = 39$. Index candles from most recent to oldest as
+\begin{equation}
+    C_0, C_{-1}, C_{-2}, \dots, C_{-(n-1)}.
+\end{equation}
+The corresponding developing POC values form a sequence
+\begin{equation}
+    \mathbf{p} = (p_0, p_1, \dots, p_{n-1}) \in \mathbb{R}^n,
+\end{equation}
+where $p_k$ denotes the POC value of candle $C_{-k}$.
+
+\begin{definition}[Continuous Bullish Pattern]
+A sequence $\mathbf{p}$ is a \emph{continuous bullish pattern} if for every $k = 0, 1, \dots, n-2$, the relation $R_k \in \{>, =\}$ holds between $p_k$ and $p_{k+1}$, i.e.,
+\begin{equation}
+    p_k \geq p_{k+1}, \quad \text{with } p_k > p_{k+1} \text{ or } p_k = p_{k+1}.
+\end{equation}
+\end{definition}
+
+\begin{definition}[Continuous Bearish Pattern]
+A sequence $\mathbf{p}$ is a \emph{continuous bearish pattern} if for every $k = 0, 1, \dots, n-2$, the relation $R_k \in \{<, =\}$ holds between $p_k$ and $p_{k+1}$, i.e.,
+\begin{equation}
+    p_k \leq p_{k+1}, \quad \text{with } p_k < p_{k+1} \text{ or } p_k = p_{k+1}.
+\end{equation}
+\end{definition}
+
+A pattern is uniquely identified by the $(n-1)$-tuple of relations $(R_0, R_1, \dots, R_{n-2})$. Two price sequences that yield the same relation tuple are considered equivalent patterns.
+
+\section{Combinatorial Enumeration}
+
+\begin{theorem}
+For any $n \ge 1$, the number of continuous bullish developing POC patterns of length $n$ is $2^{n-1}$. The number of continuous bearish patterns is also $2^{n-1}$. Consequently, the total number of distinct patterns is $2^n$.
+\end{theorem}
+
+\begin{proof}
+For a bullish pattern, each adjacent pair $(p_k, p_{k+1})$ permits exactly two relations: $>$ or $=$. The $n-1$ choices are independent. Thus the number of bullish patterns is $2^{n-1}$. An identical argument applies to bearish patterns with relations $<$ and $=$. Since the two directional families are disjoint, the total count is $2 \cdot 2^{n-1} = 2^n$.
+\end{proof}
+
+For $n = 39$, the exact total number of unique patterns is
+\begin{equation}
+    T_{39} = 2^{39}.
+\end{equation}
+
+\section{Matrix Formulation and State Transition}
+
+Define a ternary state variable $m_k$ for each transition $k$ ($0 \le k \le n-2$) as follows:
+\begin{itemize}
+    \item For a bullish pattern:
+    \begin{equation}
+        m_k = \begin{cases}
+            +1, & \text{if } R_k = \; >, \\
+            0,  & \text{if } R_k = \; =.
+        \end{cases}
+    \end{equation}
+    \item For a bearish pattern:
+    \begin{equation}
+        m_k = \begin{cases}
+            -1, & \text{if } R_k = \; <, \\
+            0,  & \text{if } R_k = \; =.
+        \end{cases}
+    \end{equation}
+\end{itemize}
+Note that in either directional family, the allowed values are either $\{+1, 0\}$ (bullish) or $\{-1, 0\}$ (bearish). Consequently, a pattern is equivalent to a ternary vector of length $n-1$:
+\begin{equation}
+    \mathbf{m} = (m_0, m_1, \dots, m_{n-2}) \in \{-1,0,+1\}^{n-1},
+\end{equation}
+subject to the constraint that all nonzero entries share the same sign.
+
+\subsection{Transition Matrix Representation}
+
+Consider the directed graph with two states $\{S_0, S_{\pm}\}$ corresponding to the last observed relation being equality ($S_0$) or strict move ($S_{\pm}$, with sign determined by direction). Transitions are unconstrained: from any state, both $S_0$ and $S_{\pm}$ are reachable. The adjacency matrix is
+\begin{equation}
+    \mathbf{A} = \begin{pmatrix}
+        1 & 1 \\
+        1 & 1
+    \end{pmatrix}.
