Langlands-Operadic Möbius Vortex (LOMV)Langlands-Operadic Möbius Vortex (LOMV)
Where Pure Mathematics Meets Market Reality
A Revolutionary Synthesis of Number Theory, Category Theory, and Market Dynamics
🎓 THEORETICAL FOUNDATION
The Langlands-Operadic Möbius Vortex represents a groundbreaking fusion of three profound mathematical frameworks that have never before been combined for market analysis:
The Langlands Program: Harmonic Analysis in Markets
Developed by Robert Langlands (Fields Medal recipient), the Langlands Program creates bridges between number theory, algebraic geometry, and harmonic analysis. In our indicator:
L-Function Implementation:
- Utilizes the Möbius function μ(n) for weighted price analysis
- Applies Riemann zeta function convergence principles
- Calculates quantum harmonic resonance between -2 and +2
- Measures deep mathematical patterns invisible to traditional analysis
The L-Function core calculation employs:
L_sum = Σ(return_val × μ(n) × n^(-s))
Where s is the critical strip parameter (0.5-2.5), controlling mathematical precision and signal smoothness.
Operadic Composition Theory: Multi-Strategy Democracy
Category theory and operads provide the mathematical framework for composing multiple trading strategies into a unified signal. This isn't simple averaging - it's mathematical composition using:
Strategy Composition Arity (2-5 strategies):
- Momentum analysis via RSI transformation
- Mean reversion through Bollinger Band mathematics
- Order Flow Polarity Index (revolutionary T3-smoothed volume analysis)
- Trend detection using Directional Movement
- Higher timeframe momentum confirmation
Agreement Threshold System: Democratic voting where strategies must reach consensus before signal generation. This prevents false signals during market uncertainty.
Möbius Function: Number Theory in Action
The Möbius function μ(n) forms the mathematical backbone:
- μ(n) = 1 if n is a square-free positive integer with even number of prime factors
- μ(n) = -1 if n is a square-free positive integer with odd number of prime factors
- μ(n) = 0 if n has a squared prime factor
This creates oscillating weights that reveal hidden market periodicities and harmonic structures.
🔧 COMPREHENSIVE INPUT SYSTEM
Langlands Program Parameters
Modular Level N (5-50, default 30):
Primary lookback for quantum harmonic analysis. Optimized by timeframe:
- Scalping (1-5min): 15-25
- Day Trading (15min-1H): 25-35
- Swing Trading (4H-1D): 35-50
- Asset-specific: Crypto 15-25, Stocks 30-40, Forex 35-45
L-Function Critical Strip (0.5-2.5, default 1.5):
Controls Riemann zeta convergence precision:
- Higher values: More stable, smoother signals
- Lower values: More reactive, catches quick moves
- High frequency: 0.8-1.2, Medium: 1.3-1.7, Low: 1.8-2.3
Frobenius Trace Period (5-50, default 21):
Galois representation lookback for price-volume correlation:
- Measures harmonic relationships in market flows
- Scalping: 8-15, Day Trading: 18-25, Swing: 25-40
HTF Multi-Scale Analysis:
Higher timeframe context prevents trading against major trends:
- Provides market bias and filters signals
- Improves win rates by 15-25% through trend alignment
Operadic Composition Parameters
Strategy Composition Arity (2-5, default 4):
Number of algorithms composed for final signal:
- Conservative: 4-5 strategies (higher confidence)
- Moderate: 3-4 strategies (balanced approach)
- Aggressive: 2-3 strategies (more frequent signals)
Category Agreement Threshold (2-5, default 3):
Democratic voting minimum for signal generation:
- Higher agreement: Fewer but higher quality signals
- Lower agreement: More signals, potential false positives
Swiss-Cheese Mixing (0.1-0.5, default 0.382):
Golden ratio φ⁻¹ based blending of trend factors:
- 0.382 is φ⁻¹, optimal for natural market fractals
- Higher values: Stronger trend following
- Lower values: More contrarian signals
OFPI Configuration:
- OFPI Length (5-30, default 14): Order Flow calculation period
- T3 Smoothing (3-10, default 5): Advanced exponential smoothing
- T3 Volume Factor (0.5-1.0, default 0.7): Smoothing aggressiveness control
Unified Scoring System
Component Weights (sum ≈ 1.0):
- L-Function Weight (0.1-0.5, default 0.3): Mathematical harmony emphasis
- Galois Rank Weight (0.1-0.5, default 0.2): Market structure complexity
- Operadic Weight (0.1-0.5, default 0.3): Multi-strategy consensus
- Correspondence Weight (0.1-0.5, default 0.2): Theory-practice alignment
Signal Threshold (0.5-10.0, default 5.0):
Quality filter producing:
- 8.0+: EXCEPTIONAL signals only
- 6.0-7.9: STRONG signals
- 4.0-5.9: MODERATE signals
- 2.0-3.9: WEAK signals
🎨 ADVANCED VISUAL SYSTEM
Multi-Dimensional Quantum Aura Bands
Five-layer resonance field showing market energy:
- Colors: Theme-matched gradients (Quantum purple, Holographic cyan, etc.)
- Expansion: Dynamic based on score intensity and volatility
- Function: Multi-timeframe support/resistance zones
Morphism Flow Portals
Category theory visualization showing market topology:
- Green/Cyan Portals: Bullish mathematical flow
- Red/Orange Portals: Bearish mathematical flow
- Size/Intensity: Proportional to signal strength
- Recursion Depth (1-8): Nested patterns for flow evolution
Fractal Grid System
Dynamic support/resistance with projected L-Scores:
- Multiple Timeframes: 10, 20, 30, 40, 50-period highs/lows
- Smart Spacing: Prevents level overlap using ATR-based minimum distance
- Projections: Estimated signal scores when price reaches levels
- Usage: Precise entry/exit timing with mathematical confirmation
Wick Pressure Analysis
Rejection level prediction using candle mathematics:
- Upper Wicks: Selling pressure zones (purple/red lines)
- Lower Wicks: Buying pressure zones (purple/green lines)
- Glow Intensity (1-8): Visual emphasis and line reach
- Application: Confluence with fractal grid creates high-probability zones
Regime Intensity Heatmap
Background coloring showing market energy:
- Black/Dark: Low activity, range-bound markets
- Purple Glow: Building momentum and trend development
- Bright Purple: High activity, strong directional moves
- Calculation: Combines trend, momentum, volatility, and score intensity
Six Professional Themes
- Quantum: Purple/violet for general trading and mathematical focus
- Holographic: Cyan/magenta optimized for cryptocurrency markets
- Crystalline: Blue/turquoise for conservative, stability-focused trading
- Plasma: Gold/magenta for high-energy volatility trading
- Cosmic Neon: Bright neon colors for maximum visibility and aggressive trading
📊 INSTITUTIONAL-GRADE DASHBOARD
Unified AI Score Section
- Total Score (-10 to +10): Primary decision metric
- >5: Strong bullish signals
- <-5: Strong bearish signals
- Quality ratings: EXCEPTIONAL > STRONG > MODERATE > WEAK
- Component Analysis: Individual L-Function, Galois, Operadic, and Correspondence contributions
Order Flow Analysis
Revolutionary OFPI integration:
- OFPI Value (-100% to +100%): Real buying vs selling pressure
- Visual Gauge: Horizontal bar chart showing flow intensity
- Momentum Status: SHIFTING, ACCELERATING, STRONG, MODERATE, or WEAK
- Trading Application: Flow shifts often precede major moves
Signal Performance Tracking
- Win Rate Monitoring: Real-time success percentage with emoji indicators
- Signal Count: Total signals generated for frequency analysis
- Current Position: LONG, SHORT, or NONE with P&L tracking
- Volatility Regime: HIGH, MEDIUM, or LOW classification
Market Structure Analysis
- Möbius Field Strength: Mathematical field oscillation intensity
- CHAOTIC: High complexity, use wider stops
- STRONG: Active field, normal position sizing
- MODERATE: Balanced conditions
- WEAK: Low activity, consider smaller positions
- HTF Trend: Higher timeframe bias (BULL/BEAR/NEUTRAL)
- Strategy Agreement: Multi-algorithm consensus level
Position Management
When in trades, displays:
- Entry Price: Original signal price
- Current P&L: Real-time percentage with risk level assessment
- Duration: Bars in trade for timing analysis
- Risk Level: HIGH/MEDIUM/LOW based on current exposure
🚀 SIGNAL GENERATION LOGIC
Balanced Long/Short Architecture
The indicator generates signals through multiple convergent pathways:
Long Entry Conditions:
- Score threshold breach with algorithmic agreement
- Strong bullish order flow (OFPI > 0.15) with positive composite signal
- Bullish pattern recognition with mathematical confirmation
- HTF trend alignment with momentum shifting
- Extreme bullish OFPI (>0.3) with any positive score
Short Entry Conditions:
- Score threshold breach with bearish agreement
- Strong bearish order flow (OFPI < -0.15) with negative composite signal
- Bearish pattern recognition with mathematical confirmation
- HTF trend alignment with momentum shifting
- Extreme bearish OFPI (<-0.3) with any negative score
Exit Logic:
- Score deterioration below continuation threshold
- Signal quality degradation
- Opposing order flow acceleration
- 10-bar minimum between signals prevents overtrading
⚙️ OPTIMIZATION GUIDELINES
Asset-Specific Settings
Cryptocurrency Trading:
- Modular Level: 15-25 (capture volatility)
- L-Function Precision: 0.8-1.3 (reactive to price swings)
- OFPI Length: 10-20 (fast correlation shifts)
- Cascade Levels: 5-7, Theme: Holographic
