Lorentzian Harmonic Flow - Adaptive ML

⚡ LORENTZIAN HARMONIC FLOW — ADAPTIVE ML COMPLETE SYSTEM

THEORETICAL FOUNDATION: TEMPORAL RELATIVITY MEETS MACHINE LEARNING

The Lorentzian Harmonic Flow Adaptive ML system represents a paradigm shift in technical analysis by addressing a fundamental limitation that plagues traditional indicators: they assume time flows uniformly across all market conditions. In reality, markets experience time compression during volatile breakouts and time dilation during consolidation. A 50-period moving average calculated during a quiet overnight session captures vastly different market information than the same calculation during a high-volume news event.

This indicator solves this problem through Lorentzian spacetime modeling, borrowed directly from Einstein's special relativity. By calculating a dynamic gamma factor (γ) that measures market velocity relative to a volatility-based "speed of light," every calculation adapts its effective lookback period to the market's intrinsic clock. Combined with a dual-memory architecture, multi-regime detection, and Bayesian strategy selection, this creates a system that genuinely learns which approaches work in which market conditions.

CRITICAL DISTINCTION: TRUE ADAPTIVE LEARNING VS STATIC CLASSIFICATION

Before diving into the system architecture, it's essential to understand how this indicator fundamentally differs from traditional "Lorentzian" implementations, particularly the well-known Lorentzian Classification indicator.

THE ORIGINAL LORENTZIAN CLASSIFICATION APPROACH:

The pioneering Lorentzian Classification indicator (Jdehorty, 2022) introduced the financial community to Lorentzian distance metrics for pattern matching. However, it used offline training methodology:

• External Training: Required Python scripts or external ML tools to train the model on historical data
• Static Model: Once trained, the model parameters remained fixed
• No Real-Time Learning: The indicator classified patterns but didn't learn from outcomes
• Look-Ahead Bias Risk: Offline training could inadvertently use future data
• Manual Retraining: To adapt to new market conditions, users had to retrain externally and reload parameters

This was groundbreaking for bringing ML concepts to Pine Script, but it wasn't truly adaptive. The model was a snapshot—trained once, deployed, static.

THIS SYSTEM: TRUE ONLINE LEARNING

The Lorentzian Harmonic Flow Adaptive ML system represents a complete architectural departure:

✅ FULLY SELF-CONTAINED:
• Zero External Dependencies: No Python scripts, no external training tools, no data exports
• 100% Pine Script: Entire learning pipeline executes within TradingView
• One-Click Deployment: Load indicator, it begins learning immediately
• No Manual Configuration: System builds its own training data in real-time

✅ GENUINE FORWARD-WALK LEARNING:
• Real-Time Adaptation: Every trade outcome updates the model
• Forward-Only Logic: System uses only past confirmed data—zero look-ahead bias
• Continuous Evolution: Parameters adapt bar-by-bar based on rolling performance
• Regime-Specific Memory: Learns which patterns work in which conditions independently

✅ GETS BETTER WITH TIME:
• Week 1: Bootstrap mode—gathering initial data across regimes
• Month 2-3: Statistical significance emerges, parameter adaptation begins
• Month 4+: Mature learning, regime-specific optimization, confident selection
• Year 2+: Deep pattern library, proven parameter sets, robust to regime shifts

✅ NO RETRAINING REQUIRED:
• Automatic Adaptation: When market structure changes, system detects via performance degradation
• Memory Refresh: Old patterns naturally decay, new patterns replace them
• Parameter Evolution: Thresholds and multipliers adjust to current conditions
• Regime Awareness: If new regime emerges, enters bootstrap mode automatically

THE FUNDAMENTAL DIFFERENCE:

Traditional Lorentzian Classification:
"Here are patterns from the past. Current state matches pattern X, which historically preceded move Y. Signal fired."
→ Static knowledge, fixed rules, periodic retraining required

LHF Adaptive ML:
"In Trending Bull regime, Strategy B has 58% win rate and 1.4 Sharpe over last 30 trades. In High Vol Range, Strategy C performs better with 61% win rate and 1.8 Sharpe. Current state is Trending Bull, so I select Strategy B. If Strategy B starts failing, I'll adapt parameters or switch strategies. I'm learning which patterns matter in which contexts, and I improve every trade."
→ Dynamic learning, contextual adaptation, self-improving system

WHY THIS MATTERS:

Markets are non-stationary. A model trained on 2023 data may fail in 2024 when Fed policy shifts, volatility regime changes, or market structure evolves. Static models require constant human intervention—retraining, re-optimization, parameter updates.

This system learns continuously. It doesn't need you to tell it when markets changed. It discovers regime shifts through performance feedback, adapts parameters accordingly, and rebuilds its pattern library organically. The system running in Month 12 is fundamentally smarter than the system in Month 1—not because you retrained it, but because it learned from 1,000+ real outcomes.

This is the difference between pattern recognition (static ML) and reinforcement learning (adaptive ML). One classifies, the other learns and improves.

PART 1: LORENTZIAN TEMPORAL DYNAMICS

Markets don't experience time uniformly. During explosive volatility, price can compress weeks of movement into minutes. During consolidation, time dilates. Traditional indicators ignore this, using fixed periods regardless of market state.

The Lorentzian approach models market time using the Lorentz factor from special relativity:

γ = 1 / √(1 - v²/c²)

Where:
• v (velocity): Trend momentum normalized by ATR, calculated as (close - close[N]) / (N × ATR)
• c (speed limit): Realized volatility + volatility bursts, multiplied by c_multiplier parameter
• γ (gamma): Time dilation factor that compresses or expands effective lookback periods

When trend velocity approaches the volatility "speed limit," gamma spikes above 1.0, compressing time. Every calculation length becomes: base_period / γ. This creates shorter, more responsive periods during explosive moves and longer, more stable periods during quiet consolidation.

The system raises gamma to an optional power (gamma_power parameter) for fine control over compression strength, then applies this temporal scaling to every calculation in the indicator. This isn't metaphor—it's quantitative adaptation to the market's intrinsic clock.

PART 2: LORENTZIAN KERNEL SMOOTHING

Traditional moving averages use uniform weights (SMA) or exponential decay (EMA). The Lorentzian kernel uses heavy-tailed weighting:

K(distance, γ) = 1 / (1 + (distance/γ)²)

This Cauchy-like distribution gives more influence to recent extremes than Gaussian assumptions suggest, capturing the fat-tailed nature of financial returns. For any calculation requiring smoothing, the system loops through historical bars, computes Lorentzian kernel weights based on temporal distance and current gamma, then produces weighted averages.

This creates adaptive smoothing that responds to local volatility structure rather than imposing rigid assumptions about price distribution.

PART 3: HARMONIC FLOW (Multi-Timeframe Momentum)

The core directional signal comes from Harmonic Flow (HFL), which blends three gamma-compressed Lorentzian smooths:

• Short Horizon: base_period × short_ratio / γ (default: 34 × 0.5 / γ ≈ 17 bars, faster with high γ)
• Mid Horizon: base_period × mid_ratio / γ (default: 34 × 1.0 / γ ≈ 34 bars, anchor timeframe)
• Long Horizon: base_period × long_ratio / γ (default: 34 × 2.5 / γ ≈ 85 bars, structural trend)

Each produces a Lorentzian-weighted smooth, converted to a z-score (distance from smooth normalized by ATR). These z-scores are then weighted-averaged:

HFL = (w_short × z_short + w_mid × z_mid + w_long × z_long) / (w_short + w_mid + w_long)

Default weights (0.45, 0.35, 0.20) favor recent momentum while respecting longer structure. Scalpers can increase short weight; swing traders can emphasize long weight. The result is a directional momentum indicator that captures multi-timeframe flow in compressed time.