+\end{equation}
+Let $\mathbf{v}_0 = (1,1)^\top$ be the initial vector (both states permissible before any comparison). The number of patterns with $n$ candles (i.e., $n-1$ transitions) is
+\begin{equation}
+    B_n = \mathbf{1}^\top \mathbf{A}^{n-2} \mathbf{v}_0,
+\end{equation}
+where $\mathbf{1} = (1,1)^\top$. Since $\mathbf{A} = \mathbf{1}\mathbf{1}^\top$, we have $\mathbf{A}^k = 2^{k-1} \mathbf{A}$ for $k \ge 1$. Hence,
+\begin{align}
+    B_n &= \mathbf{1}^\top \left( 2^{n-3} \mathbf{A} \right) \mathbf{v}_0 \nonumber \\
+        &= 2^{n-3} \mathbf{1}^\top \mathbf{A} \mathbf{1} \nonumber \\
+        &= 2^{n-3} \cdot 4 = 2^{n-1}.
+\end{align}
+This matrix derivation confirms the combinatorial count independently.
+
+\section{Conversion Between Symbolic Sequence and Ternary Matrix}
+
+We establish bidirectional conversion formulas between the symbolic sequence representation (a string of symbols $>$ and $=$, or $<$ and $=$) and the ternary matrix (row vector) encoding.
+
+\subsection{Symbolic Sequence to Ternary Matrix}
+
+Let $\Sigma$ be a string of length $n-1$ over alphabet $\{>, =\}$ for bullish, or $\{<, =\}$ for bearish. Define the mapping $f$:
+\begin{align}
+    f_{\text{bullish}}(>) &= +1, & f_{\text{bullish}}(=) &= 0, \\
+    f_{\text{bearish}}(<) &= -1, & f_{\text{bearish}}(=) &= 0.
+\end{align}
+The ternary matrix $\mathbf{M}$ of size $1 \times (n-1)$ is given by
+\begin{equation}
+    \mathbf{M}_{1,j+1} = f(\Sigma_j), \quad j = 0,1,\dots,n-2.
+\end{equation}
+That is, $\mathbf{M} = \begin{pmatrix} f(\Sigma_0) & f(\Sigma_1) & \cdots & f(\Sigma_{n-2}) \end{pmatrix}$.
+
+\subsection{Ternary Matrix to Symbolic Sequence}
+
+Conversely, given a ternary row matrix $\mathbf{M} = (m_0, m_1, \dots, m_{n-2})$ with $m_j \in \{+1,0\}$ for bullish or $\{-1,0\}$ for bearish, the symbolic sequence is obtained by applying the inverse mapping $g$:
+\begin{align}
+    g_{\text{bullish}}(+1) &= >, & g_{\text{bullish}}(0) &= =, \\
+    g_{\text{bearish}}(-1) &= <, & g_{\text{bearish}}(0) &= =.
+\end{align}
+Formally,
+\begin{equation}
+    \Sigma_j = g(m_j),
+\end{equation}
+and the sequence is $\Sigma = \Sigma_0 \Sigma_1 \cdots \Sigma_{n-2}$.
+
+These conversions are one-to-one and preserve pattern identity.
+
+\section{Illustrative Examples}
+
+We present ten randomly generated continuous developing POC patterns. For compactness, we use $n = 6$ candles (5 transitions). Each pattern is displayed with its directional label, symbolic sequence, and the corresponding $1 \times 5$ ternary matrix.
+
+\subsection{Example Patterns}
+
+\begin{table}[h]
+\centering
+\caption{Ten Random Continuous Developing POC Patterns ($n=6$)}
+\label{tab:examples}
+\begin{tabular}{c c c c}
+\toprule
+\textbf{ID} & \textbf{Direction} & \textbf{Symbolic Sequence} & \textbf{Ternary Matrix ($1 \times 5$)} \\
+\midrule
+1 & Bullish & $> \; > \; = \; > \; =$ & $\begin{pmatrix}+1 & +1 & 0 & +1 & 0\end{pmatrix}$ \\
+2 & Bullish & $= \; > \; = \; = \; >$ & $\begin{pmatrix}0 & +1 & 0 & 0 & +1\end{pmatrix}$ \\
+3 & Bearish & $< \; = \; < \; < \; =$ & $\begin{pmatrix}-1 & 0 & -1 & -1 & 0\end{pmatrix}$ \\
+4 & Bearish & $= \; = \; < \; = \; <$ & $\begin{pmatrix}0 & 0 & -1 & 0 & -1\end{pmatrix}$ \\
+5 & Bullish & $> \; = \; = \; > \; >$ & $\begin{pmatrix}+1 & 0 & 0 & +1 & +1\end{pmatrix}$ \\
+6 & Bullish & $= \; > \; > \; = \; >$ & $\begin{pmatrix}0 & +1 & +1 & 0 & +1\end{pmatrix}$ \\
+7 & Bearish & $< \; < \; = \; = \; <$ & $\begin{pmatrix}-1 & -1 & 0 & 0 & -1\end{pmatrix}$ \\
+8 & Bearish & $= \; < \; = \; < \; =$ & $\begin{pmatrix}0 & -1 & 0 & -1 & 0\end{pmatrix}$ \\
+9 & Bullish & $> \; > \; > \; = \; =$ & $\begin{pmatrix}+1 & +1 & +1 & 0 & 0\end{pmatrix}$ \\
+10 & Bearish & $< \; = \; = \; = \; <$ & $\begin{pmatrix}-1 & 0 & 0 & 0 & -1\end{pmatrix}$ \\
+\bottomrule
+\end{tabular}
+\end{table}
+
+\subsection{Visual Chart with Correct Temporal Ordering}
+
+The temporal axis is oriented from right to left, aligning with the index convention $C_0$ (current candle, $t=0$) at the rightmost position, followed by $C_{-1}$, $C_{-2}$, etc., proceeding leftwards. This accurately reflects the backward-looking nature of the pattern analysis.
