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# Kinematic Velocity Vector & Speed Envelope Pro (v4.00)
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Quantitative Newtonian Kinematics & Volatility-Normalized Velocity Suite
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---
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## 1. Summary (Introduction)
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**Velocity Pro** is an institutional-grade kinematic oscillator that models financial market dynamics using classical physics principles. Rather than simply plotting unnormalized price differences, **Velocity Pro decomposes market motion into a Directional Velocity Vector ($\vec{V}$) and an Omnidirectional Speed Scalar ($S$)**, normalized against volatility via the **Average True Range (ATR)**.
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```text
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┌────────────────────────────────────────────────────────────────────────┐
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│ KINEMATIC VELOCITY MODEL │
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├────────────────────────────────────────────────────────────────────────┤
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│ Velocity Vector (V): Directional Net Displacement per Bar in ATR units │
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│ Speed Scalar (S): Total Cumulative Path Length per Bar in ATR units │
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│ Kinematic Envelope: Symmetrical Boundaries (±S) defining 100% Motion │
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│ Efficiency │
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└────────────────────────────────────────────────────────────────────────┘
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```
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### Core Kinematic Principles
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* **The Directional Velocity Vector ($\vec{V}$):** Rendered as a 5-Zone Swapped Thermal Histogram, it measures the directional slope of price displacement.
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* **The Omnidirectional Speed Envelope ($\pm S$):** Symmetrical upper ($+S$) and lower ($-S$) boundary lines measuring the total mechanical work performed by market participants.
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* **Kinematic Efficiency ($\vec{V} = \pm S$):** When the Velocity histogram reaches or touches the outer Speed Envelope line, price is moving in a **100% straight line with zero counter-trend pullbacks**. This flags maximum institutional momentum expansion or parabolic climax exhaustion.
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---
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## 2. Mathematical Foundations & Kinematic Dynamics
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```text
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Upper Speed Envelope: +S (Maximum Path Length)
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═══════════════════════════════════════════════════════════════ clrDarkOrange
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Climax Threshold (+1.0 ATR/bar)
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─────────────────────────────────────────────────────────────── DeepSkyBlue (Bull Climax)
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Flow Threshold (+0.3 ATR/bar)
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - LightSkyBlue (Bull Flow)
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0.0 Baseline (Zero Velocity / Equilibrium)
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─────────────────────────────────────────────────────────────── Gray (Noise)
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Flow Threshold (-0.3 ATR/bar)
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Coral (Bear Flow)
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Climax Threshold (-1.0 ATR/bar)
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─────────────────────────────────────────────────────────────── OrangeRed (Bear Climax)
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Lower Speed Envelope: -S (Maximum Path Length)
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═══════════════════════════════════════════════════════════════ clrDarkOrange
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```
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### 2.1. Volatility Normalization Base (Wilder's ATR)
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$$\text{ATR}_t = \text{Wilder's RMA}(TR_t, P_{\text{ATR}})$$
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*where $P_{\text{ATR}} = \text{InpATRPeriod}$ (default: $14$).*
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---
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### 2.2. The Directional Velocity Vector ($\vec{V}_t$)
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Velocity measures the net displacement of price over lookback window $P_{\text{vel}} = \text{InpVelPeriod}$ expressed in units of ATR per bar:
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$$\Delta P_t = P_t - P_{t - P_{\text{vel}}}$$
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$$\vec{V}_t = \frac{\Delta P_t}{P_{\text{vel}} \cdot \text{ATR}_t}$$
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---
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### 2.3. The Omnidirectional Speed Scalar ($S_t$)
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Speed measures the total gross distance (Path Length) traveled by price regardless of direction, normalized in ATR units:
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$$\text{Path Length}_t = \sum_{k=0}^{P_{\text{vel}}-1} |P_{t-k} - P_{t-k-1}|$$
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$$S_t = \frac{\frac{1}{P_{\text{vel}}} \text{Path Length}_t}{\text{ATR}_t}$$
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### 2.4. Symmetrical Speed Envelope Boundaries