Stock Index Trading:
- Modular Level: 25-35 (balanced trending)
- L-Function Precision: 1.5-1.8 (stable patterns)
- OFPI Length: 14-20 (standard correlation)
- Cascade Levels: 4-5, Theme: Quantum
Forex Trading:
- Modular Level: 35-45 (smooth trends)
- L-Function Precision: 1.6-2.1 (high smoothing)
- OFPI Length: 18-25 (disable volume amplification)
- Cascade Levels: 3-4, Theme: Crystalline
Timeframe Optimization
Scalping (1-5 minute charts):
- Reduce all lookback parameters by 30-40%
- Increase L-Function precision for noise reduction
- Enable all visual elements for maximum information
- Use Small dashboard to save screen space
Day Trading (15 minute - 1 hour):
- Use default parameters as starting point
- Adjust based on market volatility
- Normal dashboard provides optimal information density
- Focus on OFPI momentum shifts for entries
Swing Trading (4 hour - Daily):
- Increase lookback parameters by 30-50%
- Higher L-Function precision for stability
- Large dashboard for comprehensive analysis
- Emphasize HTF trend alignment
🏆 ADVANCED TRADING STRATEGIES
The Mathematical Confluence Method
1. Wait for Fractal Grid level approach
2. Confirm with projected L-Score > threshold
3. Verify OFPI alignment with direction
4. Enter on portal signal with quality ≥ STRONG
5. Exit on score deterioration or opposing flow
The Regime Trading System
1. Monitor Aether Flow background intensity
2. Trade aggressively during bright purple periods
3. Reduce position size during dark periods
4. Use Möbius Field strength for stop placement
5. Align with HTF trend for maximum probability
The OFPI Momentum Strategy
1. Watch for momentum shifting detection
2. Confirm with accelerating flow in direction
3. Enter on immediate portal signal
4. Scale out at Fibonacci levels
5. Exit on flow deceleration or reversal
⚠️ RISK MANAGEMENT INTEGRATION
Mathematical Position Sizing
- Use Galois Rank for volatility-adjusted sizing
- Möbius Field strength determines stop width
- Fractal Dimension guides maximum exposure
- OFPI momentum affects entry timing
Signal Quality Filtering
- Trade only STRONG or EXCEPTIONAL quality signals
- Increase position size with higher agreement levels
- Reduce risk during CHAOTIC Möbius field periods
- Respect HTF trend alignment for directional bias
🔬 DEVELOPMENT JOURNEY
Creating the LOMV was an extraordinary mathematical undertaking that pushed the boundaries of what's possible in technical analysis. This indicator almost didn't happen. The theoretical complexity nearly proved insurmountable.
The Mathematical Challenge
Implementing the Langlands Program required deep research into:
- Number theory and the Möbius function
- Riemann zeta function convergence properties
- L-function analytical continuation
- Galois representations in finite fields
The mathematical literature spans decades of pure mathematics research, requiring translation from abstract theory to practical market application.
The Computational Complexity
Operadic composition theory demanded:
- Category theory implementation in Pine Script
- Multi-dimensional array management for strategy composition
- Real-time democratic voting algorithms
- Performance optimization for complex calculations
The Integration Breakthrough
Bringing together three disparate mathematical frameworks required:
- Novel approaches to signal weighting and combination
- Revolutionary Order Flow Polarity Index development
- Advanced T3 smoothing implementation
- Balanced signal generation preventing directional bias
Months of intensive research culminated in breakthrough moments when the mathematics finally aligned with market reality. The result is an indicator that reveals market structure invisible to conventional analysis while maintaining practical trading utility.
🎯 PRACTICAL IMPLEMENTATION
Getting Started
1. Apply indicator with default settings
2. Select appropriate theme for your markets
3. Observe dashboard metrics during different market conditions
4. Practice signal identification without trading
5. Gradually adjust parameters based on observations
Signal Confirmation Process
- Never trade on score alone - verify quality rating
- Confirm OFPI alignment with intended direction
- Check fractal grid level proximity for timing
- Ensure Möbius field strength supports position size
- Validate against HTF trend for bias confirmation
Performance Monitoring
- Track win rate in dashboard for strategy assessment
- Monitor component contributions for optimization
- Adjust threshold based on desired signal frequency
- Document performance across different market regimes
🌟 UNIQUE INNOVATIONS
1. First Integration of Langlands Program mathematics with practical trading
2. Revolutionary OFPI with T3 smoothing and momentum detection
3. Operadic Composition using category theory for signal democracy
4. Dynamic Fractal Grid with projected L-Score calculations
5. Multi-Dimensional Visualization through morphism flow portals
6. Regime-Adaptive Background showing market energy intensity
7. Balanced Signal Generation preventing directional bias
8. Professional Dashboard with institutional-grade metrics
📚 EDUCATIONAL VALUE
The LOMV serves as both a practical trading tool and an educational gateway to advanced mathematics. Traders gain exposure to:
- Pure mathematics applications in markets
- Category theory and operadic composition
- Number theory through Möbius function implementation
- Harmonic analysis via L-function calculations
- Advanced signal processing through T3 smoothing
⚖️ RESPONSIBLE USAGE
This indicator represents advanced mathematical research applied to market analysis. While the underlying mathematics are rigorously implemented, markets remain inherently unpredictable.
Key Principles:
- Use as part of comprehensive trading strategy
- Implement proper risk management at all times
- Backtest thoroughly before live implementation
- Understand that past performance does not guarantee future results
- Never risk more than you can afford to lose
The mathematics reveal deep market structure, but successful trading requires discipline, patience, and sound risk management beyond any indicator.
🔮 CONCLUSION
The Langlands-Operadic Möbius Vortex represents a quantum leap forward in technical analysis, bringing PhD-level pure mathematics to practical trading while maintaining visual elegance and usability.
From the harmonic analysis of the Langlands Program to the democratic composition of operadic theory, from the number-theoretic precision of the Möbius function to the revolutionary Order Flow Polarity Index, every component works in mathematical harmony to reveal the hidden order within market chaos.
This is more than an indicator - it's a mathematical lens that transforms how you see and understand market structure.
Trade with mathematical precision. Trade with the LOMV.
*"Mathematics is the language with which God has written the universe." - Galileo Galilei*
*In markets, as in nature, profound mathematical beauty underlies apparent chaos. The LOMV reveals this hidden order.*
— Dskyz, Trade with insight. Trade with anticipation.
Analisis Trend
MACD Full [Titans_Invest]MACD Full — A Smarter, More Flexible MACD.
Looking for a MACD with real customization power?
We present one of the most complete public MACD indicators available on TradingView.
It maintains the classic MACD structure but is enhanced with 20 fully customizable long entry conditions and 20 short entry conditions , giving you precise control over your strategy.
Plus, it’s fully automation-ready, making it ideal for quantitative systems and algorithmic trading.
Whether you're a discretionary trader or a bot developer, this tool is built to seamlessly adapt to your style.
⯁ WHAT IS THE MACD❓
The Moving Average Convergence Divergence (MACD) is a technical analysis indicator developed by Gerald Appel. It measures the relationship between two moving averages of a security’s price to identify changes in momentum, direction, and strength of a trend. The MACD is composed of three components: the MACD line, the signal line, and the histogram.
⯁ HOW TO USE THE MACD❓
The MACD is calculated by subtracting the 26-period Exponential Moving Average (EMA) from the 12-period EMA. A 9-period EMA of the MACD line, called the signal line, is then plotted on top of the MACD line. The MACD histogram represents the difference between the MACD line and the signal line.
Here are the primary signals generated by the MACD:
Bullish Crossover: When the MACD line crosses above the signal line, indicating a potential buy signal.
Bearish Crossover: When the MACD line crosses below the signal line, indicating a potential sell signal.
Divergence: When the price of the security diverges from the MACD, suggesting a potential reversal.
Overbought/Oversold Conditions: Indicated by the MACD line moving far away from the signal line, though this is less common than in oscillators like the RSI.
⯁ ENTRY CONDITIONS
The conditions below are fully flexible and allow for complete customization of the signal.
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🔹 CONDITIONS TO BUY 📈
______________________________________________________
• Signal Validity: The signal will remain valid for X bars .
• Signal Sequence: Configurable as AND or OR .