+
+Figure~\ref{fig:pattern1} depicts Pattern 1 (Bullish: $> \; > \; = \; > \; =$) with this right-to-left orientation. The $y$-axis shows relative POC value (arbitrary units decreasing for bullish).
+
+\begin{figure}[h]
+\centering
+\begin{tikzpicture}[scale=0.6]
+    % x-axis reversed: 0 on the right, negative indices to the left
+    \draw[->] (0,0) -- (6,0) node[right] {$t$ (candle index)};
+    \draw[->] (0,0) -- (0,5) node[above] {POC};
+    % Labels: C_0 at x=5, C_{-1} at x=4, ..., C_{-5} at x=0
+    \foreach \x in {0,1,2,3,4,5} {
+        \pgfmathtruncatemacro{\idx}{-\x}
+        \draw (5-\x,0.1) -- (5-\x,-0.1) node[below] {\small $C_{\idx}$};
+    }
+    % Pattern: > > = > =
+    % Starting value 5, then steps: -1, -1, 0, -1, 0
+    % Plot from right to left: C_0 (x=5, y=5), C_{-1} (x=4, y=4), ...
+    \draw[thick, blue] (5,5) -- (4,4) -- (3,3) -- (2,3) -- (1,2) -- (0,2);
+    \filldraw (5,5) circle (2pt) (4,4) circle (2pt) (3,3) circle (2pt) (2,3) circle (2pt) (1,2) circle (2pt) (0,2) circle (2pt);
+    % Annotate relations between points (placed near the line segment)
+    \node[anchor=south] at (4.5,4.5) {$>$};
+    \node[anchor=south] at (3.5,3.5) {$>$};
+    \node[anchor=south] at (2.5,3)   {$=$};
+    \node[anchor=south] at (1.5,2.5) {$>$};
+    \node[anchor=south] at (0.5,2)   {$=$};
+\end{tikzpicture}
+\caption{Visualization of Bullish Pattern 1: $> > = > =$. The right-to-left orientation places the current candle $C_0$ at the rightmost, with older candles extending leftwards.}
+\label{fig:pattern1}
+\end{figure}
+
+\section{Discussion and Consistency Verification}
+
+The enumeration $2^{39}$ demonstrates the vast theoretical space of possible continuous developing POC patterns during the pre-market session. Even under the stringent constraint of directional monotonicity, the number of distinct configurations exceeds half a trillion.
+
+The ternary matrix representation using $+1$, $0$, and $-1$ provides a compact, signed encoding that inherently encodes both the direction (sign) and the presence of a strict move. This representation is fully consistent with the symbolic sequences and the combinatorial count. The conversion formulas are bijective, ensuring that each pattern has a unique ternary vector.
+
+The state-transition matrix derivation independently confirms the count $2^{n-1}$ per direction, serving as a cross-check of the combinatorial proof. Moreover, the examples demonstrate that patterns may contain any number of equalities, including the extreme case of all $=$ symbols (ternary matrix of all zeros), which corresponds to a completely flat developing POC line.
+
+The chart orientation (right to left) aligns with the temporal indexing convention and aids in intuitive interpretation by placing the most recent information at the viewer's natural scanning direction.
+
+Extensions of this work may consider patterns where the number of consecutive equalities is bounded, or where transition probabilities are non-uniform. The present combinatorial foundation supports such generalizations without alteration of the core enumeration.
+
+\section{Conclusion}
+
+We have determined that the total number of unique continuous developing POC line patterns for a sequence of $n$ pre-market candlesticks is $2^n$, with exactly $2^{39}$ patterns for the conventional $n=39$ session. The result is derived via elementary counting and validated by a matrix state-transition framework. Formulas for interconversion between symbolic sequences and ternary matrices (using $+1$, $0$, $-1$) are provided, along with ten illustrative random patterns and a correctly oriented visual chart. This theoretical analysis establishes a fundamental reference for future pattern recognition studies.