From HFL, the system derives:
• Flow Velocity: HFL - HFL[1] (momentum acceleration)
• Flow Acceleration: Second derivative (turning points)
• Temporal Compression Index (TCI): base_period / compressed_length (shows how much time is compressed)

PART 4: DUAL MEMORY ARCHITECTURE

Markets have memory—current conditions resonate with past regimes. But memory operates on two timescales, inspiring this indicator's dual-memory design:

SHORT-TERM MEMORY (STM):
• Capacity: 100 patterns (configurable 50-200)
• Decay Rate: 0.980 (50% weight after ~35 bars)
• Update Frequency: Every 10 bars
• Purpose: Capture current regime's tactical patterns
• Storage: Recent market states with 10-bar forward outcomes
• Analogy: Hippocampus (rapid encoding, fast fade)

LONG-TERM MEMORY (LTM):
• Capacity: 512 patterns (configurable 256-1024)
• Decay Rate: 0.997 (50% weight after ~230 bars)
• Quality Gate: Only high-quality patterns admitted (adaptive threshold per regime)
• Purpose: Strategic pattern library validated across regimes
• Storage: Validated patterns from weeks/months of history
• Analogy: Neocortex (slow consolidation, persistent storage)

Each memory stores 6-dimensional feature vectors:
1. HFL (harmonic flow strength)
2. Flow Velocity (momentum)
3. Flow Acceleration (turning points)
4. Volatility (realized vol EMA)
5. Entropy (market uncertainty)
6. Gamma (time compression state)

Plus the actual outcome (10-bar forward return).

K-NEAREST NEIGHBORS (KNN) PATTERN MATCHING:

When evaluating current market state, the system queries both memories using Lorentzian distance:

distance = Σ (1 - K(|feature_current - feature_memory|, γ))

This calculates similarity across all 6 dimensions using the same Lorentzian kernel, weighted by current gamma. The system finds K nearest neighbors (default: 8), weights each by:
• Similarity: Lorentzian kernel distance
• Age: Exponential decay based on bars since pattern
• Regime: Only patterns from similar regimes count

The weighted average of these neighbors' outcomes becomes the prediction. High-confidence predictions require both high similarity and agreement between multiple neighbors.

REGIME-AWARE BLENDING:

STM and LTM predictions are blended adaptively:
• High Vol Range regime: Trust STM 70% (recent matters in chaos)
• Trending regimes: Trust LTM 70% (structure matters in trends)
• Normal regimes: 50/50 blend

Agreement metric: When STM and LTM strongly disagree, the system flags low confidence—often indicating regime transition or novel market conditions requiring caution.

PART 5: FIVE-REGIME MARKET CLASSIFICATION

Traditional regime detection stops at "trending vs ranging." This system detects five distinct market states using linear regression slope and volatility analysis:

REGIME 0: TRENDING BULL ↗
• Detection: LR slope > trend_threshold (default: 0.3)
• Characteristics: Sustained positive HFL, elevated gamma, low entropy
• Best Strategy: B (Flow Momentum)
• Trading Behavior: Follow momentum, trail stops, pyramid winners

REGIME 1: TRENDING BEAR ↘
• Detection: LR slope < -trend_threshold
• Characteristics: Sustained negative HFL, elevated gamma, low entropy
• Best Strategy: B (Flow Momentum)
• Trading Behavior: Follow momentum short, aggressive exits on reversal

REGIME 2: HIGH VOL RANGE ↔
• Detection: |slope| < threshold AND vol_ratio > vol_expansion_threshold (default: 1.5)
• Characteristics: Oscillating HFL, high gamma spikes, high entropy
• Best Strategies: A (Squeeze Breakout) or C (Memory Pattern)
• Trading Behavior: Fade extremes, tight stops, quick profits

REGIME 3: LOW VOL RANGE —
• Detection: |slope| < threshold AND vol_ratio < vol_expansion_threshold
• Characteristics: Low HFL magnitude, gamma ≈ 1, squeeze conditions
• Best Strategy: A (Squeeze Breakout)
• Trading Behavior: Wait for breakout, wide stops on breakout entry

REGIME 4: TRANSITION ⚡
• Detection: Trend reversal OR volatility spike > 1.5× threshold
• Characteristics: Erratic gamma, high entropy, conflicting signals
• Best Strategy: None (often unfavorable)
• Trading Behavior: Stand aside, wait for clarity

Each regime gets a confidence score (0-1) measuring how clearly defined it is. Low confidence indicates messy, ambiguous conditions.

PART 6: THREE INDEPENDENT TRADING STRATEGIES

Rather than one signal logic, the system implements three distinct approaches:

STRATEGY A: SQUEEZE BREAKOUT
• Logic: Bollinger Bands squeeze release + HFL direction + flow velocity confirmation
• Calculation: Compares BB width to Keltner Channel width; fires when BB expands beyond KC
• Strength Score: 70 + compression_strength × 0.3 (tighter squeeze = higher score)
• Best Regimes: Low Vol Range (3), Transition exit (4→0 or 4→1)
• Pattern: Volatility contraction → directional expansion
• Philosophy: Calm before the storm; compression precedes explosion

STRATEGY B: LORENTZIAN FLOW MOMENTUM
• Logic: Strong HFL (×flow_mult) + positive velocity + gamma > 1.1 + NOT squeezing
• Calculation: |HFL × flow_mult| > 0.12, velocity confirms direction, gamma shows acceleration
• Strength Score: |HFL × flow_mult| × 80 + gamma × 10
• Best Regimes: Trending Bull (0), Trending Bear (1)
• Pattern: Established momentum → acceleration in compressed time
• Philosophy: Trend is friend when spacetime curves

STRATEGY C: MEMORY PATTERN MATCHING
• Logic: Dual KNN prediction > threshold + high confidence + agreement + HFL confirms
• Calculation: |memory_pred| > 0.005, memory_conf > 1.0, agreement > 0.5, HFL direction matches
• Strength Score: |prediction| × 800 × agreement
• Best Regimes: High Vol Range (2), sometimes others with sufficient pattern library
• Pattern: Historical similarity → outcome resonance
• Philosophy: Markets rhyme; learn from validated patterns

Each strategy generates independent strength scores. In multi-strategy mode (enabled by default), the system selects one strategy per regime based on risk-adjusted performance. In weighted mode (multi-strategy disabled), all three fire simultaneously with configurable weights.

PART 7: ADAPTIVE LEARNING & BAYESIAN SELECTION

This is where machine learning meets trading. The system maintains 15 independent performance matrices:

3 strategies × 5 regimes = 15 tracking systems

For each [strategy, regime] combination, it tracks:
• Trade Count: Number of completed trades
• Win Count: Profitable outcomes
• Total Return: Sum of percentage returns
• Squared Returns: For variance/Sharpe calculation
• Equity Curve: Virtual P&L assuming 10% risk per trade
• Peak Equity: All-time high for drawdown calculation
• Max Drawdown: Peak-to-trough decline

RISK-ADJUSTED SCORING:

For current regime, the system scores each strategy:

Sharpe Ratio: (mean_return / std_dev) × √252
Calmar Ratio: total_return / max_drawdown
Win Rate: wins / trades

Combined Score = 0.6 × Sharpe + 0.3 × Calmar + 0.1 × Win_Rate

The strategy with highest score is selected. This is similar to Thompson Sampling (multi-armed bandits) but uses deterministic selection rather than probabilistic sampling due to Pine Script limitations.

BOOTSTRAP MODE (Critical for Understanding):

For the first min_regime_samples trades (default: 10) in each regime:
• Status: "🔥 BOOTSTRAP (X/10)" displayed in dashboard
• Behavior: All signals allowed (gathering data)
• Regime Filter: Disabled (can't judge with insufficient data)
• Purpose: Avoid cold-start problem, build statistical foundation

After reaching threshold:
• Status: "✅ FAVORABLE" (score > 0.5) or "⚠️ UNFAVORABLE" (score ≤ 0.5)
• Behavior: Only trade favorable regimes (if enable_regime_filter = true)
• Learning: Parameters adapt based on outcomes

This solves a critical problem: you can't know which strategy works in a regime without data, but you can't get data without trading. Bootstrap mode gathers initial data safely, then switches to selective mode once statistical confidence emerges.

