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# Session-Anchored Kaufman's Adaptive Moving Average (AKAMA) Pro (v1.00)
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Quantitative Session-Anchored Adaptive Equilibrium Baseline Suite
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---
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## 1. Summary (Introduction)
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**KAMA Anchored Pro (AKAMA Pro)** is a professional-grade trend and equilibrium overlay indicator that calculates **Perry Kaufman's Adaptive Moving Average anchored to specific periodic market boundaries**.
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Standard rolling moving averages carry historical baggage from low-liquidity overnight trading sessions (such as the Asian drift), leading to distorted baseline readings during high-volume regular trading hours (RTH). **AKAMA Pro eliminates cross-session pollution** by re-seeding its calculation exactly at key institutional liquidity events—such as the **London Stock Exchange (LSE) Open**, **Frankfurt Open**, **New York Cash Open**, or Weekly/Monthly open boundaries.
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```text
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┌────────────────────────────────────────────────────────────────────────┐
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│ AKAMA BASELINE CONCEPTION │
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├────────────────────────────────────────────────────────────────────────┤
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│ • Resets calculation at defined session opening bar (Anchor Bar) │
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│ • Adapts exclusively using price action within the active session │
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│ • Employs dual Odd/Even buffers to prevent diagonal connecting lines │
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│ • Provides an uncluttered dynamic support/resistance overlay │
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└────────────────────────────────────────────────────────────────────────┘
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```
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### Key Capabilities
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* **Periodic & Custom Session Anchoring:** Supports Daily Session, Weekly Open, Monthly Open, and Custom Institutional Windows (e.g., LSE `08:00 - 16:30`, London/NY Overlap `13:30 - 17:00`).
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* **Intra-Session Efficiency Adaptation:** Dynamic lookback window ($N_{\text{eff}}$) adapts immediately from the opening bar, expanding as session candles accumulate.
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* **Gapped Odd/Even Line Architecture:** Uses dual alternating buffers (`BufKAMA_Odd`, `BufKAMA_Even`) to guarantee seamless visual gaps between historical sessions without chart-crossing line artifacts.
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* **Unified 2026 MTF Framework:** Higher-timeframe session averages (e.g., H1 or H4 AKAMA) map into flat, non-warping steps on intraday execution charts (M1, M5, M15) via `DataSync_Tools.mqh`.
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* **Synthetic Heikin Ashi Support:** Fully compatible with filtered Heikin Ashi price series for noise-free institutional trend tracking.
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---
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## 2. Mathematical Foundations
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```text
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Anchor Reset (Session Open: t = 0)
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│
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├───► Local Lookback: N_eff = min(t - Anchor, ER_Period)
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│
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├───► Direction: | Price(t) - Price(t - N_eff) |
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├───► Volatility: ∑ | Price(t - j) - Price(t - j - 1) |
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│
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└───► Local AKAMA: AKAMA(t - 1) + SC(t) · [ Price(t) - AKAMA(t - 1) ]
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```
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### 2.1. Anchor Boundary Synchronization
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At each session boundary bar ($t = \text{Anchor Bar}$), the calculation re-seeds from the opening price:
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$$\text{AKAMA}_{\text{anchor}} = P_{\text{anchor}}$$
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### 2.2. Intra-Session Lookback Expansion ($N_{\text{eff}}$)
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To prevent calculation errors on the opening bars of a new session, the lookback window expands dynamically:
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$$k_t = t - \text{Anchor Bar}$$
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$$N_{\text{eff}} = \min(k_t, N_{\text{ER}})$$
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*where $N_{\text{ER}} = \text{InpErPeriod}$ (default: $10$).*
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### 2.3. Intra-Session Efficiency Ratio ($ER$)
