Quantum Rotational Field Mapping

Quantum Rotational Field Mapping (QRFM):
Phase Coherence Detection Through Complex-Plane Oscillator Analysis

Quantum Rotational Field Mapping applies complex-plane mathematics and phase-space analysis to oscillator ensembles, identifying high-probability trend ignition points by measuring when multiple independent oscillators achieve phase coherence. Unlike traditional multi-oscillator approaches that simply stack indicators or use boolean AND/OR logic, this system converts each oscillator into a rotating phasor (vector) in the complex plane and calculates the Coherence Index (CI)—a mathematical measure of how tightly aligned the ensemble has become—then generates signals only when alignment, phase direction, and pairwise entanglement all converge.

The indicator combines three mathematical frameworks: phasor representation using analytic signal theory to extract phase and amplitude from each oscillator, coherence measurement using vector summation in the complex plane to quantify group alignment, and entanglement analysis that calculates pairwise phase agreement across all oscillator combinations. This creates a multi-dimensional confirmation system that distinguishes between random oscillator noise and genuine regime transitions.

What Makes This Original

Complex-Plane Phasor Framework
This indicator implements classical signal processing mathematics adapted for market oscillators. Each oscillator—whether RSI, MACD, Stochastic, CCI, Williams %R, MFI, ROC, or TSI—is first normalized to a common [-1, 1] scale, then converted into a complex-plane representation using an in-phase (I) and quadrature (Q) component. The in-phase component is the oscillator value itself, while the quadrature component is calculated as the first difference (derivative proxy), creating a velocity-aware representation.

From these components, the system extracts:

Phase (φ): Calculated as φ = atan2(Q, I), representing the oscillator's position in its cycle (mapped to -180° to +180°)
Amplitude (A): Calculated as A = √(I² + Q²), representing the oscillator's strength or conviction
This mathematical approach is fundamentally different from simply reading oscillator values. A phasor captures both where an oscillator is in its cycle (phase angle) and how strongly it's expressing that position (amplitude). Two oscillators can have the same value but be in opposite phases of their cycles—traditional analysis would see them as identical, while QRFM sees them as 180° out of phase (contradictory).

Coherence Index Calculation
The core innovation is the Coherence Index (CI), borrowed from physics and signal processing. When you have N oscillators, each with phase φₙ, you can represent each as a unit vector in the complex plane: e^(iφₙ) = cos(φₙ) + i·sin(φₙ).

The CI measures what happens when you sum all these vectors:

Resultant Vector: R = Σ e^(iφₙ) = Σ cos(φₙ) + i·Σ sin(φₙ)

Coherence Index: CI = |R| / N

Where |R| is the magnitude of the resultant vector and N is the number of active oscillators.

The CI ranges from 0 to 1:

CI = 1.0: Perfect coherence—all oscillators have identical phase angles, vectors point in the same direction, creating maximum constructive interference
CI = 0.0: Complete decoherence—oscillators are randomly distributed around the circle, vectors cancel out through destructive interference
0 < CI < 1: Partial alignment—some clustering with some scatter
This is not a simple average or correlation. The CI captures phase synchronization across the entire ensemble simultaneously. When oscillators phase-lock (align their cycles), the CI spikes regardless of their individual values. This makes it sensitive to regime transitions that traditional indicators miss.

Dominant Phase and Direction Detection
Beyond measuring alignment strength, the system calculates the dominant phase of the ensemble—the direction the resultant vector points:

Dominant Phase: φ_dom = atan2(Σ sin(φₙ), Σ cos(φₙ))

This gives the "average direction" of all oscillator phases, mapped to -180° to +180°:

+90° to -90° (right half-plane): Bullish phase dominance
+90° to +180° or -90° to -180° (left half-plane): Bearish phase dominance
The combination of CI magnitude (coherence strength) and dominant phase angle (directional bias) creates a two-dimensional signal space. High CI alone is insufficient—you need high CI plus dominant phase pointing in a tradeable direction. This dual requirement is what separates QRFM from simple oscillator averaging.