PARAMETER ADAPTATION (Per Regime):

Three parameters adapt independently for each regime based on outcomes:

1. SIGNAL QUALITY THRESHOLD (30-90):
• Starts: base_quality_threshold (default: 60)
• Adaptation:
Win Rate < 45% → RAISE threshold by learning_rate × 10 (be pickier)
Win Rate > 55% → LOWER threshold by learning_rate × 5 (take more)
• Effect: System becomes more selective in losing regimes, more aggressive in winning regimes

2. LTM QUALITY GATE (0.2-0.8):
• Starts: 0.4 (if adaptive gate enabled)
• Adaptation:
Sharpe < 0.5 → RAISE gate by learning_rate (demand better patterns)
Sharpe > 1.5 → LOWER gate by learning_rate × 0.5 (accept more patterns)
• Effect: LTM fills with high-quality patterns from winning regimes

3. FLOW MULTIPLIER (0.5-2.0):
• Starts: 1.0
• Adaptation:
Strong win (+2%+) → MULTIPLY by (1 + learning_rate × 0.1)
Strong loss (-2%+) → MULTIPLY by (1 - learning_rate × 0.1)
• Effect: Amplifies signal strength in profitable regimes, dampens in unprofitable

Each regime evolves independently. Trending Bull might develop threshold=55, gate=0.35, mult=1.3 while High Vol Range develops threshold=70, gate=0.50, mult=0.9.

PART 8: SHADOW PORTFOLIO VALIDATION

To validate learning objectively, the system runs three virtual portfolios:

Shadow Portfolio A: Trades only Strategy A signals
Shadow Portfolio B: Trades only Strategy B signals
Shadow Portfolio C: Trades only Strategy C signals

When any signal fires:
1. Open virtual position for corresponding strategy
2. On exit, calculate P&L (10% risk per trade)
3. Update equity, win count, profit factor

Dashboard displays:
• Equity: Current virtual balance (starts $10,000)
• Win%: Overall win rate across all regimes
• PF: Profit Factor (gross_profit / gross_loss)

This transparency shows which strategies actually perform, validates the selection logic, and prevents overfitting. If Shadow C shows $12,500 equity while A and B show $9,800, it confirms Strategy C's edge.

PART 9: HISTORICAL PRE-TRAINING

The system includes historical pre-training to avoid cold-start:

On Chart Load (if enabled):
1. Scan past pretrain_bars (default: 200)
2. Calculate historical HFL, gamma, velocity, acceleration, volatility, entropy
3. Compute 10-bar forward returns as outcomes
4. Populate STM with recent patterns
5. Populate LTM with high-quality patterns (quality > 0.4)

Effect:
• Without pre-training: Memories empty, no predictions for weeks, pure bootstrap
• With pre-training: System starts with pattern library, predictions from day one

Pre-training uses only past data (no future peeking) and fills memories with validated outcomes. This dramatically accelerates learning without compromising integrity.

PART 10: COMPREHENSIVE INPUT SYSTEM

The indicator provides 50+ inputs organized into logical groups. Here are the key parameters and their market-specific guidance:

🧠 ADAPTIVE LEARNING SYSTEM:

Enable Adaptive Learning (true/false):
• Function: Master switch for regime-specific strategy selection and parameter adaptation
• Enabled: System learns which strategies work in which regimes (recommended)
• Disabled: All strategies fire simultaneously with fixed weights (simpler, less adaptive)
• Recommendation: Keep enabled for all markets; system needs 2-3 months to mature

Learning Rate (0.01-0.20):
• Function: Speed of parameter adaptation based on outcomes
• Stocks/ETFs: 0.03-0.05 (slower, more stable)
• Crypto: 0.05-0.08 (faster, adapts to volatility)
• Forex: 0.04-0.06 (moderate)
• Timeframes:
1-5min scalping: 0.08-0.10 (rapid adaptation)
15min-1H day trading: 0.05-0.07 (balanced)
4H-Daily swing: 0.03-0.05 (conservative)
• Tradeoff: Higher = responsive but may overfit; Lower = stable but slower to adapt

Min Samples Per Regime (5-30):
• Function: Trades required before exiting bootstrap mode
• Active trading (>5 signals/day): 8-10 trades
• Moderate (1-5 signals/day): 10-15 trades
• Swing (few signals/week): 5-8 trades
• Logic: Bootstrap mode until this threshold; then uses Sharpe/Calmar for regime filtering
• Tradeoff: Lower = faster exit (risky, less data); Higher = more validation (safer, slower)

🌍 REGIME DETECTION:

Regime Lookback Period (20-200):
• Function: Bars used for linear regression to classify regime
• By Timeframe:
1-5min: 30-50 bars (~2-4 hour context)
15min: 40-60 bars (daily context)
1H: 50-100 bars (weekly context)
4H: 100-150 bars (monthly context)
Daily: 50-75 bars (quarterly context)
• By Market:
Crypto: 40-60 (faster regime changes)
Forex: 50-75 (moderate stability)
Stocks: 60-100 (slower structural trends)
• Tradeoff: Shorter = more regime switches (reactive); Longer = fewer switches (stable)

Trend Strength Threshold (0.1-0.8):
• Function: Minimum normalized LR slope to classify as trending vs ranging
• Lower (0.1-0.2): More markets classified as trending
• Higher (0.4-0.6): Only strong trends qualify
• Recommendations:
Choppy markets (BTC, small caps): 0.25-0.35
Smooth trends (major FX pairs): 0.30-0.40
Strong trends (indices during bull): 0.20-0.30
• Effect: Controls sensitivity of trending vs ranging classification

Vol Expansion Factor (1.2-3.0):
• Function: Volatility ratio to classify high-vol regimes (current_vol / avg_vol)
• By Asset:
Bitcoin: 1.4-1.6 (frequent vol spikes)
Altcoins: 1.3-1.5 (very volatile)
Major FX (EUR/USD): 1.6-2.0 (stable baseline)
Stocks (SPY): 1.5-1.8 (moderate)
Penny stocks: 1.3-1.4 (always volatile)
• Impact: Higher = fewer "High Vol Range" classifications; Lower = more sensitive to volatility spikes

🎯 SIGNAL GENERATION:

Base Quality Threshold (30-90):
• Function: Starting signal strength requirement (adapts per regime)
• THIS IS YOUR MAIN SIGNAL FREQUENCY CONTROL
• Conservative (70-80): Fewer, higher-quality signals
• Balanced (55-65): Moderate signal flow
• Aggressive (40-50): More signals, more noise
• By Trading Style:
Scalping (1-5min): 50-60
Day trading (15min-1H): 60-70
Swing (4H-Daily): 65-75
• Adaptive Behavior: System raises this in losing regimes (pickier), lowers in winning regimes (take more)

Min Confidence (0.1-0.9):
• Function: Minimum confidence score to fire signal
• Calculation: (Signal_Strength / 100) × Regime_Confidence
• Recommendations:
High-frequency (scalping): 0.2-0.3 (permissive)
Day trading: 0.3-0.4 (balanced)
Swing/position: 0.4-0.6 (selective)
• Interaction: During Transition regime (low regime confidence), even strong signals may fail confidence check; creates natural regime filtering

Only Trade Favorable Regimes (true/false):
• Function: Block signals in unfavorable regimes (where all strategies have negative risk-adjusted scores)
• Enabled (Recommended): Only trades when best strategy has positive Sharpe in current regime; auto-disables during bootstrap; protects capital
• Disabled: Always allows signals regardless of historical performance; use for manual regime assessment
• Bootstrap: Auto-allows trading until min_regime_samples reached, then switches to performance-based filtering

Min Bars Between Signals (1-20):
• Function: Prevents signal spam by enforcing minimum spacing
• By Timeframe:
1min: 3-5 bars (3-5 minutes)
5min: 3-6 bars (15-30 minutes)
15min: 4-8 bars (1-2 hours)
1H: 5-10 bars (5-10 hours)
4H: 3-6 bars (12-24 hours)
Daily: 2-5 bars (2-5 days)
• Logic: After signal fires, no new signals for X bars
• Tradeoff: Lower = more reactive (may overtrade); Higher = more patient (may miss reversals)

🌀 LORENTZIAN CORE:

Base Period (10-100):
• Function: Core time period for flow calculation (gets compressed by gamma)
• THIS IS YOUR PRIMARY TIMEFRAME KNOB
• By Timeframe:
1-5min scalping: 20-30 (fast response)
15min-1H day: 30-40 (balanced)
4H swing: 40-55 (smooth)
Daily position: 50-75 (very smooth)
• By Market Character:
Choppy (crypto, small caps): 25-35 (faster)
Smooth (major FX, indices): 35-50 (moderate)
Slow (bonds, utilities): 45-65 (slower)
• Gamma Effect: Actual length = base_period / gamma; High gamma compresses to ~20 bars, low gamma expands to ~50 bars
• Default 34 (Fibonacci) works well across most assets