+
+\begin{thebibliography}{1}
+\bibitem{marketprofile}
+J. F. Dalton, \emph{Mind Over Markets: Power Trading with Market Generated Information}. Marketplace Books, 2013.
+\bibitem{combinatorics}
+R. P. Stanley, \emph{Enumerative Combinatorics}, vol. 1, 2nd ed. Cambridge University Press, 2011.
+\end{thebibliography}
+
+\end{document}

TopoDevPOC_n39.ipynb

@@ -0,0 +1,882 @@
+{
+  "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)"
+      ]
+    }
+  ]
+}

TopoDevPOC_n39.py

@@ -0,0 +1,423 @@
+# !pip -q install numpy matplotlib warp-lang torch
+#!/usr/bin/env python3
+"""
+TopoDevPOC_n39.py
+Topologically Unique Developing Point of Control Patterns
+Pre-market K-Lines, n = 39 three-minute candlesticks
+
+Paper : TopoDevPOC.tex  (ConQ Research Team, Continual Quasars)
+Compute: Vectorized NumPy + GPU Torch (T4) + Warp branchless ops
+         Architectural patterns from core_engine_v11.py (Hyper-Warp Edition)
+
+Outputs (CLI):
+  1. Total combination count for n=39
+  2. Matrix state-transition validation
+  3. 100 random ternary matrices  (1×38 each)
+  4. 100 random symbolic sequences (length-38 strings)
+  5. 100 developing_poc charts saved as PNG + ASCII CLI preview
+
+Run on Google Colab T4:
+    !python TopoDevPOC_n39.py
+"""
+
+# ── stdlib ────────────────────────────────────────────────────────────────────
+import os, sys, time, math
+import numpy as np
+
+# ── matplotlib (non-interactive for Colab CLI) ────────────────────────────────
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+import matplotlib.ticker as mticker
+
+# ── GPU setup (T4 Colab) ─────────────────────────────────────────────────────
+try:
+    import torch
+    HAS_CUDA = torch.cuda.is_available()
+    DEVICE   = 'cuda' if HAS_CUDA else 'cpu'
+except ImportError:
+    HAS_CUDA = False
+    DEVICE   = 'cpu'
+    torch    = None
+
+# Optional Warp (core_engine_v11.py pattern) ─────────────────────────────────
+HAS_WARP = False
+try:
+    import warp as wp
+    wp.init()
+    wp.set_module_options({"enable_backward": False, "fast_math": True, "max_unroll": 8})
+    HAS_WARP = bool(wp.get_cuda_devices())
+except Exception:
+    pass
+
+# ─────────────────────────────────────────────────────────────────────────────
+# CONSTANTS  (tex Section II)
+# ─────────────────────────────────────────────────────────────────────────────
+N         = 39          # pre-market 3-min candles  (C_0 … C_{-(n-1)})
+N_TRANS   = N - 1       # 38 adjacent-pair relations
+N_SAMPLES = 100
+SEED      = int(time.time() * 1000) & 0x7FFFFFFF
+
+SEP = "=" * 74
+
+# ─────────────────────────────────────────────────────────────────────────────
+# 0. HEADER
+# ─────────────────────────────────────────────────────────────────────────────
+print(SEP)
+print("  TopoDevPOC — Developing POC Pattern Enumerator")
+print(f"  n = {N} candles | {N_TRANS} transitions | device = {DEVICE}")
+if HAS_CUDA and torch:
+    print(f"  GPU = {torch.cuda.get_device_name(0)}")
+if HAS_WARP:
+    print(f"  Warp = enabled (branchless kernel path)")
+print(SEP)
+
+# ─────────────────────────────────────────────────────────────────────────────
+# SECTION 1 — COMBINATORIAL ENUMERATION  (tex Theorem, Sec. III)
+#
+#   Bullish:  each of (n-1) transitions ∈ {>, =}  → 2^(n-1) patterns
+#   Bearish:  each of (n-1) transitions ∈ {<, =}  → 2^(n-1) patterns
+#   Total   : 2^(n-1) + 2^(n-1) = 2^n  (disjoint families)
+#   n=39    : 2^39 = 549,755,813,888
+# ─────────────────────────────────────────────────────────────────────────────
+TOTAL = 1 << N          # exact Python int (arbitrary precision)
+HALF  = 1 << (N - 1)
+
+print(f"\n[THEOREM]  Total unique developing POC patterns for n={N}")
+print(f"  Bullish (non-increasing) : 2^{N-1} = {HALF:,}")
+print(f"  Bearish (non-decreasing) : 2^{N-1} = {HALF:,}")
+print(f"  Total  (2^{N})           : {TOTAL:,}")
+
+# ─────────────────────────────────────────────────────────────────────────────
+# SECTION 2 — MATRIX STATE-TRANSITION VALIDATION  (tex Sec. IV)
+#
+#   States  : S_0 (equality), S_± (strict move)
+#   A = [[1,1],[1,1]]   (fully-connected 2-state digraph)
+#   v_0 = [1,1]^T       (both states reachable initially)
+#
+#   B_n = 1^T · A^(n-2) · v_0
+#       = 2^(n-3) · 1^T · A · 1     (using A^k = 2^(k-1)·A for k≥1)
+#       = 2^(n-3) · 4  =  2^(n-1)   per direction
+#
+#   Implementation: exact Python-int matrix exponentiation (no float rounding)
+# ─────────────────────────────────────────────────────────────────────────────
+
+def _mm2(A, B):
+    """Exact 2×2 matrix multiply with Python arbitrary-precision ints."""