Entanglement Matrix and Pairwise Coherence
While the CI measures global alignment, the entanglement matrix measures local pairwise relationships. For every pair of oscillators (i, j), the system calculates:

E(i,j) = |cos(φᵢ - φⱼ)|

This represents the phase agreement between oscillators i and j:

E = 1.0: Oscillators are in-phase (0° or 360° apart)
E = 0.0: Oscillators are in quadrature (90° apart, orthogonal)
E between 0 and 1: Varying degrees of alignment
The system counts how many oscillator pairs exceed a user-defined entanglement threshold (e.g., 0.7). This entangled pairs count serves as a confirmation filter: signals require not just high global CI, but also a minimum number of strong pairwise agreements. This prevents false ignitions where CI is high but driven by only two oscillators while the rest remain scattered.

The entanglement matrix creates an N×N symmetric matrix that can be visualized as a web—when many cells are bright (high E values), the ensemble is highly interconnected. When cells are dark, oscillators are moving independently.

Phase-Lock Tolerance Mechanism
A complementary confirmation layer is the phase-lock detector. This calculates the maximum phase spread across all oscillators:

For all pairs (i,j), compute angular distance: Δφ = |φᵢ - φⱼ|, wrapping at 180°

Max Spread = maximum Δφ across all pairs

If max spread < user threshold (e.g., 35°), the ensemble is considered phase-locked—all oscillators are within a narrow angular band.

This differs from entanglement: entanglement measures pairwise cosine similarity (magnitude of alignment), while phase-lock measures maximum angular deviation (tightness of clustering). Both must be satisfied for the highest-conviction signals.

Multi-Layer Visual Architecture
QRFM includes six visual components that represent the same underlying mathematics from different perspectives:

Circular Orbit Plot: A polar coordinate grid showing each oscillator as a vector from origin to perimeter. Angle = phase, radius = amplitude. This is a real-time snapshot of the complex plane. When vectors converge (point in similar directions), coherence is high. When scattered randomly, coherence is low. Users can see phase alignment forming before CI numerically confirms it.

Phase-Time Heat Map: A 2D matrix with rows = oscillators and columns = time bins. Each cell is colored by the oscillator's phase at that time (using a gradient where color hue maps to angle). Horizontal color bands indicate sustained phase alignment over time. Vertical color bands show moments when all oscillators shared the same phase (ignition points). This provides historical pattern recognition.

Entanglement Web Matrix: An N×N grid showing E(i,j) for all pairs. Cells are colored by entanglement strength—bright yellow/gold for high E, dark gray for low E. This reveals which oscillators are driving coherence and which are lagging. For example, if RSI and MACD show high E but Stochastic shows low E with everything, Stochastic is the outlier.

Quantum Field Cloud: A background color overlay on the price chart. Color (green = bullish, red = bearish) is determined by dominant phase. Opacity is determined by CI—high CI creates dense, opaque cloud; low CI creates faint, nearly invisible cloud. This gives an atmospheric "feel" for regime strength without looking at numbers.

Phase Spiral: A smoothed plot of dominant phase over recent history, displayed as a curve that wraps around price. When the spiral is tight and rotating steadily, the ensemble is in coherent rotation (trending). When the spiral is loose or erratic, coherence is breaking down.

Dashboard: A table showing real-time metrics: CI (as percentage), dominant phase (in degrees with directional arrow), field strength (CI × average amplitude), entangled pairs count, phase-lock status (locked/unlocked), quantum state classification ("Ignition", "Coherent", "Collapse", "Chaos"), and collapse risk (recent CI change normalized to 0-100%).

Each component is independently toggleable, allowing users to customize their workspace. The orbit plot is the most essential—it provides intuitive, visual feedback on phase alignment that no numerical dashboard can match.

Core Components and How They Work Together
1. Oscillator Normalization Engine
The foundation is creating a common measurement scale. QRFM supports eight oscillators:

RSI: Normalized from [0, 100] to [-1, 1] using overbought/oversold levels (70, 30) as anchors
MACD Histogram: Normalized by dividing by rolling standard deviation, then clamped to [-1, 1]
Stochastic %K: Normalized from [0, 100] using (80, 20) anchors
CCI: Divided by 200 (typical extreme level), clamped to [-1, 1]
Williams %R: Normalized from [-100, 0] using (-20, -80) anchors
MFI: Normalized from [0, 100] using (80, 20) anchors
ROC: Divided by 10, clamped to [-1, 1]
TSI: Divided by 50, clamped to [-1, 1]
Each oscillator can be individually enabled/disabled. Only active oscillators contribute to phase calculations. The normalization removes scale differences—a reading of +0.8 means "strongly bullish" regardless of whether it came from RSI or TSI.