Velocity Period (5-50):
• Function: Window for trend velocity calculation: (price_now - price[N]) / (N × ATR)
• By Timeframe:
1-5min scalping: 8-12 (fast momentum)
15min-1H day: 12-18 (balanced)
4H swing: 14-21 (smooth trend)
Daily: 18-30 (structural trend)
• By Market:
Crypto (fast moves): 10-14
Stocks (moderate): 14-20
Forex (smooth): 18-25
• Impact: Feeds into gamma calculation (v/c ratio); shorter = more sensitive to velocity spikes → higher gamma
• Relationship: Typically vel_period ≈ base_period / 2 to 2/3

Speed-of-Market (c) (0.5-3.0):
• Function: "Speed limit" for gamma calculation: c = realized_vol + vol_burst × c_multiplier
• By Asset Volatility:
High vol (BTC, TSLA): 1.0-1.3 (lower c = more compression)
Medium vol (SPY, EUR/USD): 1.3-1.6 (balanced)
Low vol (bonds, utilities): 1.6-2.5 (higher c = less compression)
• What It Does:
Lower c → velocity hits "speed limit" sooner → higher gamma → more compression
Higher c → velocity rarely hits limit → gamma stays near 1 → less adaptation
• Effect on Signals: More compression (low c) = faster regime detection, more responsive; Less compression (high c) = smoother, less adaptive
• Tuning: Start at 1.4; if gamma always ~1.0, lower to 1.0-1.2; if gamma spikes >5 often, raise to 1.6-2.0

Gamma Power (0.5-2.0):
• Function: Exponent applied to gamma: final_gamma = gamma^power
• Compression Strength:
0.5-0.8: Softens compression (gamma 4 → 2)
1.0: Linear (gamma 4 → 4) [RECOMMENDED]
1.2-2.0: Amplifies compression (gamma 4 → 16)
• Use Cases:
Reduce power (<1.0) if adaptive lengths swing too wildly or getting whipsawed
Increase power (>1.0) for more aggressive regime adaptation in fast markets
• Most users should leave at 1.0; only adjust if gamma behavior needs tuning

Max Kernel Lookback (20-200):
• Function: Computational limit for Lorentzian smoothing (performance control)
• Recommendations:
Fast PC / simple chart: 80-100
Slow PC / complex chart: 40-60
Mobile / lots of indicators: 30-50
• Impact: Each kernel smoothing loops through this many bars; higher = more accurate but slower
• Default 60 balances accuracy and speed; lower to 40-50 if indicator is slow

🎼 HARMONIC FLOW:

Short Horizon (0.2-1.0):
• Function: Fast timeframe multiplier: short_length = base_period × short_ratio / gamma
• Default: 0.5 (captures 2× faster flow than base)
• By Style:
Scalping: 0.3-0.4 (very fast)
Day trading: 0.4-0.6 (moderate)
Swing: 0.5-0.7 (balanced)
• Effect: Lower = more weight on micro-moves; Higher = smooths out fast fluctuations

Mid Horizon (0.5-2.0):
• Function: Medium timeframe multiplier: mid_length = base_period × mid_ratio / gamma
• Default: 1.0 (equals base_period, anchor timeframe)
• Usually keep at 1.0 unless specific strategy needs fine-tuning

Long Horizon (1.0-5.0):
• Function: Slow timeframe multiplier: long_length = base_period × long_ratio / gamma
• Default: 2.5 (captures trend/structure)
• By Style:
Scalping: 1.5-2.0 (less long-term influence)
Day trading: 2.0-3.0 (balanced)
Swing: 2.5-4.0 (strong trend component)
• Effect: Higher = more emphasis on larger structure; Lower = more reactive to recent price action

Short Weight (0-1):
Mid Weight (0-1):
Long Weight (0-1):
• Function: Relative importance in HFL calculation (should sum to 1.0)
• Defaults: Short: 0.45, Mid: 0.35, Long: 0.20 (day trading balanced)
• Preset Configurations:

SCALPING (fast response):
Short: 0.60, Mid: 0.30, Long: 0.10

DAY TRADING (balanced):
Short: 0.45, Mid: 0.35, Long: 0.20 [DEFAULT]

SWING (trend-following):
Short: 0.25, Mid: 0.35, Long: 0.40

• Effect: More short weight = responsive but noisier; More long weight = smoother but laggier

🧠 DUAL MEMORY SYSTEM:

Enable Pattern Memory (true/false):
• Function: Master switch for KNN pattern matching via dual memory
• Enabled (Recommended): Strategy C (Memory Pattern) can fire; memory predictions influence all strategies; prediction arcs shown; heatmaps available
• Disabled: Only Strategy A and B available; faster performance (less computation); pure technical analysis (no pattern matching)
• Keep enabled for full system capabilities; disable only if CPU-constrained or testing pure flow signals

STM Size (50-200):
• Function: Short-Term Memory capacity (recent pattern storage)
• Characteristics: Fast decay (0.980), captures current regime, updates every 10 bars, tactical pattern matching
• Sizing:
Active markets (crypto): 80-120
Moderate (stocks): 100-150
Slow (bonds): 50-100
• By Timeframe:
1-15min: 60-100 (captures few hours of patterns)
1H: 80-120 (captures days)
4H-Daily: 100-150 (captures weeks/months)
• Tradeoff: More = better recent pattern coverage; Less = faster computation
• Default 100 is solid for most use cases

LTM Size (256-1024):
• Function: Long-Term Memory capacity (validated pattern storage)
• Characteristics: Slow decay (0.997), only high-quality patterns (gated), regime-specific recall, strategic pattern library
• Sizing:
Fast PC: 512-768
Medium PC: 384-512 [DEFAULT]
Slow PC/Mobile: 256-384
• By Data Needs:
High-frequency (lots of patterns): 512-1024
Moderate activity: 384-512
Low-frequency (swing): 256-384
• Performance Impact: Each KNN search loops through entire LTM; 512 = good balance of coverage and speed; if slow, drop to 256-384
• Fills over weeks/months with validated patterns

STM Decay (0.95-0.995):
• Function: Short-Term Memory age decay rate: age_weight = decay^bars_since_pattern
• Decay Rates:
0.950: Aggressive fade (50% weight after 14 bars)
0.970: Moderate fade (50% after 23 bars)
0.980: Balanced (50% after 35 bars) [DEFAULT]
0.990: Slow fade (50% after 69 bars)
• By Timeframe:
1-5min: 0.95-0.97 (fast markets, old patterns irrelevant)
15min-1H: 0.97-0.98 (balanced)
4H-Daily: 0.98-0.99 (slower decay)
• Philosophy: STM should emphasize RECENT patterns; lower decay = only very recent matters; 0.980 works well for most cases

LTM Decay (0.99-0.999):
• Function: Long-Term Memory age decay rate
• Decay Rates:
0.990: 50% weight after 69 bars
0.995: 50% weight after 138 bars
0.997: 50% weight after 231 bars [DEFAULT]
0.999: 50% weight after 693 bars
• Philosophy: LTM should retain value for LONG periods; pattern from 6 months ago might still matter
• Usage:
Fast-changing markets: 0.990-0.995
Stable markets: 0.995-0.998
Structural patterns: 0.998-0.999
• Warning: Be careful with very high decay (>0.998); market structure changes, old patterns may mislead
• 0.997 balances long-term memory with regime evolution

K Neighbors (3-21):
• Function: Number of similar patterns to query in KNN search
• By Sample Size:
Small dataset (<100 patterns): 3-5
Medium dataset (100-300): 5-8 [DEFAULT]
Large dataset (300-1000): 8-13
Very large (>1000): 13-21
• Tradeoff:
Fewer K (3-5): More reactive to closest matches; noisier; outlier-sensitive; better when patterns very distinct
More K (13-21): Smoother, more stable predictions; may dilute strong signals; better when patterns overlap
• Rule of Thumb: K ≈ √(memory_size) / 3; For STM=100, LTM=512: K ≈ 8-10 ideal