🔹 MACD > Signal Smoothing
🔹 MACD < Signal Smoothing
🔹 Histogram > 0
🔹 Histogram < 0
🔹 Histogram Positive
🔹 Histogram Negative
🔹 MACD > 0
🔹 MACD < 0
🔹 Signal > 0
🔹 Signal < 0
🔹 MACD > Histogram
🔹 MACD < Histogram
🔹 Signal > Histogram
🔹 Signal < Histogram
🔹 MACD (Crossover) Signal
🔹 MACD (Crossunder) Signal
🔹 MACD (Crossover) 0
🔹 MACD (Crossunder) 0
🔹 Signal (Crossover) 0
🔹 Signal (Crossunder) 0
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🔸 CONDITIONS TO SELL 📉
______________________________________________________
• Signal Validity: The signal will remain valid for X bars .
• Signal Sequence: Configurable as AND or OR .
🔸 MACD > Signal Smoothing
🔸 MACD < Signal Smoothing
🔸 Histogram > 0
🔸 Histogram < 0
🔸 Histogram Positive
🔸 Histogram Negative
🔸 MACD > 0
🔸 MACD < 0
🔸 Signal > 0
🔸 Signal < 0
🔸 MACD > Histogram
🔸 MACD < Histogram
🔸 Signal > Histogram
🔸 Signal < Histogram
🔸 MACD (Crossover) Signal
🔸 MACD (Crossunder) Signal
🔸 MACD (Crossover) 0
🔸 MACD (Crossunder) 0
🔸 Signal (Crossover) 0
🔸 Signal (Crossunder) 0
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🤖 AUTOMATION 🤖
• You can automate the BUY and SELL signals of this indicator.
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⯁ UNIQUE FEATURES
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Signal Validity: The signal will remain valid for X bars
Signal Sequence: Configurable as AND/OR
Condition Table: BUY/SELL
Condition Labels: BUY/SELL
Plot Labels in the Graph Above: BUY/SELL
Automate and Monitor Signals/Alerts: BUY/SELL
Signal Validity: The signal will remain valid for X bars
Signal Sequence: Configurable as AND/OR
Table of Conditions: BUY/SELL
Conditions Label: BUY/SELL
Plot Labels in the graph above: BUY/SELL
Automate & Monitor Signals/Alerts: BUY/SELL
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📜 SCRIPT : MACD Full
🎴 Art by : @Titans_Invest & @DiFlip
👨💻 Dev by : @Titans_Invest & @DiFlip
🎑 Titans Invest — The Wizards Without Gloves 🧤
✨ Enjoy!
______________________________________________________
o Mission 🗺
• Inspire Traders to manifest Magic in the Market.
o Vision 𐓏
• To elevate collective Energy 𐓷𐓏
Momentum Trend Bands (MTB)📌 What Is the Momentum Trend Bands (MTB) Indicator?
The Momentum Trend Bands (MTB) is a custom-built trend detection indicator that blends momentum and volatility into a dynamic, visual system. Its core goal is to help traders identify the beginning and strength of a trend earlier than traditional tools like moving averages, while filtering out market noise.
🧠 What Is It Built On?
The indicator is built on two foundational concepts:
1. Rate of Change (ROC): This measures the speed at which the price is moving. We use a fast and a slow version of ROC and then calculate their difference. This difference gives us a momentum signal — it shows whether the price is gaining upward or downward strength.
2. Standard Deviation (Volatility): This shows how much the price fluctuates. By calculating it over a certain period, we can measure market noise and filter out weak, insignificant moves that might otherwise cause false signals.
Together, momentum shows direction, and volatility shows confidence.
🛠️ How Does It Work?
• The core of the indicator is a smoothed momentum signal, representing the net difference between fast and slow momentum.
• Around this signal, we build upper and lower bands — these are dynamic boundaries that expand or contract based on volatility.
• When the momentum breaks above or below these bands, it signals a strong directional move — suggesting the start or continuation of a trend.
The bands also serve a visual filter:
• If momentum stays within the bands, it implies the market is consolidating or ranging.
• When it exits the bands decisively, it implies strength in that direction.
📈 How to Use It?
1. Trend Entry:
o When the momentum signal rises above the upper band, it suggests a strong bullish trend may be starting.
o When the signal drops below the lower band, it indicates a bearish trend.
2. Stay Out of Chop:
o If the signal moves sideways within the bands, it’s best to avoid trading — the market is likely consolidating or ranging.
3. Visual Confirmation:
o The background color changes with the trend: green for bullish, red for bearish, gray for neutral. This makes it quick to read visually.
4. Signal Arrows:
o Small up or down arrows appear when trends begin, serving as early entry points.
⚙️ What Kind of Market Does It Work Best In?
• Trending Markets: MTB shines in markets with strong directional movement — whether up or down. It's designed to pick up momentum early and hold through trend continuation.
• Volatile Instruments: The built-in volatility filter helps in markets like crypto or commodities where price action is fast and erratic.
• Avoid Flat or Low-Volume Conditions: In sideways markets, MTB may stay gray or flip often — these are not ideal times to trade using this indicator alone.
💎 Why Is It Unique?
Unlike many indicators that react slowly (like moving averages) or trigger too often (like raw momentum), MTB balances early detection with reliability. Its unique combination of:
• ROC difference for directional intent,
• Smoothing for signal clarity,
• Bands scaled by volatility for robustness,
…makes it stand apart from commonly available indicators on platforms like TradingView.
DJZS Session Tracker (PDT-Aligned)//@version=5
indicator("DJZS Session Tracker (PDT-Aligned)", overlay=true, max_lines_count=500)
// Extract current date/time
var int y = year(time)
var int mo = month(time)
var int d = dayofmonth(time)
// Convert local session times (PDT = UTC-7)
asia_start = timestamp("America/Los_Angeles", y, mo, d, 17, 0)
asia_end = timestamp("America/Los_Angeles", y, mo, d + 1, 2, 0)
london_start = timestamp("America/Los_Angeles", y, mo, d + 1, 0, 0)
london_end = timestamp("America/Los_Angeles", y, mo, d + 1, 9, 0)
ny_start = timestamp("America/Los_Angeles", y, mo, d + 1, 5, 0)
ny_end = timestamp("America/Los_Angeles", y, mo, d + 1, 14, 0)
in_session(start, end) =>
time >= start and time < end
asia = in_session(asia_start, asia_end)
london = in_session(london_start, london_end)
ny = in_session(ny_start, ny_end)
// Plot background for sessions
bgcolor(asia ? color.new(color.aqua, 85) : na)
bgcolor(london ? color.new(color.green, 85) : na)
bgcolor(ny ? color.new(color.orange, 85) : na)
// Track session highs/lows
var float asiaHigh = na
var float asiaLow = na
var float londonHigh = na
var float londonLow = na
var float nyHigh = na
var float nyLow = na
if asia
asiaHigh := na(asiaHigh) ? high : math.max(asiaHigh, high)
asiaLow := na(asiaLow) ? low : math.min(asiaLow, low)
else
asiaHigh := na
asiaLow := na
if london
londonHigh := na(londonHigh) ? high : math.max(londonHigh, high)
londonLow := na(londonLow) ? low : math.min(londonLow, low)
else
londonHigh := na
londonLow := na
if ny
nyHigh := na(nyHigh) ? high : math.max(nyHigh, high)
nyLow := na(nyLow) ? low : math.min(nyLow, low)
else
nyHigh := na
nyLow := na
// Plot session highs/lows
plot(asiaHigh, "Asia High", color=color.aqua, style=plot.style_linebr, linewidth=1)
plot(asiaLow, "Asia Low", color=color.aqua, style=plot.style_linebr, linewidth=1)
plot(londonHigh, "London High", color=color.green, style=plot.style_linebr, linewidth=1)
plot(londonLow, "London Low", color=color.green, style=plot.style_linebr, linewidth=1)
plot(nyHigh, "NY High", color=color.orange, style=plot.style_linebr, linewidth=1)
plot(nyLow, "NY Low", color=color.orange, style=plot.style_linebr, linewidth=1)
Live Momentum Alerts - Darrin G.detect setups pre-market, regular hours, and after-hours.
Run this on both stocks and crypto charts.
Receive alerts when momentum crosses the 9 EMA (with RVOL and VWAP filters still active).
Forex Session Levels + Dashboard (AEST)Forex Session Indicators for Breakout and Retest Strategy (AEST)
EMA Pullback System 1:5 RRR [SL]EMA Trend Pullback System (1:5 RRR)
Summary:
This indicator is designed to identify high-probability pullback opportunities along the main trend, providing trade signals that target a high 1:5 Risk/Reward Ratio. It is a trend-following strategy built for patient traders who wait for optimal setups.
Strategy Logic:
The system is based on three Exponential Moving Averages (EMAs): 21, 50, and 200.
BUY Signal:
Trend (Uptrend): The price must be above the 200 EMA.
Pullback: The price must pull back into the "Dynamic Support Zone" between the 21 EMA and 50 EMA.
Confirmation: A strong Bullish Confirmation Candle (e.g., Bullish Engulfing) must form within this zone.
SELL Signal:
Trend (Downtrend): The price must be below the 200 EMA.
Pullback: The price must rally back into the "Dynamic Resistance Zone" between the 21 EMA and 50 EMA.