2. Analytic Signal Construction
For each active oscillator at each bar, the system constructs the analytic signal:

In-Phase (I): The normalized oscillator value itself
Quadrature (Q): The bar-to-bar change in the normalized value (first derivative approximation)

This creates a 2D representation: (I, Q). The phase is extracted as:

φ = atan2(Q, I) × (180 / π)

This maps the oscillator to a point on the unit circle. An oscillator at the same value but rising (positive Q) will have a different phase than one that is falling (negative Q). This velocity-awareness is critical—it distinguishes between "at resistance and stalling" versus "at resistance and breaking through."

The amplitude is extracted as:

A = √(I² + Q²)

This represents the distance from origin in the (I, Q) plane. High amplitude means the oscillator is far from neutral (strong conviction). Low amplitude means it's near zero (weak/transitional state).

3. Coherence Calculation Pipeline
For each bar (or every Nth bar if phase sample rate > 1 for performance):

Step 1: Extract phase φₙ for each of the N active oscillators
Step 2: Compute complex exponentials: Zₙ = e^(i·φₙ·π/180) = cos(φₙ·π/180) + i·sin(φₙ·π/180)
Step 3: Sum the complex exponentials: R = Σ Zₙ = (Σ cos φₙ) + i·(Σ sin φₙ)
Step 4: Calculate magnitude: |R| = √[(Σ cos φₙ)² + (Σ sin φₙ)²]
Step 5: Normalize by count: CI_raw = |R| / N
Step 6: Smooth the CI: CI = SMA(CI_raw, smoothing_window)

The smoothing step (default 2 bars) removes single-bar noise spikes while preserving structural coherence changes. Users can adjust this to control reactivity versus stability.

The dominant phase is calculated as:

φ_dom = atan2(Σ sin φₙ, Σ cos φₙ) × (180 / π)

This is the angle of the resultant vector R in the complex plane.

4. Entanglement Matrix Construction
For all unique pairs of oscillators (i, j) where i < j:

Step 1: Get phases φᵢ and φⱼ
Step 2: Compute phase difference: Δφ = φᵢ - φⱼ (in radians)
Step 3: Calculate entanglement: E(i,j) = |cos(Δφ)|
Step 4: Store in symmetric matrix: matrix[j] = matrix[j] = E(i,j)

The matrix is then scanned: count how many E(i,j) values exceed the user-defined threshold (default 0.7). This count is the entangled pairs metric.

For visualization, the matrix is rendered as an N×N table where cell brightness maps to E(i,j) intensity.

5. Phase-Lock Detection
Step 1: For all unique pairs (i, j), compute angular distance: Δφ = |φᵢ - φⱼ|
Step 2: Wrap angles: if Δφ > 180°, set Δφ = 360° - Δφ
Step 3: Find maximum: max_spread = max(Δφ) across all pairs
Step 4: Compare to tolerance: phase_locked = (max_spread < tolerance)

If phase_locked is true, all oscillators are within the specified angular cone (e.g., 35°). This is a boolean confirmation filter.

6. Signal Generation Logic
Signals are generated through multi-layer confirmation:

Long Ignition Signal:

CI crosses above ignition threshold (e.g., 0.80)
AND dominant phase is in bullish range (-90° < φ_dom < +90°)
AND phase_locked = true
AND entangled_pairs >= minimum threshold (e.g., 4)
Short Ignition Signal:

CI crosses above ignition threshold
AND dominant phase is in bearish range (φ_dom < -90° OR φ_dom > +90°)
AND phase_locked = true
AND entangled_pairs >= minimum threshold
Collapse Signal:

CI at bar [5] minus CI at current bar > collapse threshold (e.g., 0.55)
AND CI at bar [5] was above 0.6 (must collapse from coherent state, not from already-low state)
These are strict conditions. A high CI alone does not generate a signal—dominant phase must align with direction, oscillators must be phase-locked, and sufficient pairwise entanglement must exist. This multi-factor gating dramatically reduces false signals compared to single-condition triggers.