Adaptive Quality Gate (true/false):
• Function: Adapts LTM entry threshold per regime based on Sharpe ratio
• Enabled: Quality gate adapts: Low Sharpe → RAISE gate (demand better patterns); High Sharpe → LOWER gate (accept more patterns); each regime has independent gate
• Disabled: Fixed quality gate (0.4 default) for all regimes
• Recommended: Keep ENABLED; helps LTM focus on proven pattern types per regime; prevents weak patterns from polluting memory

🎯 MULTI-STRATEGY SYSTEM:

Enable Strategy Learning (true/false):
• Function: Core learning feature for regime-specific strategy selection
• Enabled: Tracks 3 strategies × 5 regimes = 15 performance matrices; selects best strategy per regime via Sharpe/Calmar/WinRate; adaptive strategy switching
• Disabled: All strategies fire simultaneously (weighted combination); no regime-specific selection; simpler but less adaptive
• Recommended: ENABLED (this is the core of the adaptive system); disable only for testing or simplification

Strategy A Weight (0-1):
• Function: Weight for Strategy A (Squeeze Breakout) when multi-strategy disabled
• Characteristics: Fires on Bollinger squeeze release; best in Low Vol Range, Transition; compression → expansion pattern
• When Multi-Strategy OFF: Default 0.33 (equal weight); increase to 0.4-0.5 for choppy ranges with breakouts; decrease to 0.2-0.3 for trending markets
• When Multi-Strategy ON: This is ignored (system auto-selects based on performance)

Strategy B Weight (0-1):
• Function: Weight for Strategy B (Lorentzian Flow) when multi-strategy disabled
• Characteristics: Fires on strong HFL + velocity + gamma; best in Trending Bull/Bear; momentum → acceleration pattern
• When Multi-Strategy OFF: Default 0.33; increase to 0.4-0.5 for trending markets; decrease to 0.2-0.3 for choppy/ranging markets
• When Multi-Strategy ON: Ignored (auto-selected)

Strategy C Weight (0-1):
• Function: Weight for Strategy C (Memory Pattern) when multi-strategy disabled
• Characteristics: Fires when dual KNN predicts strong move; best in High Vol Range; requires memory system enabled + sufficient data
• When Multi-Strategy OFF: Default 0.34; increase to 0.4-0.6 if strong pattern repetition and LTM has >200 patterns; decrease to 0.2-0.3 if new to system; set to 0.0 if memory disabled
• When Multi-Strategy ON: Ignored (auto-selected)

📚 PRE-TRAINING:

Historical Pre-Training (true/false):
• Function: Bootstrap feature that fills memory on chart load
• Enabled: Scans past bars to populate STM/LTM before live trading; calculates historical outcomes (10-bar forward returns); builds initial pattern library; system starts with context, not blank slate
• Disabled: Memories only populate in real-time; takes weeks to build pattern library
• Recommended: ENABLED (critical for avoiding "cold start" problem); disable only for testing clean learning

Training Bars (50-500):
• Function: How many historical bars to scan on load (limited by available history)
• Recommendations:
1-5min charts: 200-300 (few hours of history)
15min-1H: 200-400 (days/weeks)
4H: 300-500 (months)
Daily: 200-400 (years)
• Performance:
100 bars: ~1 second
300 bars: ~2-3 seconds
500 bars: ~4-5 seconds
• Sweet Spot: 200-300 (enough patterns without slow load)
• If chart loads slowly: Reduce to 100-150

🎨 VISUALIZATION:

Show Regime Background (true/false):
• Function: Color-code background by current regime
• Colors: Trending Bull (green tint), Trending Bear (red tint), High Vol Range (orange tint), Low Vol Range (blue tint), Transition (purple tint)
• Helps visually track regime changes

Show Flow Bands (true/false):
• Function: Plot upper/lower bands based on HFL strength
• Shows dynamic support/resistance zones; green fill = bullish flow; red fill = bearish flow
• Useful for visual trend confirmation

Show Confidence Meter (true/false):
• Function: Plot signal confidence (0-100) in separate pane
• Calculation: (Signal_Strength / 100) × Regime_Confidence
• Gold line = current confidence; dashed line = minimum threshold
• Signals fire when confidence exceeds threshold

Show Prediction Arc (true/false):
• Function: Dashed line projecting expected price move based on memory prediction
• NOT a price target - a probability vector; steep arc = strong expected move; flat arc = weak/uncertain prediction
• Green = bullish prediction; red = bearish prediction

Show Signals (true/false):
• Function: Triangle markers at entry points
• ▲ Green = Long signal; ▼ Red = Short signal
• Markers show on bar close (non-repainting)

🏆 DASHBOARD:

Show Dashboard (true/false):
• Function: Main info panel showing all system metrics
• Sections: Lorentzian Core, Regime, Dual Memory, Adaptive Parameters, Regime Performance, Shadow Portfolios, Current Signal Status
• Essential for understanding system state

Dashboard Position: Top Left, Top Right, Bottom Left, Bottom Right

Individual Section Toggles:
• System Stats: Lorentzian Core section (Gamma, v/c, HFL, TCI)
• Memory Stats: Dual Memory section (STM/LTM predictions, agreement)
• Shadow Portfolios: Shadow Portfolio table (equity, win%, PF)
• Adaptive Params: Adaptive Parameters section (threshold, quality gate, flow mult)

🔥 HEATMAPS:

Show Dual Heatmaps (true/false):
• Function: Visual pattern density maps for STM and LTM
• Layout: X-axis = pattern age (left=recent, right=old); Y-axis = outcome direction (top=bearish, bottom=bullish); Color intensity = pattern count; Color hue = bullish (green) vs bearish (red)
• Warning: Can clutter chart; disable if not using

Heatmap Position: Screen position for heatmaps (STM at selected position, LTM offset)

Resolution (5-15):
• Function: Grid resolution (bins)
• Higher = more detailed but smaller cells; Lower = clearer but less granular
• 10 is good balance; reduce to 6-8 if hard to read

PART 11: DASHBOARD METRICS EXPLAINED

The comprehensive dashboard provides real-time transparency into every aspect of the adaptive system:

⚡ LORENTZIAN CORE SECTION:

Gamma (γ):
• Range: 1.0 to ~10.0 (capped)
• Interpretation:
γ ≈ 1.0-1.2: Normal market time, low velocity
γ = 1.5-2.5: Moderate compression, trending
γ = 3.0-5.0: High compression, explosive moves
γ > 5.0: Extreme compression, parabolic volatility
• Usage: High gamma = system operating in compressed time; expect shorter effective periods and faster adaptation

v/c (Velocity / Speed Limit):
• Range: 0.0 to 0.999 (approaches but never reaches 1.0)
• Interpretation:
v/c < 0.3: Slow market, low momentum
v/c = 0.4-0.7: Moderate trending
v/c > 0.7: Approaching "speed limit," high velocity
v/c > 0.9: Parabolic move, system at limit
• Color Coding: Red (>0.7), Gold (0.4-0.7), Green (<0.4)
• Usage: High v/c warns of extreme conditions where trend may exhaust

HFL (Harmonic Flow):
• Range: Typically -3.0 to +3.0 (can exceed in extremes)
• Interpretation:
HFL > 0: Bullish flow
HFL < 0: Bearish flow
|HFL| > 0.5: Strong directional bias
|HFL| < 0.2: Weak, indecisive
• Color: Green (positive), Red (negative)
• Usage: Primary directional indicator; strategies often require HFL confirmation

TCI (Temporal Compression Index):
• Calculation: base_period / compressed_length
• Interpretation:
TCI ≈ 1.0: No compression, normal time
TCI = 1.5-2.5: Moderate compression
TCI > 3.0: Significant compression
• Usage: Shows how much time is being compressed; mirrors gamma but more intuitive

╔═══ REGIME SECTION ═══╗

Current:
• Display: Regime name with icon (Trending Bull ↗, Trending Bear ↘, High Vol Range ↔, Low Vol Range —, Transition ⚡)
• Color: Gold for visibility
• Usage: Know which regime you're in; check regime performance to see expected strategy behavior

Confidence:
• Range: 0-100%
• Interpretation:
>70%: Very clear regime definition
40-70%: Moderate clarity
<40%: Ambiguous, mixed conditions
• Color: Green (>70%), Gold (40-70%), Red (<40%)
• Usage: High confidence = trust regime classification; low confidence = regime may be transitioning