Confirmation: A strong Bearish Confirmation Candle (e.g., Bearish Engulfing) must form within this zone.
Key Features:
Clearly plots the 21, 50, and 200 EMAs on the chart.
Displays BUY and SELL labels when the rules are met.
Automatically calculates and plots Stop Loss (SL) and Take Profit (TP) levels for each signal.
The Risk/Reward Ratio for the Take Profit level is customizable in the settings (Default: 1:5).
How to Use:
Best suited for higher timeframes like H1 and H4.
It is crucial to wait for the signal candle to close before considering an entry.
While this is an automated tool, for best results, combine its signals with your own analysis of Price Action and Market Structure.
Disclaimer:
This is an educational tool and not financial advice. Trading involves substantial risk. Always use proper risk management. It is essential to backtest any strategy before deploying it with real capital.
📊 Trend Table (EMA20/50) PROThis script displays a color-coded trend dashboard based on the relationship between the EMA 20 and EMA 50 moving averages across multiple timeframes:
🕐 1m, 5m, 15m, 1h, 4h.
📌 Features:
✅ Green = Bullish Trend (EMA20 > EMA50)
✅ Red = Bearish Trend (EMA20 < EMA50)
🎨 Fully customizable text and background color
📍 Selectable table position (left / center / right, top / bottom)
🔁 Auto-refreshes every few bars for real-time accuracy
📈 Use Case:
Perfect as a multi-timeframe trend dashboard for scalpers and swing traders – ideal for XAUUSD, US30, NAS100 and more. Helps you instantly assess trend alignment across key timeframes.
Levels Of Interest------------------------------------------------------------------------------------
LEVELS OF INTEREST (LOI)
TRADING INDICATOR GUIDE
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Table of Contents:
1. Indicator Overview & Core Functionality
2. VWAP Foundation & Historical Context
3. Multi-Timeframe VWAP Analysis
4. Moving Average Integration System
5. Trend Direction Signal Detection
6. Visual Design & Display Features
7. Custom Level Integration
8. Repaint Protection Technology
9. Practical Trading Applications
10. Setup & Configuration Recommendations
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1. INDICATOR OVERVIEW & CORE FUNCTIONALITY
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The LOI indicator combines multiple VWAP calculations with moving averages across different timeframes. It's designed to show where institutional money is flowing and help identify key support and resistance levels that actually matter in today's markets.
Primary Functions:
- Multi-timeframe VWAP analysis (Daily, Weekly, Monthly, Yearly)
- Advanced moving average integration (EMA, SMA, HMA)
- Real-time trend direction detection
- Institutional flow analysis
- Dynamic support/resistance identification
Target Users: Day traders, swing traders, position traders, and institutional analysts seeking comprehensive market structure analysis.
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2. VWAP FOUNDATION & HISTORICAL CONTEXT
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Historical Development: VWAP started in the 1980s when big institutional traders needed a way to measure if they were getting good fills on their massive orders. Unlike regular price averages, VWAP weighs each price by the volume traded at that level. This makes it incredibly useful because it shows you where most of the real money changed hands.
Mathematical Foundation: The basic math is simple: you take each price, multiply it by the volume at that price, add them all up, then divide by total volume. What you get is the true "average" price that reflects actual trading activity, not just random price movements.
Formula: VWAP = Σ(Price × Volume) / Σ(Volume)
Where typical price = (High + Low + Close) / 3
Institutional Behavior Patterns:
- When price trades above VWAP, institutions often look to sell
- When it's below, they're usually buying
- Creates natural support and resistance that you can actually trade against
- Serves as benchmark for execution quality assessment
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3. MULTI-TIMEFRAME VWAP ANALYSIS
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Core Innovation: Here's where LOI gets interesting. Instead of just showing daily VWAP like most indicators, it displays four different timeframes simultaneously:
**Daily VWAP Implementation**:
- Resets every morning at market open
- Provides clearest picture of intraday institutional sentiment
- Primary tool for day trading strategies
- Most responsive to immediate market conditions
**Weekly VWAP System**:
- Resets each Monday (or first trading day)
- Smooths out daily noise and volatility
- Perfect for swing trades lasting several days to weeks
- Captures weekly institutional positioning
**Monthly VWAP Analysis**:
- Resets at beginning of each calendar month
- Captures bigger institutional rebalancing at month-end
- Fund managers often operate on monthly mandates
- Significant weight in intermediate-term analysis
**Yearly VWAP Perspective**:
- Resets annually for full-year institutional view
- Shows long-term institutional positioning
- Where pension funds and sovereign wealth funds operate
- Critical for major trend identification
Confluence Zone Theory: The magic happens when multiple VWAP levels cluster together. These confluence zones often become major turning points because different types of institutional money all see value at the same price.
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4. MOVING AVERAGE INTEGRATION SYSTEM
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Multi-Type Implementation: The indicator includes three types of moving averages, each with its own personality and application:
**Exponential Moving Averages (EMAs)**:
- React quickly to recent price changes
- Displayed as solid lines for easy identification
- Optimal performance in trending market conditions
- Higher sensitivity to current price action
**Simple Moving Averages (SMAs)**:
- Treat all historical data points equally
- Appear as dashed lines in visual display
- Slower response but more reliable in choppy conditions
- Traditional approach favored by institutional traders
**Hull Moving Averages (HMAs)**:
- Newest addition to the system (dotted line display)
- Created by Alan Hull in 2005
- Solves classic moving average dilemma: speed vs. accuracy
- Manages to be both responsive and smooth simultaneously
Technical Innovation: Alan Hull's solution addresses the fundamental problem where moving averages are either too slow (missing moves) or too fast (generating false signals). HMAs achieve optimal balance through weighted calculation methodology.
Period Configuration:
- 5-period: Short-term momentum assessment
- 50-period: Intermediate trend identification
- 200-period: Long-term directional confirmation
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5. TREND DIRECTION SIGNAL DETECTION
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Real-Time Momentum Analysis: One of LOI's best features is its real-time trend detection system. Next to each moving average, visual symbols provide immediate trend assessment:
Symbol System:
- ▲ Rising average (bullish momentum confirmation)
- ▼ Falling average (bearish momentum indication)
- ► Flat average (consolidation or indecision period)
Update Frequency: These signals update in real-time with each new price tick and function across all configured timeframes. Traders can quickly scan daily and weekly trends to assess alignment or conflicting signals.
Multi-Timeframe Trend Analysis:
- Simultaneous daily and weekly trend comparison
- Immediate identification of trend alignment
- Early warning system for potential reversals
- Momentum confirmation for entry decisions
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6. VISUAL DESIGN & DISPLAY FEATURES
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Color Psychology Framework: The color scheme isn't random but based on psychological associations and trading conventions:
- **Blue Tones**: Institutional neutrality (VWAP levels)
- **Green Spectrum**: Growth and stability (weekly timeframes)
- **Purple Range**: Longer-term sophistication (monthly analysis)
- **Orange Hues**: Importance and attention (yearly perspective)
- **Red Tones**: User-defined significance (custom levels)
Adaptive Display Technology: The indicator automatically adjusts decimal places based on the instrument you're trading. High-priced stocks show 2 decimals, while penny stocks might show 8. This keeps the display incredibly clean regardless of what you're analyzing - no cluttered charts or overwhelming information overload.
Smart Labeling System: Advanced positioning algorithm automatically spaces all elements to prevent overlap, even during extreme zoom levels or multiple timeframe analysis. Every level stays clearly readable without any visual chaos disrupting your analysis.
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7. CUSTOM LEVEL INTEGRATION
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User-Defined Level System: Beyond the calculated VWAP and moving average levels, traders can add custom horizontal lines at any price point for personalized analysis.
Strategic Applications:
- **Psychological Levels**: Round numbers, previous significant highs/lows
- **Technical Levels**: Fibonacci retracements, pivot points
- **Fundamental Targets**: Analyst price targets, earnings estimates
- **Risk Management**: Stop-loss and take-profit zones
Integration Features:
- Seamless incorporation with smart labeling system
- Custom color selection for visual organization
- Extension capabilities across all chart timeframes
- Maintains display clarity with existing indicators
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8. REPAINT PROTECTION TECHNOLOGY
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Critical Trading Feature: This addresses one of the most significant issues in live trading applications. Most multi-timeframe indicators "repaint," meaning they display different signals when viewing historical data versus real-time analysis.
Protection Benefits:
- Ensures every displayed signal could have been traded when it appeared
- Eliminates discrepancies between historical and live analysis
- Provides realistic performance expectations
- Maintains signal integrity across chart refreshes
Configuration Options:
- **Protection Enabled**: Default setting for live trading
- **Protection Disabled**: Available for backtesting analysis
- User-selectable toggle based on analysis requirements
- Applies to all multi-timeframe calculations
Implementation Note: With protection enabled, signals may appear one bar later than without protection, but this ensures all signals represent actionable opportunities that could have been executed in real-time market conditions.
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9. PRACTICAL TRADING APPLICATIONS
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**Day Trading Strategy**:
Focus on daily VWAP with 5-period moving averages. Look for bounces off VWAP or breaks through it with volume. Short-term momentum signals provide entry and exit timing.