+    return [
+        [A[0][0]*B[0][0] + A[0][1]*B[1][0],  A[0][0]*B[0][1] + A[0][1]*B[1][1]],
+        [A[1][0]*B[0][0] + A[1][1]*B[1][0],  A[1][0]*B[0][1] + A[1][1]*B[1][1]],
+    ]
+
+def _mpow2(M, k):
+    """Fast 2×2 matrix power, exact ints, O(log k)."""
+    if k == 0: return [[1,0],[0,1]]
+    if k == 1: return M
+    h = _mpow2(M, k >> 1)
+    s = _mm2(h, h)
+    return s if (k & 1) == 0 else _mm2(s, M)
+
+A_mat  = [[1,1],[1,1]]
+v0     = [1, 1]
+A_pow  = _mpow2(A_mat, N - 2)
+# 1^T · A^(n-2) · v0
+Av0_0  = A_pow[0][0]*v0[0] + A_pow[0][1]*v0[1]
+Av0_1  = A_pow[1][0]*v0[0] + A_pow[1][1]*v0[1]
+B_n    = Av0_0 + Av0_1          # = 1^T · (A^(n-2)·v0)
+
+print(f"\n[MATRIX]  A = [[1,1],[1,1]] | v_0 = [1,1]^T")
+print(f"  A^{N-2} = [[{A_pow[0][0]}, {A_pow[0][1]}],")
+print(f"             [{A_pow[1][0]}, {A_pow[1][1]}]]")
+print(f"  B_{N} = 1^T · A^{N-2} · v_0 = {B_n:,}")
+print(f"  Expected 2^{{n-1}}           = {HALF:,}")
+assert B_n == HALF,          f"Matrix B_n mismatch: {B_n} ≠ {HALF}"
+assert 2 * B_n == TOTAL,     f"Total mismatch: {2*B_n} ≠ {TOTAL}"
+print(f"  [OK] 2 × {B_n:,} = {TOTAL:,}  ✓")
+
+# ─────────────────────────────────────────────────────────────────────────────
+# SECTION 3 — PATTERN ENCODING SCHEME
+#
+#   Each of the 2^39 patterns maps bijectively to a 39-bit integer:
+#     bit  0          : direction   (0 = Bullish, 1 = Bearish)
+#     bits 1 … N-1   : transitions  (1 = strict move, 0 = equality)
+#
+#   pattern_id ∈ [0, 2^39)   uniquely identifies every valid pattern.
+#
+#   Ternary matrix m ∈ {+1,0}^(n-1) for bullish,
+#                  m ∈ {-1,0}^(n-1) for bearish.
+#   Bijection: m_k = sign(direction) × trans_bit_k
+# ─────────────────────────────────────────────────────────────────────────────
+
+# ─────────────────────────────────────────────────────────────────────────────
+# SECTION 4 — GPU-ACCELERATED RANDOM SAMPLING
+#   Generate (N_SAMPLES × N) binary matrix at once on T4 GPU.
+#   Inspired by core_engine_v11.py XOR-shift PRNG kernel design.
+#   bits[:,0]  = direction flags
+#   bits[:,1:] = N_TRANS transition flags per pattern
+# ─────────────────────────────────────────────────────────────────────────────
+
+t_sample = time.perf_counter()
+
+if HAS_WARP:
+    # ── Warp branchless path (core_engine_v11.py style) ─────────────────────
+    # Launch one thread per sample; XOR-shift fills N bits per thread.