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Directional net change and total path volatility are computed strictly within the session boundaries:
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$$\text{Direction}_t = | P_t - P_{t - N_{\text{eff}}} |$$
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$$\text{Volatility}_t = \sum_{j=0}^{N_{\text{eff}}-1} | P_{t-j} - P_{t-j-1} |$$
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$$\text{ER}_t = \begin{cases} \frac{\text{Direction}_t}{\text{Volatility}_t}, & \text{if } \text{Volatility}_t > 10^{-9} \\ 0.0, & \text{otherwise} \end{cases}$$
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### 2.4. Local Scaled Smoothing Constant ($\text{SC}_t$)
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The smoothing constant scales between the fastest ($F$) and slowest ($S$) exponential factors:
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$$\alpha_{\text{fast}} = \frac{2}{F + 1}, \quad\quad \alpha_{\text{slow}} = \frac{2}{S + 1}$$
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$$\text{SC}_t = \left[ \text{ER}_t \cdot (\alpha_{\text{fast}} - \alpha_{\text{slow}}) + \alpha_{\text{slow}} \right]^2$$
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### 2.5. Recursive AKAMA Update
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$$\text{AKAMA}_t = \text{AKAMA}_{t-1} + \text{SC}_t \cdot (P_t - \text{AKAMA}_{t-1})$$
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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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│ KAMA_Anchored_Calculator.mqh │
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│ (Core Engine: Stateless Anchor & Local KAMA Engine) │
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└──────────────────────────┬─────────────────────────────┘
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│ Outputs AKAMA Odd/Even Buffers in O(1)
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▼
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┌────────────────────────────────────────────────────────┐
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│ KAMA_Anchored_Pro.mq5 │
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│ (Unified Wrapper: Native Timeframe & MTF Engine) │
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├──────────────────────────┬─────────────────────────────┤
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│ Buffer Layer (2) │ MTF & Session Management │
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│ • BufKAMA_Odd (DATA) │ • DataSync_Tools.mqh │
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│ • BufKAMA_Even (DATA) │ • Staircase Flat-Force │
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│ • Gapped Line Engine │ • Odd/Even Period Toggle │
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└──────────────────────────┴─────────────────────────────┘
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```
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1. **Stateless Deterministic Engine:** `CKamaAnchoredCalculator` processes all session transitions deterministically by comparing timestamps directly, eliminating static memory corruption during real-time tick recalculations.
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2. **Gapped Odd/Even Dual Buffering:**
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* Odd session periods populate `BufKAMA_Odd` while `BufKAMA_Even = EMPTY_VALUE`.
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* Even session periods populate `BufKAMA_Even` while `BufKAMA_Odd = EMPTY_VALUE`.
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* This ensures MetaTrader 5 renders crisp, disconnected segments without diagonal lines connecting session ends to session starts.
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3. **2026 MTF Framework with Staircase Solution:** Higher-timeframe session averages map into flat, synchronized steps on lower-timeframe charts via `first_bar_of_forming_htf` dynamic anchoring and `DataSync_Tools.mqh`.
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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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### Anchor Settings
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* `InpResetPeriod` (*default: `ANCHOR_PERIOD_SESSION`*): Periodic anchor reset mode (`ANCHOR_PERIOD_SESSION`, `ANCHOR_PERIOD_WEEK`, `ANCHOR_PERIOD_MONTH`, `ANCHOR_PERIOD_CUSTOM_SESSION`).
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* `InpTzShift` (*default: `0`*): Timezone offset in hours to align midnight resets with broker server time.
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* `InpCustomStart` (*default: `"08:00"`*): Session start time (`HH:MM`) when using `ANCHOR_PERIOD_CUSTOM_SESSION` (e.g., LSE Open).
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* `InpCustomEnd` (*default: `"17:00"`*): Session end time (`HH:MM`) when using `ANCHOR_PERIOD_CUSTOM_SESSION` (e.g., LSE Close).
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### KAMA Core Settings
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* `InpErPeriod` (*default: `10`*): Lookback period ($N$) for the KAMA Efficiency Ratio.
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* `InpFastEmaPeriod` (*default: `2`*): Fastest smoothing period ($F$) during high directional efficiency.