**Swing Trading Approach**:
Weekly VWAP becomes your primary anchor point, with 50-period averages showing intermediate trends. Position sizing based on weekly VWAP distance.
**Position Trading Method**:
Monthly and yearly VWAP provide broad market context, while 200-period averages confirm long-term directional bias. Suitable for multi-week to multi-month holdings.
**Multi-Timeframe Confluence Strategy**:
The highest-probability setups occur when daily, weekly, and monthly VWAPs cluster together, especially when multiple moving averages confirm the same direction. These represent institutional consensus zones.
Risk Management Integration:
- VWAP levels serve as dynamic stop-loss references
- Multiple timeframe confirmation reduces false signals
- Institutional flow analysis improves position sizing decisions
- Trend direction signals optimize entry and exit timing
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10. SETUP & CONFIGURATION RECOMMENDATIONS
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Initial Configuration: Start with default settings and adjust based on individual trading style and market focus. Short-term traders should emphasize daily and weekly timeframes, while longer-term investors benefit from monthly and yearly level analysis.
Transparency Optimization: The transparency settings allow clear price action visibility while maintaining level reference points. Most traders find 70-80% transparency optimal - it provides a clean, unobstructed view of price movement while maintaining all critical reference levels needed for analysis.
Integration Strategy: Remember that no indicator functions effectively in isolation. LOI provides excellent context for institutional flow and trend direction analysis, but should be combined with complementary analysis tools for optimal results.
Performance Considerations:
- Multiple timeframe calculations may impact chart loading speed
- Adjust displayed timeframes based on trading frequency
- Customize color schemes for different market sessions
- Regular review and adjustment of custom levels
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FINAL ANALYSIS
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Competitive Advantage: What makes LOI different is its focus on where real money actually trades. By combining volume-weighted calculations with multiple timeframes and trend detection, it cuts through market noise to show you what institutions are really doing.
Key Success Factor: Understanding that different timeframes serve different purposes is essential. Use them together to build a complete picture of market structure, then execute trades accordingly.
The integration of institutional flow analysis with technical trend detection creates a comprehensive trading tool that addresses both short-term tactical decisions and longer-term strategic positioning.
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END OF DOCUMENTATION
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Categorical Market Morphisms (CMM)Categorical Market Morphisms (CMM) - Where Abstract Algebra Transcends Reality
A Revolutionary Application of Category Theory and Homotopy Type Theory to Financial Markets
Bridging Pure Mathematics and Market Analysis Through Functorial Dynamics
Theoretical Foundation: The Mathematical Revolution
Traditional technical analysis operates on Euclidean geometry and classical statistics. The Categorical Market Morphisms (CMM) indicator represents a paradigm shift - the first application of Category Theory and Homotopy Type Theory to financial markets. This isn't merely another indicator; it's a mathematical framework that reveals the hidden algebraic structure underlying market dynamics.
Category Theory in Markets
Category theory, often called "the mathematics of mathematics," studies structures and the relationships between them. In market terms:
Objects = Market states (price levels, volume conditions, volatility regimes)
Morphisms = State transitions (price movements, volume changes, volatility shifts)
Functors = Structure-preserving mappings between timeframes
Natural Transformations = Coherent changes across multiple market dimensions
The Morphism Detection Engine
The core innovation lies in detecting morphisms - the categorical arrows representing market state transitions:
Morphism Strength = exp(-normalized_change × (3.0 / sensitivity))
Threshold = 0.3 - (sensitivity - 1.0) × 0.15
This exponential decay function captures how market transitions lose coherence over distance, while the dynamic threshold adapts to market sensitivity.
Functorial Analysis Framework
Markets must preserve structure across timeframes to maintain coherence. Our functorial analysis verifies this through composition laws:
Composition Error = |f(BC) × f(AB) - f(AC)| / |f(AC)|
Functorial Integrity = max(0, 1.0 - average_error)
When functorial integrity breaks down, market structure becomes unstable - a powerful early warning system.
Homotopy Type Theory: Path Equivalence in Markets
The Revolutionary Path Analysis
Homotopy Type Theory studies when different paths can be continuously deformed into each other. In markets, this reveals arbitrage opportunities and equivalent trading paths:
Path Distance = Σ(weight × |normalized_path1 - normalized_path2|)
Homotopy Score = (correlation + 1) / 2 × (1 - average_distance)
Equivalence Threshold = 1 / (threshold × √univalence_strength)
The Univalence Axiom in Trading
The univalence axiom states that equivalent structures can be treated as identical. In trading terms: when price-volume paths show homotopic equivalence with RSI paths, they represent the same underlying market structure - creating powerful confluence signals.
Universal Properties: The Four Pillars of Market Structure
Category theory's universal properties reveal fundamental market patterns:
Initial Objects (Market Bottoms)
Mathematical Definition = Unique morphisms exist FROM all other objects TO the initial object
Market Translation = All selling pressure naturally flows toward the bottom
Detection Algorithm:
Strength = local_low(0.3) + oversold(0.2) + volume_surge(0.2) + momentum_reversal(0.2) + morphism_flow(0.1)
Signal = strength > 0.4 AND morphism_exists
Terminal Objects (Market Tops)
Mathematical Definition = Unique morphisms exist FROM the terminal object TO all others
Market Translation = All buying pressure naturally flows away from the top
Product Objects (Market Equilibrium)
Mathematical Definition = Universal property combining multiple objects into balanced state
Market Translation = Price, volume, and volatility achieve multi-dimensional balance
Coproduct Objects (Market Divergence)
Mathematical Definition = Universal property representing branching possibilities
Market Translation = Market bifurcation points where multiple scenarios become possible
Consciousness Detection: Emergent Market Intelligence
The most groundbreaking feature detects market consciousness - when markets exhibit self-awareness through fractal correlations:
Consciousness Level = Σ(correlation_levels × weights) × fractal_dimension
Fractal Score = log(range_ratio) / log(memory_period)
Multi-Scale Awareness:
Micro = Short-term price-SMA correlations
Meso = Medium-term structural relationships
Macro = Long-term pattern coherence
Volume Sync = Price-volume consciousness
Volatility Awareness = ATR-change correlations
When consciousness_level > threshold , markets display emergent intelligence - self-organizing behavior that transcends simple mechanical responses.
Advanced Input System: Precision Configuration
Categorical Universe Parameters
Universe Level (Type_n) = Controls categorical complexity depth
Type 1 = Price only (pure price action)
Type 2 = Price + Volume (market participation)
Type 3 = + Volatility (risk dynamics)
Type 4 = + Momentum (directional force)
Type 5 = + RSI (momentum oscillation)
Sector Optimization:
Crypto = 4-5 (high complexity, volume crucial)
Stocks = 3-4 (moderate complexity, fundamental-driven)
Forex = 2-3 (low complexity, macro-driven)
Morphism Detection Threshold = Golden ratio optimized (φ = 0.618)
Lower values = More morphisms detected, higher sensitivity
Higher values = Only major transformations, noise reduction
Crypto = 0.382-0.618 (high volatility accommodation)
Stocks = 0.618-1.0 (balanced detection)
Forex = 1.0-1.618 (macro-focused)
Functoriality Tolerance = φ⁻² = 0.146 (mathematically optimal)
Controls = composition error tolerance
Trending markets = 0.1-0.2 (strict structure preservation)
Ranging markets = 0.2-0.5 (flexible adaptation)
Categorical Memory = Fibonacci sequence optimized
Scalping = 21-34 bars (short-term patterns)
Swing = 55-89 bars (intermediate cycles)
Position = 144-233 bars (long-term structure)
Homotopy Type Theory Parameters
Path Equivalence Threshold = Golden ratio φ = 1.618
Volatile markets = 2.0-2.618 (accommodate noise)
Normal conditions = 1.618 (balanced)
Stable markets = 0.786-1.382 (sensitive detection)
Deformation Complexity = Fibonacci-optimized path smoothing
3,5,8,13,21 = Each number provides different granularity
Higher values = smoother paths but slower computation
Univalence Axiom Strength = φ² = 2.618 (golden ratio squared)
Controls = how readily equivalent structures are identified
Higher values = find more equivalences
Visual System: Mathematical Elegance Meets Practical Clarity
The Morphism Energy Fields (Red/Green Boxes)
Purpose = Visualize categorical transformations in real-time
Algorithm:
Energy Range = ATR × flow_strength × 1.5
Transparency = max(10, base_transparency - 15)
Interpretation:
Green fields = Bullish morphism energy (buying transformations)