+    _seed_wp = SEED
+
+    @wp.kernel
+    def k_rng_bits(seed: int, N_cols: int,
+                   out: wp.array(dtype=wp.int8)):
+        tid = wp.tid()
+        rng = wp.uint32(seed) ^ wp.uint32(tid)
+        if rng == wp.uint32(0):
+            rng = wp.uint32(123456789)
+        base = tid * N_cols
+        for col in range(N_cols):
+            rng = rng ^ (rng << wp.uint32(13))
+            rng = rng ^ (rng >> wp.uint32(17))
+            rng = rng ^ (rng << wp.uint32(5))
+            out[base + col] = wp.int8(int(rng) & 1)
+
+    out_wp  = wp.zeros(N_SAMPLES * N, dtype=wp.int8, device='cuda')
+    wp.launch(k_rng_bits, dim=N_SAMPLES, block_dim=128,
+              inputs=[_seed_wp, N, out_wp], device='cuda')
+    wp.synchronize()
+    bits_np = out_wp.numpy().reshape(N_SAMPLES, N)
+    print(f"\n[SAMPLE]  {N_SAMPLES} patterns sampled via Warp XOR-shift kernel")
+
+elif HAS_CUDA and torch is not None:
+    # ── Torch GPU path ───────────────────────────────────────────────────────
+    gen = torch.Generator(device='cuda')
+    gen.manual_seed(SEED)
+    bits_t  = torch.randint(0, 2, (N_SAMPLES, N), device='cuda',
+                            generator=gen, dtype=torch.int8)
+    bits_np = bits_t.cpu().numpy()
+    print(f"\n[SAMPLE]  {N_SAMPLES} patterns sampled on GPU (torch.randint)")
+
+else:
+    # ── CPU NumPy fallback ────────────────────────────────────────────────────
+    rng_cpu = np.random.default_rng(SEED)
+    bits_np = rng_cpu.integers(0, 2, size=(N_SAMPLES, N), dtype=np.int8)
+    print(f"\n[SAMPLE]  {N_SAMPLES} patterns sampled on CPU (NumPy)")
+
+sample_ms = (time.perf_counter() - t_sample) * 1e3
+print(f"          Sampling time: {sample_ms:.2f} ms")
+
+# ─────────────────────────────────────────────────────────────────────────────
+# SECTION 5 — VECTORISED DECODING  (NumPy, no Python loops over patterns)
+#
+#   bits[:,0]   → direction array  (0=Bullish, 1=Bearish), shape (100,)
+#   bits[:,1:]  → trans array,     shape (100, 38)
+#   ternary_mat: +trans if Bullish, -trans if Bearish  → shape (100, 38)
+#   sign: Bullish→+1, Bearish→-1, broadcast multiply
+# ─────────────────────────────────────────────────────────────────────────────
+
+dir_bits  = bits_np[:, 0].astype(np.int8)      # 0 or 1
+trans     = bits_np[:, 1:].astype(np.int8)      # (100,38), values 0 or 1
+signs     = 1 - 2 * dir_bits                    # 0→+1 (bull), 1→-1 (bear)
+ternary   = (signs[:, None] * trans).astype(np.int8)  # (100,38): +1/0/-1
+
+# Compact 39-bit pattern IDs
+pows64    = (np.uint64(1) << np.arange(N, dtype=np.uint64))
+pat_ids   = (bits_np.astype(np.uint64) * pows64[None, :]).sum(axis=1)
+
+# Symbolic sequences: vectorised char lookup
+#   Bullish (sign=+1): trans=1 → '>', trans=0 → '='
+#   Bearish (sign=-1): trans=1 → '<', trans=0 → '='
+SYM_BULL = np.array(['=', '>'], dtype='<U1')   # index by trans bit
+SYM_BEAR = np.array(['=', '<'], dtype='<U1')
+sym_matrix = np.where(dir_bits[:, None] == 0,
+                      SYM_BULL[trans],
+                      SYM_BEAR[trans])          # (100, 38)
+
+# POC price sequence (right-to-left: p[0]=C_0=newest, p[N-1]=C_{-(N-1)}=oldest)
+#   p_raw[i, k] = POC of candle C_{-k} for sample i
+#   Transition k: p[k] = p[k+1] + ternary[k]
+#   Build by cumsum from oldest→newest: p_raw[:, N-1] = 50, then forward
+BASE    = 50.0
+step    = 1.0
+p_raw   = np.zeros((N_SAMPLES, N), dtype=np.float32)
+p_raw[:, N-1] = BASE
+# Vectorised: cumulative sum of ternary (columns N-2 down to 0)
+for k in range(N-2, -1, -1):
+    p_raw[:, k] = p_raw[:, k+1] + ternary[:, k].astype(np.float32) * step
+
+# Display order: oldest(left) → newest(right)
+# poc_disp[:, j] = p_raw[:, N-1-j]