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* `InpSlowEmaPeriod` (*default: `30`*): Slowest smoothing period ($S$) during consolidation.
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* `InpSourcePrice` (*default: `PRICE_CLOSE_STD`*): Input price series (Standard OHLC or Synthetic Heikin Ashi).
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### Visual Settings
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* `InpColorKAMA` (*default: `clrOrange`*): Color of the AKAMA line.
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* `InpStyleKAMA` (*default: `STYLE_SOLID`*): Line style (Solid, Dash, Dot).
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* `InpWidthKAMA` (*default: `2`*): Line thickness.
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---
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## 5. Institutional Trading Playbooks (The Anchor Baseline Advantage)
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```text
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┌────────────────────────────────────────────────────────────────────────┐
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│ HOW INSTITUTIONS USE ANCHORED KAMA │
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├────────────────────────────────────────────────────────────────────────┤
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│ 1. LSE Open Baseline: Anchored at 08:00 London to capture pure European│
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│ institutional order flow and breakout direction. │
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│ 2. Weekly Fair Value: Anchored to Monday 00:00 to serve as the macro │
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│ institutional benchmark for the trading week. │
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│ 3. Dynamic S/R Flips: Retests of a rising/falling AKAMA provide high- │
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│ conviction pullback entry triggers. │
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└────────────────────────────────────────────────────────────────────────┘
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```
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### 5.1. The London Open Institutional Baseline (LSE Open)
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* **Setup:** Configure `InpResetPeriod = ANCHOR_PERIOD_CUSTOM_SESSION`, `InpCustomStart = "08:00"`, `InpCustomEnd = "16:30"`.
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* **Execution:** At the 08:00 London bell, the AKAMA baseline seeds from the opening print. If initial order flow is strongly bullish, AKAMA accelerates upward with low lag:
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* **Bullish Bias:** Price holds above rising AKAMA $\rightarrow$ Focus exclusively on long intraday continuations.
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* **Bearish Bias:** Price holds below falling AKAMA $\rightarrow$ Focus exclusively on short intraday continuations.
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### 5.2. Weekly Fair Value Equilibrium (Monday Anchor)
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* **Setup:** Set `InpResetPeriod = ANCHOR_PERIOD_WEEK`.
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* **Strategic Context:** Weekly AKAMA represents the volume-independent, efficiency-weighted mean for the entire trading week.
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* **Execution:** Pullbacks from extreme weekly deviations back into the Weekly AKAMA offer high-probability mean-reversion retests or structural continuation bounces.
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### 5.3. Multi-Timeframe Macro Anchor Alignment
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* Attach an **H1-calculated AKAMA** onto an **M5 execution chart**.
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* The flat, synchronized steps clearly show whether intraday pullbacks are respecting the macro institutional baseline, allowing traders to enter with tight risk and macro trend confluence.
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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** | `BufKAMA_Odd` | `INDICATOR_DATA` | Anchored KAMA Values (Odd Session Periods) |
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| **1** | `BufKAMA_Even` | `INDICATOR_DATA` | Anchored KAMA Values (Even Session Periods - Gapped) |
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### MQL5 Reading Example (`iCustom` Helper)
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```mql5
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// Helper to extract the single valid AKAMA value from Odd/Even buffers
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double GetAKAMAValue(const int handle, const int bar_shift)
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{
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double odd[1], even[1];
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if(CopyBuffer(handle, 0, bar_shift, 1, odd) <= 0) return EMPTY_VALUE;
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if(CopyBuffer(handle, 1, bar_shift, 1, even) <= 0) return EMPTY_VALUE;
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if(odd[0] != EMPTY_VALUE && odd[0] > 0.0)
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return odd[0];
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if(even[0] != EMPTY_VALUE && even[0] > 0.0)
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return even[0];
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return EMPTY_VALUE; // Outside active session hours
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}
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```
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*All buffers strictly maintain non-series chronological order (`ArraySetAsSeries = false`), ensuring seamless, high-speed integration with MetaTrader 5 Expert Advisors.*
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