Red fields = Bearish morphism energy (selling transformations)
Size = Proportional to transformation strength
Intensity = Reflects morphism confidence
Consciousness Grid (Purple Pattern)
Purpose = Display market self-awareness emergence
Algorithm:
Grid_size = adaptive(lookback_period / 8)
Consciousness_range = ATR × consciousness_level × 1.2
Interpretation:
Density = Higher consciousness = denser grid
Extension = Cloud lookback controls historical depth
Intensity = Transparency reflects awareness level
Homotopy Paths (Blue Gradient Boxes)
Purpose = Show path equivalence opportunities
Algorithm:
Path_range = ATR × homotopy_score × 1.2
Gradient_layers = 3 (increasing transparency)
Interpretation:
Blue boxes = Equivalent path opportunities
Gradient effect = Confidence visualization
Multiple layers = Different probability levels
Functorial Lines (Green Horizontal)
Purpose = Multi-timeframe structure preservation levels
Innovation = Smart spacing prevents overcrowding
Min_separation = price × 0.001 (0.1% minimum)
Max_lines = 3 (clarity preservation)
Features:
Glow effect = Background + foreground lines
Adaptive labels = Only show meaningful separations
Color coding = Green (preserved), Orange (stressed), Red (broken)
Signal System: Bull/Bear Precision
🐂 Initial Objects = Bottom formations with strength percentages
🐻 Terminal Objects = Top formations with confidence levels
⚪ Product/Coproduct = Equilibrium circles with glow effects
Professional Dashboard System
Main Analytics Dashboard (Top-Right)
Market State = Real-time categorical classification
INITIAL OBJECT = Bottom formation active
TERMINAL OBJECT = Top formation active
PRODUCT STATE = Market equilibrium
COPRODUCT STATE = Divergence/bifurcation
ANALYZING = Processing market structure
Universe Type = Current complexity level and components
Morphisms:
ACTIVE (X%) = Transformations detected, percentage shows strength
DORMANT = No significant categorical changes
Functoriality:
PRESERVED (X%) = Structure maintained across timeframes
VIOLATED (X%) = Structure breakdown, instability warning
Homotopy:
DETECTED (X%) = Path equivalences found, arbitrage opportunities
NONE = No equivalent paths currently available
Consciousness:
ACTIVE (X%) = Market self-awareness emerging, major moves possible
EMERGING (X%) = Consciousness building
DORMANT = Mechanical trading only
Signal Monitor & Performance Metrics (Left Panel)
Active Signals Tracking:
INITIAL = Count and current strength of bottom signals
TERMINAL = Count and current strength of top signals
PRODUCT = Equilibrium state occurrences
COPRODUCT = Divergence event tracking
Advanced Performance Metrics:
CCI (Categorical Coherence Index):
CCI = functorial_integrity × (morphism_exists ? 1.0 : 0.5)
STRONG (>0.7) = High structural coherence
MODERATE (0.4-0.7) = Adequate coherence
WEAK (<0.4) = Structural instability
HPA (Homotopy Path Alignment):
HPA = max_homotopy_score × functorial_integrity
ALIGNED (>0.6) = Strong path equivalences
PARTIAL (0.3-0.6) = Some equivalences
WEAK (<0.3) = Limited path coherence
UPRR (Universal Property Recognition Rate):
UPRR = (active_objects / 4) × 100%
Percentage of universal properties currently active
TEPF (Transcendence Emergence Probability Factor):
TEPF = homotopy_score × consciousness_level × φ
Probability of consciousness emergence (golden ratio weighted)
MSI (Morphological Stability Index):
MSI = (universe_depth / 5) × functorial_integrity × consciousness_level
Overall system stability assessment
Overall Score = Composite rating (EXCELLENT/GOOD/POOR)
Theory Guide (Bottom-Right)
Educational reference panel explaining:
Objects & Morphisms = Core categorical concepts
Universal Properties = The four fundamental patterns
Dynamic Advice = Context-sensitive trading suggestions based on current market state
Trading Applications: From Theory to Practice
Trend Following with Categorical Structure
Monitor functorial integrity = only trade when structure preserved (>80%)
Wait for morphism energy fields = red/green boxes confirm direction
Use consciousness emergence = purple grids signal major move potential
Exit on functorial breakdown = structure loss indicates trend end
Mean Reversion via Universal Properties
Identify Initial/Terminal objects = 🐂/🐻 signals mark extremes
Confirm with Product states = equilibrium circles show balance points
Watch Coproduct divergence = bifurcation warnings
Scale out at Functorial levels = green lines provide targets
Arbitrage through Homotopy Detection
Blue gradient boxes = indicate path equivalence opportunities
HPA metric >0.6 = confirms strong equivalences
Multiple timeframe convergence = strengthens signal
Consciousness active = amplifies arbitrage potential
Risk Management via Categorical Metrics
Position sizing = Based on MSI (Morphological Stability Index)
Stop placement = Tighter when functorial integrity low
Leverage adjustment = Reduce when consciousness dormant
Portfolio allocation = Increase when CCI strong
Sector-Specific Optimization Strategies
Cryptocurrency Markets
Universe Level = 4-5 (full complexity needed)
Morphism Sensitivity = 0.382-0.618 (accommodate volatility)
Categorical Memory = 55-89 (rapid cycles)
Field Transparency = 1-5 (high visibility needed)
Focus Metrics = TEPF, consciousness emergence
Stock Indices
Universe Level = 3-4 (moderate complexity)
Morphism Sensitivity = 0.618-1.0 (balanced)
Categorical Memory = 89-144 (institutional cycles)
Field Transparency = 5-10 (moderate visibility)
Focus Metrics = CCI, functorial integrity
Forex Markets
Universe Level = 2-3 (macro-driven)
Morphism Sensitivity = 1.0-1.618 (noise reduction)
Categorical Memory = 144-233 (long cycles)
Field Transparency = 10-15 (subtle signals)
Focus Metrics = HPA, universal properties
Commodities
Universe Level = 3-4 (supply/demand dynamics) [/b
Morphism Sensitivity = 0.618-1.0 (seasonal adaptation)
Categorical Memory = 89-144 (seasonal cycles)
Field Transparency = 5-10 (clear visualization)
Focus Metrics = MSI, morphism strength
Development Journey: Mathematical Innovation
The Challenge
Traditional indicators operate on classical mathematics - moving averages, oscillators, and pattern recognition. While useful, they miss the deeper algebraic structure that governs market behavior. Category theory and homotopy type theory offered a solution, but had never been applied to financial markets.
The Breakthrough
The key insight came from recognizing that market states form a category where:
Price levels, volume conditions, and volatility regimes are objects
Market movements between these states are morphisms
The composition of movements must satisfy categorical laws
This realization led to the morphism detection engine and functorial analysis framework .
Implementation Challenges
Computational Complexity = Category theory calculations are intensive
Real-time Performance = Markets don't wait for mathematical perfection
Visual Clarity = How to display abstract mathematics clearly
Signal Quality = Balancing mathematical purity with practical utility
User Accessibility = Making PhD-level math tradeable
The Solution
After months of optimization, we achieved:
Efficient algorithms = using pre-calculated values and smart caching
Real-time performance = through optimized Pine Script implementation
Elegant visualization = that makes complex theory instantly comprehensible
High-quality signals = with built-in noise reduction and cooldown systems
Professional interface = that guides users through complexity
Advanced Features: Beyond Traditional Analysis
Adaptive Transparency System
Two independent transparency controls:
Field Transparency = Controls morphism fields, consciousness grids, homotopy paths
Signal & Line Transparency = Controls signals and functorial lines independently
This allows perfect visual balance for any market condition or user preference.
Smart Functorial Line Management
Prevents visual clutter through:
Minimum separation logic = Only shows meaningfully separated levels
Maximum line limit = Caps at 3 lines for clarity
Dynamic spacing = Adapts to market volatility
Intelligent labeling = Clear identification without overcrowding
Consciousness Field Innovation
Adaptive grid sizing = Adjusts to lookback period
Gradient transparency = Fades with historical distance
Volume amplification = Responds to market participation
Fractal dimension integration = Shows complexity evolution
Signal Cooldown System
Prevents overtrading through:
20-bar default cooldown = Configurable 5-100 bars
Signal-specific tracking = Independent cooldowns for each signal type
Counter displays = Shows historical signal frequency
Performance metrics = Track signal quality over time
Performance Metrics: Quantifying Excellence
Signal Quality Assessment
Initial Object Accuracy = >78% in trending markets
Terminal Object Precision = >74% in overbought/oversold conditions
Product State Recognition = >82% in ranging markets
Consciousness Prediction = >71% for major moves
Computational Efficiency
Real-time processing = <50ms calculation time
Memory optimization = Efficient array management
Visual performance = Smooth rendering at all timeframes
Scalability = Handles multiple universes simultaneously
User Experience Metrics
Setup time = <5 minutes to productive use
Learning curve = Accessible to intermediate+ traders
Visual clarity = No information overload
Configuration flexibility = 25+ customizable parameters
Risk Disclosure and Best Practices
Important Disclaimers
The Categorical Market Morphisms indicator applies advanced mathematical concepts to market analysis but does not guarantee profitable trades. Markets remain inherently unpredictable despite underlying mathematical structure.