+poc_disp = p_raw[:, ::-1].copy()   # (100, 39), column 0=oldest, col N-1=newest
+
+# ─────────────────────────────────────────────────────────────────────────────
+# OUTPUT 1 — TERNARY MATRICES  (100 × 38)
+# ─────────────────────────────────────────────────────────────────────────────
+print(f"\n{SEP}")
+print(f"  OUTPUT 1 — TERNARY MATRICES  (1×{N_TRANS}, values ∈ {{-1,0,+1}})")
+print(f"  Format: [#] Direction | PatternID | M = [m_0 … m_37]")
+print(SEP)
+
+for i in range(N_SAMPLES):
+    d_label = "Bullish" if dir_bits[i] == 0 else "Bearish"
+    pid     = int(pat_ids[i])
+    row_str = np.array2string(ternary[i], separator=',',
+                              max_line_width=400).replace('\n','')
+    print(f"  [{i+1:3d}] {d_label:7s} | ID={pid:>15d} | M={row_str}")
+
+# ─────────────────────────────────────────────────────────────────────────────
+# OUTPUT 2 — SYMBOLIC SEQUENCES  (length 38)
+# ─────────────────────────────────────────────────────────────────────────────
+print(f"\n{SEP}")
+print(f"  OUTPUT 2 — SYMBOLIC SEQUENCES  (Σ, length {N_TRANS})")
+print(f"  Format: [#] Direction | PatternID | Σ = σ_0 σ_1 … σ_37")
+print(SEP)
+
+for i in range(N_SAMPLES):
+    d_label = "Bullish" if dir_bits[i] == 0 else "Bearish"
+    pid     = int(pat_ids[i])
+    seq_str = ' '.join(sym_matrix[i])
+    print(f"  [{i+1:3d}] {d_label:7s} | ID={pid:>15d} | Σ = {seq_str}")
+
+# ─────────────────────────────────────────────────────────────────────────────
+# OUTPUT 3 — CHARTS
+#   (a) Full matplotlib figure: 10×10 grid, saved to PNG
+#   (b) ASCII CLI preview for first 10 patterns
+# ─────────────────────────────────────────────────────────────────────────────
+print(f"\n{SEP}")
+print(f"  OUTPUT 3 — DEVELOPING POC CHARTS  (100 patterns)")
+print(SEP)
+
+# ── x-axis: position 0=oldest C_{-(N-1)}, N-1=newest C_0 ──────────────────
+x_pos  = np.arange(N, dtype=np.float32)
+x_tick_pos = [0, 9, 19, 29, N-1]
+x_tick_lbl = [f'C_{{-{N-1}}}', f'C_{{-29}}', f'C_{{-19}}', f'C_{{-9}}', 'C_0']
+
+ROWS, COLS = 10, 10
+fig = plt.figure(figsize=(COLS * 3.2, ROWS * 2.0))
+fig.suptitle(
+    f"TopoDevPOC — 100 Random Developing POC Patterns   "
+    f"n={N} pre-market 3-min K-lines\n"
+    f"Total pattern space: 2^{N} = {TOTAL:,}   "
+    f"(Bullish: {HALF:,}  |  Bearish: {HALF:,})",
+    fontsize=10, y=1.005
+)
+
+for i in range(N_SAMPLES):
+    ax  = fig.add_subplot(ROWS, COLS, i + 1)
+    poc = poc_disp[i]
+    is_bull = (dir_bits[i] == 0)
+    color   = '#1a6eb5' if is_bull else '#c0392b'
+    label   = 'B↑' if is_bull else 'B↓'
+
+    # Background shade
+    ax.set_facecolor('#f7f9fc' if is_bull else '#fdf4f4')
+
+    # POC line
+    ax.plot(x_pos, poc, color=color, linewidth=1.2, zorder=3)
+
+    # Mark strict-move positions (non-zero ternary in display coords)
+    # Transition k corresponds to display segment [N-2-k, N-1-k]
+    # Highlight the newer-side node at display index N-1-k = N-1-k
+    strict_k   = np.where(ternary[i] != 0)[0]          # transition indices
+    strict_disp = (N - 1 - strict_k).astype(int)        # display x-positions
+    if strict_disp.size > 0:
+        ax.scatter(strict_disp, poc[strict_disp],
+                   color=color, s=5, zorder=5, linewidths=0)
+
+    # Flat segments (equality)
+    flat_k     = np.where(ternary[i] == 0)[0]
+    flat_disp  = (N - 1 - flat_k).astype(int)
+    if flat_disp.size > 0:
+        ax.scatter(flat_disp, poc[flat_disp],
+                   color='gray', s=3, zorder=4, linewidths=0, alpha=0.5)
+
+    n_strict = int(np.abs(ternary[i]).sum())
+    pid_short = int(pat_ids[i]) % 10**9      # last 9 digits for readability
+    ax.set_title(f"#{i+1} {label}  mv={n_strict}  …{pid_short:09d}",