Mode:
• States:
🔥 BOOTSTRAP (X/10): Still gathering data for this regime
✅ FAVORABLE: Best strategy has positive risk-adjusted score (>0.5)
⚠️ UNFAVORABLE: All strategies have negative scores (≤0.5)
• Color: Orange (bootstrap), Green (favorable), Red (unfavorable)
• Critical Importance: This tells you whether the system will trade or stand aside (if regime filter enabled)

╔═══ DUAL MEMORY KNN SECTION ═══╗

STM (Size):
• Display: Number of patterns currently in STM (0 to stm_size)
• Interpretation: Should fill to capacity within hours/days; if not filling, check that memory is enabled

STM Pred:
• Range: Typically -0.05 to +0.05 (representing -5% to +5% expected 10-bar move)
• Color: Green (positive), Red (negative)
• Usage: STM's prediction based on recent patterns; emphasis on current regime

LTM (Size):
• Display: Number of patterns in LTM (0 to ltm_size)
• Interpretation: Fills slowly (weeks/months); only validated high-quality patterns; check quality gate if not filling

LTM Pred:
• Range: Similar to STM pred
• Color: Green (positive), Red (negative)
• Usage: LTM's prediction based on long-term validated patterns; more strategic than tactical

Agreement:
• Display:
✅ XX%: Strong agreement (>70%) - both memories aligned
⚠️ XX%: Moderate agreement (40-70%) - some disagreement
❌ XX%: Conflict (<40%) - memories strongly disagree
• Color: Green (>70%), Gold (40-70%), Red (<40%)
• Critical Usage: Low agreement often precedes regime change or signals novel conditions; Strategy C won't fire with low agreement

╔═══ ADAPTIVE PARAMS SECTION ═══╗

Threshold:
• Display: Current regime's signal quality threshold (30-90)
• Interpretation: Higher = pickier; lower = more permissive
• Watch For: If steadily rising in a regime, system is struggling (low win rate); if falling, system is confident
• Default: Starts at base_quality_threshold (usually 60)

Quality:
• Display: Current regime's LTM quality gate (0.2-0.8)
• Interpretation: Minimum quality score for pattern to enter LTM
• Watch For: If rising, system demanding higher-quality patterns; if falling, accepting more diverse patterns
• Default: Starts at 0.4

Flow Mult:
• Display: Current regime's flow multiplier (0.5-2.0)
• Interpretation: Amplifies or dampens HFL for Strategy B
• Watch For: If >1.2, system found strong edge in flow signals; if <0.8, flow signals underperforming
• Default: Starts at 1.0

Learning:
• Display: ✅ ON or ❌ OFF
• Shows whether adaptive learning is enabled
• Color: Green (on), Red (off)

╔═══ REGIME PERFORMANCE SECTION ═══╗

This table shows ONLY the current regime's statistics:

S (Strategy):
• Display: A, B, or C
• Color: Gold if selected strategy; gray if not
• Shows which strategies have data in this regime

Trades:
• Display: Number of completed trades for this [strategy, regime] pair
• Interpretation: Blank or low numbers mean bootstrap mode; >10 means statistical significance building

Win%:
• Display: Win rate percentage
• Color: Green (>55%), White (45-55%), Red (<45%)
• Interpretation: 52%+ is good; 58%+ is excellent; <45% means struggling
• Note: Short-term variance is normal; judge after 20+ trades

Sharpe:
• Display: Annualized Sharpe ratio
• Color: Green (>1.0), White (0-1.0), Red (<0)
• Interpretation:
>2.0: Exceptional (rare)
1.0-2.0: Good
0.5-1.0: Acceptable
0-0.5: Marginal
<0: Losing
• Usage: Primary metric for strategy selection (60% weight in score)

╔═══ SHADOW PORTFOLIOS SECTION ═══╗

Shows virtual equity tracking across ALL regimes (not just current):

S (Strategy):
• Display: A, B, or C
• Color: Gold if currently selected strategy; gray otherwise

Equity:
• Display: Current virtual balance (starts $10,000)
• Color: Green (>$10,000), White ($9,500-$10,000), Red (<$9,500)
• Interpretation: Which strategy is actually making virtual money across all conditions
• Note: 10% risk per trade assumed

Win%:
• Display: Overall win rate across all regimes
• Color: Green (>55%), White (45-55%), Red (<45%)
• Interpretation: Aggregate performance; strategy may do well in some regimes and poorly in others

PF (Profit Factor):
• Display: Gross profit / gross loss
• Color: Green (>1.5), White (1.0-1.5), Red (<1.0)
• Interpretation:
>2.0: Excellent
1.5-2.0: Good
1.2-1.5: Acceptable
1.0-1.2: Marginal
<1.0: Losing
• Usage: Confirms win rate; high PF with moderate win rate means winners >> losers

╔═══ STATUS BAR ═══╗

Display States:
• 🟢 LONG: Currently in long position (green background)
• 🔴 SHORT: Currently in short position (red background)
• ⬆️ LONG SIGNAL: Long signal present but not yet confirmed (waiting for bar close)
• ⬇️ SHORT SIGNAL: Short signal present but not yet confirmed
• ⚪ NEUTRAL: No position, no signal (white background)

Usage: Immediate visual confirmation of system state; check before manually entering/exiting

PART 12: VISUAL ELEMENT INTERPRETATION

REGIME BACKGROUND COLORS:

Green Tint: Trending Bull regime - expect Strategy B (Flow) to dominate; focus on long momentum
Red Tint: Trending Bear regime - expect Strategy B (Flow) shorts; focus on short momentum
Orange Tint: High Vol Range - expect Strategy A (Squeeze) or C (Memory); trade breakouts or patterns
Blue Tint: Low Vol Range - expect Strategy A (Squeeze); wait for compression release
Purple Tint: Transition regime - often unfavorable; system may stand aside; high uncertainty

Usage: Quick visual regime identification without reading dashboard

FLOW BANDS:

Upper Band: close + HFL × ATR × 1.5
Lower Band: close - HFL × ATR × 1.5
Green Fill: HFL positive (bullish flow); bands act as dynamic support/resistance in uptrend
Red Fill: HFL negative (bearish flow); bands act as dynamic resistance/support in downtrend

Usage:
• Bullish flow: Price bouncing off lower band = trend continuation; breaking below = possible reversal
• Bearish flow: Price rejecting upper band = trend continuation; breaking above = possible reversal

CONFIDENCE METER (Separate Pane):

Gold Line: Current signal confidence (0-100)
Dashed Line: Minimum confidence threshold
Interpretation:
• Line above threshold: Signal likely to fire if strength sufficient
• Line below threshold: Even if signal logic met, won't fire (insufficient confidence)
• Gradual rise: Signal building strength
• Sharp spike: Sudden conviction (check if sustainable)

Usage: Real-time signal probability; helps anticipate upcoming entries

PREDICTION ARC:

Dashed Line: Projects from current close to expected price 8 bars forward
Green Arc: Bullish memory prediction
Red Arc: Bearish memory prediction
Steep Arc: High conviction (strong expected move)
Flat Arc: Low conviction (weak/uncertain move)

Important: NOT a price target; this is a probability vector based on KNN outcomes; actual price may differ
Usage: Directional bias from pattern matching; confirms or contradicts flow signals

SIGNAL MARKERS:

▲ Green Triangle (below bar):
• Long signal confirmed on bar close
• Entry on next bar open
• Non-repainting (appears after bar closes)

▼ Red Triangle (above bar):
• Short signal confirmed on bar close
• Entry on next bar open
• Non-repainting

Size: Tiny (unobtrusive)
Text: "L" or "S" in marker

Usage: Historical signal record; alerts should fire on these; verify against dashboard status

DUAL HEATMAPS (If Enabled):

STM HEATMAP:
• X-axis: Pattern age (left = recent, right = older, typically 0-50 bars)
• Y-axis: Outcome direction (top = bearish outcomes, bottom = bullish outcomes)
• Color Intensity: Brightness = pattern count in that cell
• Color Hue: Green tint (bullish), Red tint (bearish), Gray (neutral)

Interpretation:
• Dense bottom-left: Many recent bullish patterns (bullish regime)
• Dense top-left: Many recent bearish patterns (bearish regime)
• Scattered: Mixed outcomes, ranging regime
• Empty areas: Few patterns (low data)

LTM HEATMAP:
• Similar layout but X-axis spans wider age range (0-500+ bars)
• Shows long-term pattern distribution
• Denser = more validated patterns

Comparison Usage:
• If STM and LTM heatmaps look similar: Current regime matches historical patterns (high agreement)
• If STM bottom-heavy but LTM top-heavy: Recent bullish activity contradicts historical bearish patterns (low agreement, transition signal)

PART 13: DEVELOPMENT STORY

The creation of the Lorentzian Harmonic Flow Adaptive ML system represents over six months of intensive research, mathematical exploration, and iterative refinement. What began as a theoretical investigation into applying special relativity to market time evolved into a complete adaptive learning framework.