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$$\text{Speed (+)}_t = +S_t, \quad\quad \text{Speed (-)}_t = -S_t$$
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---
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### 2.5. Swapped Thermal 5-Zone Palette Classification
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| State Index | Color | Classification | Kinematic Trigger | Market Interpretation |
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| :---: | :---: | :--- | :--- | :--- |
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| **0.0** | `clrGray` | **Neutral / No Edge** | $\|\vec{V}_t\| < 0.30$ | Low kinetic energy; consolidation chop. |
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| **1.0** | `clrLightSkyBlue` | **Bullish Flow** | $+0.30 \le \vec{V}_t < +1.00$ | Healthy upward velocity; trend expansion active. |
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| **2.0** | `clrDeepSkyBlue` | **Bullish Climax** | $\vec{V}_t \ge +1.00$ | High-speed upward impulse; near maximum efficiency. |
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| **3.0** | `clrCoral` | **Bearish Flow** | $-1.00 < \vec{V}_t \le -0.30$ | Healthy downward velocity; trend expansion active. |
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| **4.0** | `clrOrangeRed` | **Bearish Climax** | $\vec{V}_t \le -1.00$ | High-speed downward impulse; near maximum efficiency. |
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---
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## 3. MQL5 Architecture & Engineering Standards
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```text
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┌────────────────────────────────────────────────────────┐
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│ Velocity_Calculator.mqh │
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│ (Core Math: Computes ATR, Velocity & Speed Envelopes│
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└──────────────────────────┬─────────────────────────────┘
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│ Outputs Velocity, Color, Speed (+/-)
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▼
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┌────────────────────────────────────────────────────────┐
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│ Velocity_Pro.mq5 │
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│ (Unified Wrapper: Native Timeframe & MTF Engine) │
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├──────────────────────────┬─────────────────────────────┤
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│ Buffer Layer (5) │ Centralized Framework │
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│ • Velocity (HISTOGRAM) │ • DataSync_Tools.mqh │
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│ • Color Index (COLOR) │ • MovingAverage_Engine │
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│ • Speed Envelopes (2) │ • 4 Kinematic Levels │
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│ • Signal MA Line (1) │ • Staircase Flat-Force │
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└──────────────────────────┴─────────────────────────────┘
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```
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1. **Modular Kinematic Engine:** `CVelocityCalculator` encapsulates `CATRCalculator` and `CHeikinAshi_Calculator` via composition, guaranteeing zero memory fragmentation.
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2. **2026 MTF Framework with Staircase Solution:** Higher-timeframe kinematic vectors map into synchronized, flat steps on lower-timeframe execution charts via `first_bar_of_forming_htf` dynamic anchoring and `DataSync_Tools.mqh`.
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3. **Signal MA Smoothing Engine:** Integrates `MovingAverage_Engine.mqh` to apply all 8 moving average algorithms (including Volume-Weighted VWMA) over the raw Velocity vector.
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---
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## 4. Parameters Reference
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### Timeframe Settings
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* `InpTimeframe` (*default: `PERIOD_CURRENT`*): Calculation timeframe. When set to `PERIOD_CURRENT`, it operates in native zero-lag mode. When set to a higher timeframe (e.g., `PERIOD_M15`, `PERIOD_H1`), it activates the synchronized MTF engine.
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### Velocity Kinematics Settings
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* `InpVelPeriod` (*default: `3`*): Lookback period ($P_{\text{vel}}$) for computing the velocity displacement vector.
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* `InpATRPeriod` (*default: `14`*): Wilder's lookback period ($P_{\text{ATR}}$) for volatility normalization.
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* `InpThresholdLow` (*default: `0.3`*): Flow Zone threshold ($\pm 0.30$ ATR/bar).
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* `InpThresholdHigh` (*default: `1.0`*): Climax Zone threshold ($\pm 1.00$ ATR/bar).
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* `InpSourcePrice` (*default: `PRICE_CLOSE_STD`*): Price source for velocity calculation.
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* `InpATRSource` (*default: `ATR_SOURCE_STANDARD`*): Volatility source for ATR calculation.
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### Speed Envelope Settings
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* `InpShowSpeed` (*default: `true`*): Toggle visibility of the symmetrical Speed Envelopes ($\pm S$).
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* `InpColorSpeed` (*default: `clrDarkOrange`*): Color of the Speed Envelope lines.
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* `InpStyleSpeed` (*default: `STYLE_SOLID`*): Line style of Speed Envelopes.