+                 fontsize=5.5, pad=2, color=color)
+
+    ax.set_xlim(-0.5, N - 0.5)
+    ax.set_xticks(x_tick_pos)
+    ax.set_xticklabels(['←old', '', '', '', 'new→'], fontsize=3.5)
+    ax.tick_params(axis='y', labelsize=3.5)
+    ax.yaxis.set_major_locator(mticker.MaxNLocator(4))
+    for sp in ('top', 'right'):
+        ax.spines[sp].set_visible(False)
+    ax.spines['left'].set_color(color)
+    ax.spines['left'].set_linewidth(1.5)
+    ax.spines['bottom'].set_color('#cccccc')
+
+plt.tight_layout(rect=[0, 0, 1, 1])
+chart_path = "TopoDevPOC_n39_100samples.png"
+plt.savefig(chart_path, dpi=110, bbox_inches='tight')
+plt.close(fig)
+print(f"  [SAVED] {chart_path}")
+
+# ── ASCII CLI chart for first 10 patterns ────────────────────────────────────
+H  = 7          # chart height in rows
+W  = 39         # chart width  = N
+
+print(f"\n  ASCII CLI Charts — first 10 samples (right side = C_0 = newest)\n")
+for i in range(10):
+    poc    = poc_disp[i]
+    d_lbl  = "Bullish" if dir_bits[i] == 0 else "Bearish"
+    pid    = int(pat_ids[i])
+    n_mv   = int(np.abs(ternary[i]).sum())
+    pmin, pmax = poc.min(), poc.max()
+    span   = pmax - pmin if pmax != pmin else 1.0
+
+    # Map each x-position to a row
+    rows   = (H - 1 - ((poc - pmin) / span * (H - 1))).round().astype(int)
+    rows   = np.clip(rows, 0, H - 1)
+
+    grid   = [[' '] * W for _ in range(H)]
+    for j in range(W):
+        r = rows[j]
+        # Strict-move node in the pair ending at display j:
+        # transition index k = N-1-j  (if j < N-1)
+        is_strict = (j < N - 1) and (ternary[i, N - 2 - j] != 0)
+        grid[r][j] = '●' if is_strict else '·'
+    # Connect with horizontal dash where poc is flat
+    for row_idx in range(H):
+        line = grid[row_idx]
+        for j in range(1, W):
+            if line[j] == ' ' and rows[j] == row_idx:
+                line[j] = '-'
+
+    print(f"  [{i+1:2d}] {d_lbl:7s} | ID={pid} | strict_moves={n_mv}/{N_TRANS}")
+    poc_hi = poc[N-1]; poc_lo = poc[0]
+    print(f"       POC range: oldest={poc_lo:.0f}  →  newest={poc_hi:.0f}")
+    print(f"       ┌{'─'*W}┐")
+    for row_idx in range(H):
+        print(f"       │{''.join(grid[row_idx])}│")
+    print(f"       └{'─'*W}┘")
+    sym_preview = ' '.join(sym_matrix[i, :12]) + ' …'
+    print(f"       Σ (first 12): {sym_preview}\n")
+
+# ─────────────────────────────────────────────────────────────────────────────
+# FINAL SUMMARY
+# ���────────────────────────────────────────────────────────────────────────────
+total_ms = (time.perf_counter() - t_sample) * 1e3
+print(SEP)
+print("  SUMMARY")
+print(SEP)
+print(f"  n (candles)                = {N}")
+print(f"  Transitions per pattern    = {N_TRANS}")
+print(f"  Total patterns  [2^{N}]    = {TOTAL:,}")
+print(f"  Bullish         [2^{N-1}]  = {HALF:,}")
+print(f"  Bearish         [2^{N-1}]  = {HALF:,}")
+print(f"  Matrix B_n validated       = {B_n:,}  ✓")
+print(f"  Samples generated          = {N_SAMPLES}")
+print(f"  Chart file                 = {chart_path}")
+print(f"  Compute device             = {DEVICE}")
+print(f"  Wall-clock (sample+decode) = {total_ms:.2f} ms")
+print(SEP)
+print()
+print("  CONVERSION FORMULAS  (tex Sec. V)")
+print("  Symbolic → Ternary:")
+print("    Bullish: '>' → +1,  '=' →  0")
+print("    Bearish: '<' → -1,  '=' →  0")
+print("  Ternary → Symbolic:")
+print("    +1 → '>',  0 → '=',  -1 → '<'")
+print()
+print("  TEMPORAL CONVENTION:")
+print(f"    Chart x-axis: left = C_{{-{N-1}}} (oldest) → right = C_0 (newest)")
+print("    Bullish pattern: POC non-increasing toward right (higher on left)")
+print("    Bearish pattern: POC non-decreasing toward right (lower on left)")
+print(SEP)