THE CHALLENGE:

The fundamental problem was this: markets don't experience time uniformly, yet every indicator treats a 50-period calculation the same whether markets are exploding or sleeping. Traditional adaptive indicators adjust parameters based on volatility, but this is reactive—by the time you measure high volatility, the explosive move is over. What was needed was a framework that measured the market's intrinsic velocity relative to its own structural limits, then compressed time itself proportionally.

THE LORENTZIAN INSIGHT:

Einstein's special relativity provides exactly this framework through the Lorentz factor. When an object approaches the speed of light, time dilates—but from the object's reference frame, it experiences time compression. By treating price velocity as analogous to relativistic velocity and volatility structure as the "speed limit," we could calculate a gamma factor that compressed lookback periods during explosive moves.

The mathematics were straightforward in theory but devilishly complex in implementation. Pine Script has no native support for dynamically-sized arrays or recursive functions, forcing creative workarounds. The Lorentzian kernel smoothing required nested loops through historical bars, calculating kernel weights on the fly—a computational nightmare. Early versions crashed or produced bizarre artifacts (negative gamma values, infinite loops during volatility spikes).

Optimization took weeks. Limiting kernel lookback to 60 bars while still maintaining smoothing quality. Pre-calculating gamma once per bar and reusing it across all calculations. Caching intermediate results. The final implementation balances mathematical purity with computational reality.

THE MEMORY ARCHITECTURE:

With temporal compression working, the next challenge was pattern memory. Simple moving average systems have no memory—they forget yesterday's patterns immediately. But markets are non-stationary; what worked last month may not work today. The solution: dual-memory architecture inspired by cognitive neuroscience.

Short-Term Memory (STM) would capture tactical patterns—the hippocampus of the system. Fast encoding, fast decay, always current. Long-Term Memory (LTM) would store validated strategic patterns—the neocortex. Slow consolidation, persistent storage, regime-spanning wisdom.

The KNN implementation nearly broke me. Calculating Lorentzian distance across 6 dimensions for 500+ patterns per query, applying age decay, filtering by regime, finding K nearest neighbors without native sorting functions—all while maintaining sub-second execution. The breakthrough came from realizing we could use destructive sorting (marking found neighbors as "infinite distance") rather than maintaining separate data structures.

Pre-training was another beast. To populate memory with historical patterns, the system needed to scan hundreds of past bars, calculate forward outcomes, and insert patterns—all on chart load without timing out. The solution: cap at 200 bars, optimize loops, pre-calculate features. Now it works seamlessly.

THE REGIME DETECTION:

Five-regime classification emerged from empirical observation. Traditional trending/ranging dichotomy missed too much nuance. Markets have at least four distinct states: trending up, trending down, volatile range, quiet range—plus a chaotic transition state. Linear regression slope quantifies trend; volatility ratio quantifies expansion; combining them creates five natural clusters.

But classification is useless without regime-specific learning. That meant tracking 15 separate performance matrices (3 strategies × 5 regimes), computing Sharpe ratios and Calmar ratios for sparse data, implementing Bayesian-like strategy selection. The bootstrap mode logic alone took dozens of iterations—too strict and you never get data, too permissive and you blow up accounts during learning.

THE ADAPTIVE LAYER:

Parameter adaptation was conceptually elegant but practically treacherous. Each regime needed independent thresholds, quality gates, and multipliers that adapted based on outcomes. But naive gradient descent caused oscillations—win a few trades, lower threshold, take worse signals, lose trades, raise threshold, miss good signals. The solution: exponential smoothing via learning rate (α) and separate scoring for selection vs adaptation.

Shadow portfolios provided objective validation. By running virtual accounts for all strategies simultaneously, we could see which would have won even when not selected. This caught numerous bugs where selection logic was sound but execution was flawed, or vice versa.

THE DASHBOARD & VISUALIZATION:

A learning system is useless if users can't understand what it's doing. The dashboard went through five complete redesigns. Early versions were information dumps—too much data, no hierarchy, impossible to scan. The final version uses visual hierarchy (section headers, color coding, strategic whitespace) and progressive disclosure (show current regime first, then performance, then parameters).

The dual heatmaps were a late addition but proved invaluable for pattern visualization. Seeing STM cluster in one corner while LTM distributed broadly immediately signals regime novelty. Traders grasp this visually faster than reading disagreement percentages.

THE TESTING GAUNTLET:

Testing adaptive systems is uniquely challenging. Static backtest results mean nothing—the system should improve over time. Early "tests" showed abysmal performance because bootstrap periods were included. The breakthrough: measure pre-learning baseline vs post-learning performance. A system going from 48% win rate (first 50 trades) to 56% win rate (trades 100-200) is succeeding even if absolute performance seems modest.

Edge cases broke everything repeatedly. What happens when a regime never appears in historical data? When all strategies fail simultaneously? When memory fills with only bearish patterns during a bull run? Each required careful handling—bootstrap modes, forced diversification, quality gates.

THE DOCUMENTATION:

This isn't an indicator you throw on a chart with default settings and trade immediately. It's a learning system that requires understanding. The input tooltips alone contain over 10,000 words of guidance—market-specific recommendations, timeframe-specific settings, tradeoff explanations. Every parameter needed not just a description but a philosophical justification and practical tuning guide.

The code comments span 500+ lines explaining theory, implementation decisions, edge cases. Future maintainers (including myself in six months) need to understand not just what the code does but why certain approaches were chosen over alternatives.

WHAT ALMOST DIDN'T WORK:

The entire project nearly collapsed twice. First, when initial Lorentzian smoothing produced complete noise—hours of debugging revealed a simple indexing error where I was accessing instead of [i+1] in the kernel loop. One character, entire system broken.

Second, when memory predictions showed zero correlation with outcomes. Turned out the KNN distance metric was dominated by the gamma dimension (values 1-10) drowning out normalized features (values -1 to 1). Solution: apply kernel transformation to all dimensions, not just final distance. Obvious in retrospect, maddening at the time.

THE PHILOSOPHY:

This system embodies a specific philosophy: markets are learnable but non-stationary. No single strategy works forever, but regime-specific patterns persist. Time isn't uniform, memory isn't perfect, prediction isn't possible—but probabilistic edges exist for those willing to track them rigorously.

It rejects the premise that indicators should give universal advice. Instead, it says: "In this regime, based on similar past states, Strategy B has a 58% win rate and 1.4 Sharpe. Strategy A has 45% and 0.2 Sharpe. I recommend B. But we're still in bootstrap for Strategy C, so I'm gathering data. Check back in 5 trades."

That humility—knowing what it knows and what it doesn't—is what makes it robust.