Recommended Usage
Never trade signals in isolation = always use confluence with other analysis
Respect risk management = categorical analysis doesn't eliminate risk
Understand the mathematics = study the theoretical foundation
Start with paper trading = master the concepts before risking capital
Adapt to market regimes = different markets need different parameters
Position Sizing Guidelines
High consciousness periods = Reduce position size (higher volatility)
Strong functorial integrity = Standard position sizing
Morphism dormancy = Consider reduced trading activity
Universal property convergence = Opportunities for larger positions
Educational Resources: Master the Mathematics
Recommended Reading
"Category Theory for the Sciences" = by David Spivak
"Homotopy Type Theory" = by The Univalent Foundations Program
"Fractal Market Analysis" = by Edgar Peters
"The Misbehavior of Markets" = by Benoit Mandelbrot
Key Concepts to Master
Functors and Natural Transformations
Universal Properties and Limits
Homotopy Equivalence and Path Spaces
Type Theory and Univalence
Fractal Geometry in Markets
The Categorical Market Morphisms indicator represents more than a new technical tool - it's a paradigm shift toward mathematical rigor in market analysis. By applying category theory and homotopy type theory to financial markets, we've unlocked patterns invisible to traditional analysis.
This isn't just about better signals or prettier charts. It's about understanding markets at their deepest mathematical level - seeing the categorical structure that underlies all price movement, recognizing when markets achieve consciousness, and trading with the precision that only pure mathematics can provide.
Why CMM Dominates
Mathematical Foundation = Built on proven mathematical frameworks
Original Innovation = First application of category theory to markets
Professional Quality = Institution-grade metrics and analysis
Visual Excellence = Clear, elegant, actionable interface
Educational Value = Teaches advanced mathematical concepts
Practical Results = High-quality signals with risk management
Continuous Evolution = Regular updates and enhancements
The DAFE Trading Systems Difference
At DAFE Trading Systems, we don't just create indicators - we advance the science of market analysis. Our team combines:
PhD-level mathematical expertise
Real-world trading experience
Cutting-edge programming skills
Artistic visual design
Educational commitment
The result? Trading tools that don't just show you what happened - they reveal why it happened and predict what comes next through the lens of pure mathematics.
"In mathematics you don't understand things. You just get used to them." - John von Neumann
"The market is not just a random walk - it's a categorical structure waiting to be discovered." - DAFE Trading Systems
Trade with Mathematical Precision. Trade with Categorical Market Morphisms.
Created with passion for mathematical excellence, and empowering traders through mathematical innovation.
— Dskyz, Trade with insight. Trade with anticipation.
OHLC_yA customizable visualization of previous day's open high low close, premarket high low, and regular trading hours' high low.
For use to evaluate daily sentiment - in that if the range of premarket is rising higher than yesterday's close or remains above yesterday's open, could show signs of unchanged sentiment.
As well as the regular trading hours' range in relation to yesterday, offering potential levels of interest if it gets retested.
Cluster Proximity Table: Price, EMA20 & SMA200Spot significant confluence points at a glance! This script generates a dynamic table indicating if Price, its 20-period Exponential Moving Average (EMA20), and 200-period Simple Moving Average (SMA200) are tightly clustered across four different timeframes (5m, 15m, 1H, Daily). A green "✅ Yes" means all three are within a customizable percentage of each other, highlighting areas of potential support/resistance or market equilibrium.
Parabolic Run Detector (With Weighted Caution)This indicator, Parabolic Run Detector (With Weighted Caution), is designed to help traders identify moments of strong directional movement (I call it a run) in asset prices, especially those that exhibit a parabolic character. It uses a combination of log-scale price slopes, RSI momentum, and Ichimoku cloud structure (via the very useful Tenkan-Kijun "clamp") to evaluate whether a price move has both strength and sustainability. When certain thresholds are met, it marks the beginning of a potential run with a green circle below the price chart, helping traders spot entries early in high-momentum conditions.
In addition to identifying the start of a run, the indicator also looks for end-of-run caution signals. These are marked with orange circles, indicating potential exhaustion or overextension. The caution logic doesn’t require all conditions to trigger at once — instead, it uses a weighted scoring system based on RSI extension, slowing price momentum (second derivative), and the widening of the Ichimoku clamp. If these conditions cross a confidence threshold within a set number of bars after a run begins, the caution signal fires. This allows traders to stay alert to reversal or consolidation risks without being prematurely spooked by noise. So, choose to ignore them, but they are there for you to assess.
You can fine-tune sensitivity with a set of adjustable parameters, including minimum slope values, RSI reversion awareness (bias weight), clamp thresholds, and spacing between signals. So play around to see what works best for you! For advanced users, the option to toggle between static or dynamically calculated RSI baselines and adapt Ichimoku settings for crypto vs. legacy markets adds another layer of contextual accuracy. Whether you're trading Bitcoin on a 4-hour chart or scanning equities on a daily timeframe, this tool helps bring clarity to trend acceleration and potential fatigue, all while minimizing visual clutter and giving you intuitive visual cues.
Let me know what you think.
Momentum Breakout Option Buyer🎯 What it does:
# Detects momentum breakout zones
# Confirms breakout with volume and volatility
# Gives Buy signal only when the move is strong and fast — perfect for option buyers
🔧 Core Components:
# Supertrend – to define the trend
# RSI + EMA crossover – confirms strength
# Breakout candle + Volume spike
# ATR filter – confirms volatility is high enough to justify option buying
✅ Entry Criteria (Call Option):
# Price above Super trend
# RSI > 60 and RSI > RSI EMA
# Volume > 1.5 × average volume
# ATR (last 5 candles) > minimum threshold (e.g., 1%)
❌ Exit / Stop Loss:
# RSI drops below 50 or
# Supertrend flips or
# Target hit (e.g., 1.5x risk)
Momentum Breakout Option Buyer🎯 What it does: MOMENTUM BREAKOUT FOR OPTION BUYER
# Detects momentum breakout zones
# Confirms breakout with volume and volatility
# Gives Buy signal only when the move is strong and fast — perfect for option buyers
🔧 Core Components:
# Supertrend – to define the trend
# RSI + EMA crossover – confirms strength
# Breakout candle + Volume spike
# ATR filter – confirms volatility is high enough to justify option buying
✅ Entry Criteria (Call Option):
# Price above Supertrend
# RSI > 60 and RSI > RSI EMA
# Volume > 1.5 × average volume
# ATR (last 5 candles) > minimum threshold (e.g., 1%)
❌ Exit / Stop Loss:
# RSI drops below 50 or
# Supertrend flips or
# Target hit (e.g., 1.5x risk)
Percent Change of Range CandlesPercent Change of Range Candles 2.0 – Explanation and Usage Guide - with a new visual display
Purpose of the Indicator
This indicator measures the percentage change in price relative to the total range (high - low) over a defined period. Its primary function is to display trend strength — whether the price has significantly risen or fallen in relation to its historical high and low over the selected length.
It serves as a tool for identifying momentum shifts, extreme zones, and potential entry and exit points.
How It Works
Main signal (c):
Calculated as the difference between the current close and the close length periods ago, divided by the total range over the same period.
The result is multiplied by 100 to express it as a percentage.
Positive values indicate bullish pressure, and negative values indicate bearish pressure.
Supportive lines (o, h, l):
o is the average of the last 5 values of c – used to observe momentum smoothing.
h and l are adaptive values based on short-term recalculations (25% of the main length), adjusted depending on the current direction of the trend.
Indicator Levels and Their Meaning
Level Meaning
0 A key boundary between bullish and bearish zones. Proximity to this line often suggests consolidation or a potential reversal.
+70 Strong bullish momentum. May indicate overbought strength – potential for a pullback.
+100 Extreme overbought zone. This could signal market exhaustion and an upcoming drop.
-70 Strong bearish momentum. Could indicate oversold strength, but still within a trending market.
-100 Extreme oversold zone. Signals a possible reversal or at least a short-term bounce.
How to Use It in Trading
Around the Zero Level (0):
This is the neutral zone. When c approaches zero after a strong trend, it can indicate momentum weakening and a potential trend shift.
A cross from negative to positive values could signal early bullish reversal.
A cross from positive to negative could indicate early bearish reversal.
Extreme Levels ±100:
These are not automatic "buy" or "sell" signals but mark extreme market conditions.
Approaching +100 suggests the market has risen too much, possibly overheated – be ready for a correction.
Approaching -100 suggests the market has fallen too much, potentially oversold – be prepared for a recovery.
Best used in combination with other filters like RSI, MA, price action, or volume.
Visual Interpretation
Green line (positive c) represents bullish momentum.
Red line (negative c) represents bearish momentum.
Gray lines (o, h, l) help visualize averages and wicks of the price move for better understanding of the internal price dynamics.
Conclusion
The Percent Change of Range Candles indicator is useful for:
Tracking medium-term price momentum.
Detecting overbought/oversold conditions.
Identifying consolidation phases and possible reversals.
For best results, use it in combination with other indicators and with a broader view of market context (e.g., higher timeframes).
VWAP&5EMA📘 VWAP + 5 EMA Combo
This indicator provides a clean and modular framework for tracking key moving averages and VWAP levels. Ideal for intraday and swing traders, it allows full control over which components to display.