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* `InpWidthSpeed` (*default: `1`*): Line thickness of Speed Envelopes.
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### Signal Line Settings
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* `InpShowSignal` (*default: `true`*): Toggle visibility of the smoothed Signal MA line.
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* `InpSignalPeriod` (*default: `5`*): Lookback period for the signal line.
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* `InpSignalType` (*default: `EMA`*): Smoothing algorithm (`SMA`, `EMA`, `SMMA`, `LWMA`, `TMA`, `DEMA`, `TEMA`, `VWMA`).
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* `InpColorSignal` (*default: `clrFireBrick`*): Color applied to the signal line plot.
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### Indicator Levels
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* `InpLevelClimaxPos` (*default: `1.0`*): Bullish Climax level line.
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* `InpLevelFlowPos` (*default: `0.3`*): Bullish Flow level line.
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* `InpLevelFlowNeg` (*default: `-0.3`*): Bearish Flow level line.
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* `InpLevelClimaxNeg` (*default: `-1.0`*): Bearish Climax level line.
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* `InpLevelColor` (*default: `clrSilver`*): Color of horizontal level lines.
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* `InpLevelStyle` (*default: `STYLE_DOT`*): Line style of horizontal level lines.
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---
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## 5. Quantitative Trading Playbooks
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```text
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┌────────────────────────────────────────────────────────────────────────┐
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│ KINEMATIC VELOCITY PLAYBOOKS │
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├────────────────────────────────────────────────────────────────────────┤
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│ 1. 100% Efficiency Climax: Velocity hits Speed Envelope (V = ±S). │
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│ Take profit or prepare mean-reversion. │
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│ 2. Flow Momentum Entry: Velocity breaks > +0.3 (LightSkyBlue) with │
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│ Signal MA cross = Long Continuation. │
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│ 3. Kinematic Squeeze: Speed Envelope contracts to narrow corridor,│
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│ preceding an explosive velocity expansion. │
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└────────────────────────────────────────────────────────────────────────┘
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```
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### 5.1. The 100% Kinematic Efficiency Climax ($\vec{V} = \pm S$)
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* **Context:** Price is surging aggressively.
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* **Condition:** The Velocity histogram bar touches or pushes directly against the **`Speed (+)`** envelope line ($+S$).
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* **Kinematic Interpretation:** Every tick of movement is purely directional with zero structural friction. This represents peak impulse power.
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* **Action:** Tighten trailing stop-losses. When Velocity drops back inside the Speed Envelope and crosses below the Signal MA line, close or scale out long positions.
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### 5.2. Flow Zone Trend Continuation ($\pm 0.30 \dots \pm 1.00$)
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* **Bullish Trigger:** Velocity crosses above `+0.30 (LightSkyBlue)` AND crosses above the Signal MA line $\rightarrow$ High-probability long trend entry.
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* **Bearish Trigger:** Velocity crosses below `-0.30 (Coral)` AND crosses below the Signal MA line $\rightarrow$ High-probability short trend entry.
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### 5.3. Multi-Timeframe Macro Kinematic Filter
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* Attach an **H1-calculated Velocity Pro** onto an **M5 execution chart**.
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* Only take M5 long breakout trades when **H1 Velocity is positive and above +0.30**.
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---
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## 6. Indicator Buffer Map (For Developers & EA Integration)
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| Buffer Index | Name | Type | Description |
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| :---: | :---: | :--- | :--- |
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| **0** | `BufVel` | `INDICATOR_DATA` | Normalized Directional Velocity Vector ($\vec{V}$) |
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| **1** | `BufCol` | `INDICATOR_COLOR_INDEX` | Swapped Thermal 5-Zone Palette Index ($0.0 \dots 4.0$) |
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| **2** | `BufSpeedPos` | `INDICATOR_DATA` | Symmetrical Top Speed Envelope ($+S$) |
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| **3** | `BufSpeedNeg` | `INDICATOR_DATA` | Symmetrical Bottom Speed Envelope ($-S$) |
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| **4** | `BufSignal` | `INDICATOR_DATA` | Smoothed Signal Moving Average Plot |
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*All buffers strictly maintain non-series chronological order (`ArraySetAsSeries = false`), ensuring instant compatibility with Expert Advisors via `iCustom()`.*
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