PART 14: PROFESSIONAL USAGE PROTOCOL

PHASE 1: DEPLOYMENT (Week 1-4)

Initial Setup:
1. Load indicator on primary trading chart with default settings
2. Verify historical pre-training enabled (should see ~200 patterns in STM/LTM on first load)
3. Enable all dashboard sections for maximum transparency
4. Set alerts but DO NOT trade real money

Observation Checklist:
• Dashboard Validation:
✓ Lorentzian Core shows reasonable gamma (1-5 range, not stuck at 1.0 or spiking to 10)
✓ HFL oscillates with price action (not flat or random)
✓ Regime classifications make intuitive sense
✓ Confidence scores vary appropriately

• Memory System:
✓ STM fills within first few hours/days of real-time bars
✓ LTM grows gradually (few patterns per day, quality-gated)
✓ Predictions show directional bias (not always 0.0)
✓ Agreement metric fluctuates with regime changes

• Bootstrap Tracking:
✓ Dashboard shows "🔥 BOOTSTRAP (X/10)" for each regime
✓ Trade counts increment on regime-specific signals
✓ Different regimes reach threshold at different rates

Paper Trading:
• Take EVERY signal (ignore unfavorable warnings during bootstrap)
• Log each trade: entry price, regime, selected strategy, outcome
• Calculate your actual P&L assuming proper risk management (1-2% risk per trade)
• Do NOT judge system performance yet—focus on understanding behavior

Troubleshooting:
• No signals for days:
- Check base_quality_threshold (try lowering to 50-55)
- Verify enable_regime_filter not blocking all regimes
- Confirm signal confidence threshold not too high (try 0.25)

• Signals every bar:
- Raise base_quality_threshold to 65-70
- Increase min_bars_between to 8-10
- Check if gamma spiking excessively (raise c_multiplier)

• Memory not filling:
- Confirm enable_memory = true
- Verify historical pre-training completed (check STM size after load)
- May need to wait 10 bars for first real-time update

PHASE 2: VALIDATION (Week 5-12)

Statistical Emergence:
By week 5-8, most regimes should exit bootstrap. Look for:

✓ Regime Performance Clarity:
- At least 2-3 strategies showing positive Sharpe in their favored regimes
- Clear separation (Strategy B strong in Trending, Strategy A strong in Low Vol Range, etc.)
- Win rates stabilizing around 50-60% for winning strategies

✓ Shadow Portfolio Divergence:
- Virtual portfolios showing clear winners ($10K → $11K+) and losers ($10K → $9K-)
- Profit factors >1.3 for top strategy
- System selection aligning with best shadow portfolio

✓ Parameter Adaptation:
- Thresholds varying per regime (not stuck at initial values)
- Quality gates adapting (some regimes higher, some lower)
- Flow multipliers showing regime-specific optimization

Validation Questions:

1. Do patterns make intuitive sense?
- Strategy B (Flow) dominating Trending Bull/Bear? ✓ Expected
- Strategy A (Squeeze) succeeding in Low Vol Range? ✓ Expected
- Strategy C (Memory) working in High Vol Range? ✓ Expected
- Random strategy winning everywhere? ✗ Problem

2. Is unfavorable filtering working?
- Regimes with negative Sharpe showing "⚠️ UNFAVORABLE"? ✓ System protecting capital
- Transition regime often unfavorable? ✓ Expected
- All regimes perpetually unfavorable? ✗ Settings too strict or asset unsuitable

3. Are memories agreeing appropriately?
- High agreement during stable regimes? ✓ Expected
- Low agreement during transitions? ✓ Expected (novel conditions)
- Perpetual conflict? ✗ Check memory sizes or decay rates

Fine-Tuning (If Needed):

Too Many Signals in Losing Regimes:
→ Increase learning_rate to 0.07-0.08 (faster adaptation)
→ Raise base_quality_threshold by 5-10 points
→ Enable regime filter if disabled

Missing Profitable Setups:
→ Lower base_quality_threshold by 5-10 points
→ Reduce min_confidence to 0.25-0.30
→ Check if bootstrap mode blocking trades (let it complete)

Excessive Parameter Swings:
→ Reduce learning_rate to 0.03-0.04
→ Increase min_regime_samples to 15-20 (more data before adaptation)

Memory Disagreement Too Frequent:
→ Increase LTM size to 768-1024 (broader pattern library)
→ Lower adaptive_quality_gate requirement (allow more patterns)
→ Increase K neighbors to 10-12 (smoother predictions)

PHASE 3: LIVE TRADING (Month 4+)

Pre-Launch Checklist:

1. ✓ At least 3 regimes show positive Sharpe (>0.8)
2. ✓ Top shadow portfolio shows >53% win rate and >1.3 profit factor
3. ✓ Parameters have stabilized (not changing more than 10% per month)
4. ✓ You understand every dashboard metric and can explain regime/strategy behavior
5. ✓ You have proper risk management plan independent of this system

Position Sizing:

Conservative (Recommended for Month 4-6):
• Risk per trade: 0.5-1.0% of account
• Max concurrent positions: 1-2
• Total exposure: 10-25% of intended full size

Moderate (Month 7-12):
• Risk per trade: 1.0-1.5% of account
• Max concurrent positions: 2-3
• Total exposure: 25-50% of intended size

Full Scale (Year 2+):
• Risk per trade: 1.5-2.0% of account
• Max concurrent positions: 3-5
• Total exposure: 100% (still following risk limits)

Entry Execution:

On Signal Confirmation:
1. Verify dashboard shows signal type (▲ LONG or ▼ SHORT)
2. Check regime mode (avoid if "⚠️ UNFAVORABLE" unless testing)
3. Note selected strategy (A/B/C) and its regime Sharpe
4. Verify memory agreement if Strategy C selected (want >60%)

Entry Method:
• Market entry: Next bar open after signal (for exact backtest replication)
• Limit entry: Slight improvement (2-3 ticks) if confident in direction

Stop Loss Placement:
• Strategy A (Squeeze): Beyond opposite band or recent swing point
• Strategy B (Flow): 1.5-2.0 ATR from entry against direction
• Strategy C (Memory): Based on predicted move magnitude (tighter if pred > 2%)

Exit Management:

System Exit Signals:
• Opposite signal fires: Immediate exit, potential reversal entry
• 20 bars no exit signal: System implies position stale, consider exiting
• Regime changes to unfavorable: Tighten stop, consider partial exit

Manual Exit Conditions:
• Stop loss hit: Take loss, log for validation (system expects some losses)
• Profit target hit: If using fixed targets (2-3R typical)
• Major news event: Flatten during high-impact news (system can't predict these)

Warning Signs (Exit Criteria):

🚨 Stop Trading If:
1. All regimes show negative Sharpe for 4+ weeks (market structure changed)
2. Your results >20% worse than shadow portfolios (execution problem)
3. Parameters hitting extremes (thresholds >85 or <35 across all regimes)
4. Memory agreement <30% for extended periods (unprecedented conditions)
5. Account drawdown >20% (risk management failure, system or otherwise)

⚠️ Reduce Size If:
1. Win rate drops 10%+ from peak (temporary regime shift)
2. Selected strategy underperforming another by >30% (selection lag)
3. Consecutive losses >5 (variance or problem, reduce until clarity)
4. Major market regime change (Fed policy shift, war, etc. - let system re-adapt)

PART 15: THEORETICAL IMPLICATIONS & LIMITATIONS

WHAT THIS SYSTEM REPRESENTS:

Contextual Bandits:
The regime-specific strategy selection implements a contextual multi-armed bandit problem. Each strategy is an "arm," each regime is a "context," and we select arms to maximize expected reward given context. This is reinforcement learning applied to trading.

Experience Replay:
The dual-memory architecture mirrors DeepMind's DQN breakthrough. STM = recent experience buffer; LTM = validated experience replay. This prevents catastrophic forgetting while enabling rapid adaptation—a key challenge in neural network training.

Meta-Learning:
The system learns how to learn. Parameter adaptation adjusts the system's own sensitivity and selectivity based on outcomes. This is "learning to learn"—optimizing the optimization process itself.

Non-Stationary Optimization:
Traditional backtesting assumes stationarity (past patterns persist). This system assumes non-stationarity and continuously adapts. The goal isn't finding "the best parameters" but tracking the moving optimum.

Regime-Conditional Policies:
Rather than a single strategy for all conditions, this implements regime-specific policies. This is contextual decision-making—environment state determines action selection.

FINAL WISDOM:

"The market is a complex adaptive system. To trade it successfully, one must also adapt. This indicator provides the framework—memory, learning, regime awareness—but wisdom comes from understanding when to trade, when to stand aside, and when to defer to conditions the system hasn't yet learned. The edge isn't in the algorithm alone; it's in the partnership between mathematical rigor and human judgment."

— Inspired by the intersection of Einstein's relativity, Kahneman's behavioral economics, and decades of quantitative trading research

Taking you to school. — Dskyz, Trade with insight. Trade with anticipation.