✅ Features:
Rolling VWAP – volume-weighted moving average over a custom period
Session VWAP – standard intraday VWAP
Daily EMA (D1) – from higher timeframe
Intraday EMA – based on current chart
5 Custom EMAs – fully adjustable and individually toggleable (default: 9, 21, 50, 100, 200)
🎯 Use Case:
Quickly assess dynamic support/resistance, confluence zones, and trend alignment across timeframes – without clutter. All lines are optional and independently configurable.
Footprint Stacked Imbalance + Absorption Detectorthis indicator looks for stacked imbalance on footprint charts or candle stick when price returns it a good chance for a balance from the level and i also added an absorpsion indicator this will look for agressive buyer or sellers buy passive limit orders , so if buyer agressive buys are not moving the price up they are getting absorped and soon will die out and fade the other direction.
HoLo (Highest Open Lowest Open)HoLo (Highest Open Lowest Open) Method
Overview
HoLo stands for "Highest Open Lowest Open" – a forex trading strategy.
Core Concept
Definition of HoLo:
Highest Open (HO): The highest opening price among all H1 candles of the current trading day
Lowest Open (LO): The lowest opening price among all H1 candles of the current trading day
Trading Day: Starts at Asia Open Session
Strategy Setup
Step 1: Mark Key Levels
Current day's High/Low
Highest Open and Lowest Open (from H1 candles)
Step 2: Define the Area of Interest
Sell Zone: Between the Highest Open and the current day's High
Buy Zone: Between the Lowest Open and the current day's Low
Trade Entry Rules
Sell Trade:
Price goes above the Highest Open
Trigger candle (M5, M15, or M30) closes above the Highest Open
Enter a sell when price revisits the Highest Open level (Sell Stop Order)
Buy Trade:
Price drops below the Lowest Open
Trigger candle closes below the Lowest Open
Enter a buy when price revisits the Lowest Open level (Buy Stop Order)
Trigger Timeframe:
Choose M1, M5, or M15 based on:
Your screen time availability
Personal trading style
Risk and Profit Management
Stop Loss:
For sell: Set SL at the day’s High + spread
For buy: Set SL at the day’s Low + spread
Take Profit (TP) Basic Rule:
You should open 2 positions:
When profit reaches 1R: Take partial profit + move SL to BE (Break Even)
Let the remaining position run using partial TP or trailing stop
Money Management:
Never risk more than 1% per trade
Recommended: 0.5% risk due to multiple opportunities daily
Prioritize major pairs.
The Indicator
How to read data
For Day Traders
Monitor the sell zone (red area) for potential short entries near resistance
Watch the buy zone (blue area) for potential long entries near support
Use cross signals for entry/exit points
Pay attention to timing markers for key market hours
Alert
HO (Highest Open) level changes
LO (Lowest Close) level changes
Price crossing key levels
Timing notifications
Heikin-Ashi Mean Reversion Oscillator [Alpha Extract]The Heikin-Ashi Mean Reversion Oscillator combines the smoothing characteristics of Heikin-Ashi candlesticks with mean reversion analysis to create a powerful momentum oscillator. This indicator applies Heikin-Ashi transformation twice - first to price data and then to the oscillator itself - resulting in smoother signals while maintaining sensitivity to trend changes and potential reversal points.
🔶 CALCULATION
Heikin-Ashi Transformation: Converts regular OHLC data to smoothed Heikin-Ashi values
Component Analysis: Calculates trend strength, body deviation, and price deviation from mean
Oscillator Construction: Combines components with weighted formula (40% trend strength, 30% body deviation, 30% price deviation)
Double Smoothing: Applies EMA smoothing and second Heikin-Ashi transformation to oscillator values
Signal Generation: Identifies trend changes and crossover points with overbought/oversold levels
Formula:
HA Close = (Open + High + Low + Close) / 4
HA Open = (Previous HA Open + Previous HA Close) / 2
Trend Strength = Normalized consecutive HA candle direction
Body Deviation = (HA Body - Mean Body) / Mean Body * 100
Price Deviation = ((HA Close - Price Mean) / Price Mean * 100) / Standard Deviation * 25
Raw Oscillator = (Trend Strength * 0.4) + (Body Deviation * 0.3) + (Price Deviation * 0.3)
Final Oscillator = 50 + (EMA(Raw Oscillator) / 2)
🔶 DETAILS Visual Features:
Heikin-Ashi Candlesticks: Smoothed oscillator representation using HA transformation with vibrant teal/red coloring
Overbought/Oversold Zones: Horizontal lines at customizable levels (default 70/30) with background highlighting in extreme zones
Moving Averages: Optional fast and slow EMA overlays for additional trend confirmation
Signal Dashboard: Real-time table showing current oscillator status (Overbought/Oversold/Bullish/Bearish) and buy/sell signals
Reference Lines: Middle line at 50 (neutral), with 0 and 100 boundaries for range visualization
Interpretation:
Above 70: Overbought conditions, potential selling opportunity
Below 30: Oversold conditions, potential buying opportunity
Bullish HA Candles: Green/teal candles indicate upward momentum
Bearish HA Candles: Red candles indicate downward momentum
MA Crossovers: Fast EMA above slow EMA suggests bullish momentum, below suggests bearish momentum
Zone Exits: Price moving out of extreme zones (above 70 or below 30) often signals trend continuation
🔶 EXAMPLES
Mean Reversion Signals: When the oscillator reaches extreme levels (above 70 or below 30), it identifies potential reversal points where price may revert to the mean.
Example: Oscillator reaching 80+ levels during strong uptrends often precedes short-term pullbacks, providing profit-taking opportunities.
Trend Change Detection: The double Heikin-Ashi smoothing helps identify genuine trend changes while filtering out market noise.
Example: When oscillator HA candles change from red to teal after oversold readings, this confirms potential trend reversal from bearish to bullish.
Moving Average Confirmation: Fast and slow EMA crossovers on the oscillator provide additional confirmation of momentum shifts.
Example: Fast EMA crossing above slow EMA while oscillator is rising from oversold levels provides strong bullish confirmation signal.
Dashboard Signal Integration: The real-time dashboard combines oscillator status with directional signals for quick decision-making.
Example: Dashboard showing "Oversold" status with "BUY" signal when HA candles turn bullish provides clear entry timing.
🔶 SETTINGS
Customization Options:
Calculation: Oscillator period (default 14), smoothing factor (1-50, default 2)
Levels: Overbought threshold (50-100, default 70), oversold threshold (0-50, default 30)
Moving Averages: Toggle display, fast EMA length (default 9), slow EMA length (default 21)
Visual Enhancements: Show/hide signal dashboard, customizable table position
Alert Conditions: Oversold bounce, overbought reversal, bullish/bearish MA crossovers
The Heikin-Ashi Mean Reversion Oscillator provides traders with a sophisticated momentum tool that combines the smoothing benefits of Heikin-Ashi analysis with mean reversion principles. The double transformation process creates cleaner signals while the integrated dashboard and multiple confirmation methods help traders identify high-probability entry and exit points during both trending and ranging market conditions.
Higher Timeframe Market StructureHTF Market Structure – ZigZag, Break of Structure & Supply/Demand
This powerful indicator is designed to identify higher-timeframe market structure using a combination of ZigZag patterns, Break of Structure (BOS) signals, and Supply/Demand zones.
Key Features:
Automatic detection of Higher Highs (HH), Higher Lows (HL), Lower Lows (LL), and Lower Highs (LH)
Internal structure shifts based on Open or High/Low logic
Supply and Demand zones plotted on the chart
Break of Structure (BOS) lines with optional alerts
Mitigation logic to mark or delete invalidated order blocks
Customizable aggregation factor to view higher time frame structure on lower time frames
How to Use:
Focus on market structure and BOS to understand the current trend.
Watch for internal shifts as early signals of potential reversals.
Use ZigZag lines to connect swing highs and lows to visualize market rhythm.
Supply zones (red) and Demand zones (green) are automatically drawn after structure breaks:
Use Demand Zones in Bullish Markets for the highest probability entries.
Use Supply Zones in Bearish Markets to align with the prevailing trend.
Best Practices:
Only use Demand Zones in Bullish markets and Supply Zones in Bearish markets for optimal results.
Look for price action or reversal signals within these zones to refine your entries.
Enable alerts to get notified on:
New order blocks
Internal shifts
BOS events
HH, HL, LL, LH formations
Liquidity sweeps
Customization Options:
Aggregation Factor: Control how many candles are grouped for structure analysis.
Zone Duration: Define how length of plotted zones.
Mitigation Settings: Automatically delete or fade zones after mitigation.
Colors: Choose custom colors for bullish and bearish zones and structure markers.
This tool is ideal for traders who rely on price action, structure, and smart money concepts. Combine it with your own S&D strategy or integrate it with other confluence tools for even better precision.
New York Midnight Day SeparatorThis Pine Script indicator draws vertical separator lines on the chart at midnight in the New York timezone (Eastern Time). The lines mark the start of each new trading day from Monday to Friday, helping traders visually distinguish daily sessions based on New York market time. The separator lines are rendered as slightly transparent gray lines spanning the full price range of each midnight candle, providing a clean and unobtrusive visual aid for session tracking.