Calculation Methodology
Phase 1: Oscillator Computation and Normalization
On each bar, the system calculates the raw values for all enabled oscillators using standard Pine Script functions:

RSI: ta.rsi(close, length)
MACD: ta.macd() returning histogram component
Stochastic: ta.stoch() smoothed with ta.sma()
CCI: ta.cci(close, length)
Williams %R: ta.wpr(length)
MFI: ta.mfi(hlc3, length)
ROC: ta.roc(close, length)
TSI: ta.tsi(close, short, long)
Each raw value is then passed through a normalization function:

normalize(value, overbought_level, oversold_level) = 2 × (value - oversold) / (overbought - oversold) - 1

This maps the oscillator's typical range to [-1, 1], where -1 represents extreme bearish, 0 represents neutral, and +1 represents extreme bullish.

For oscillators without fixed ranges (MACD, ROC, TSI), statistical normalization is used: divide by a rolling standard deviation or fixed divisor, then clamp to [-1, 1].

Phase 2: Phasor Extraction
For each normalized oscillator value val:

I = val (in-phase component)
Q = val - val[1] (quadrature component, first difference)

Phase calculation:

phi_rad = atan2(Q, I)
phi_deg = phi_rad × (180 / π)

Amplitude calculation:

A = √(I² + Q²)

These values are stored in arrays: osc_phases[n] and osc_amps[n] for each oscillator n.

Phase 3: Complex Summation and Coherence
Initialize accumulators:

sum_cos = 0
sum_sin = 0

For each oscillator n = 0 to N-1:

phi_rad = osc_phases[n] × (π / 180)
sum_cos += cos(phi_rad)
sum_sin += sin(phi_rad)

Resultant magnitude:

resultant_mag = √(sum_cos² + sum_sin²)

Coherence Index (raw):

CI_raw = resultant_mag / N

Smoothed CI:

CI = SMA(CI_raw, smoothing_window)

Dominant phase:

phi_dom_rad = atan2(sum_sin, sum_cos)
phi_dom_deg = phi_dom_rad × (180 / π)

Phase 4: Entanglement Matrix Population
For i = 0 to N-2:
For j = i+1 to N-1:
phi_i = osc_phases × (π / 180)
phi_j = osc_phases[j] × (π / 180)
delta_phi = phi_i - phi_j
E = |cos(delta_phi)|

matrix_index_ij = i × N + j
matrix_index_ji = j × N + i
entangle_matrix[matrix_index_ij] = E
entangle_matrix[matrix_index_ji] = E

if E >= threshold:
entangled_pairs += 1
The matrix uses flat array storage with index mapping: index(row, col) = row × N + col.

Phase 5: Phase-Lock Check
max_spread = 0

For i = 0 to N-2:
For j = i+1 to N-1:
delta = |osc_phases - osc_phases[j]|
if delta > 180:
delta = 360 - delta
max_spread = max(max_spread, delta)

phase_locked = (max_spread < tolerance)

Phase 6: Signal Evaluation
Ignition Long:

ignition_long = (CI crosses above threshold) AND
(phi_dom > -90 AND phi_dom < 90) AND
phase_locked AND
(entangled_pairs >= minimum)

Ignition Short:

ignition_short = (CI crosses above threshold) AND
(phi_dom < -90 OR phi_dom > 90) AND
phase_locked AND
(entangled_pairs >= minimum)

Collapse:

CI_prev = CI[5]
collapse = (CI_prev - CI > collapse_threshold) AND (CI_prev > 0.6)

All signals are evaluated on bar close. The crossover and crossunder functions ensure signals fire only once when conditions transition from false to true.

Phase 7: Field Strength and Visualization Metrics
Average Amplitude:

avg_amp = (Σ osc_amps[n]) / N

Field Strength:

field_strength = CI × avg_amp

Collapse Risk (for dashboard):

collapse_risk = (CI[5] - CI) / max(CI[5], 0.1)
collapse_risk_pct = clamp(collapse_risk × 100, 0, 100)

Quantum State Classification:

if (CI > threshold AND phase_locked):
state = "Ignition"
else if (CI > 0.6):
state = "Coherent"
else if (collapse):
state = "Collapse"
else:
state = "Chaos"

Phase 8: Visual Rendering
Orbit Plot: For each oscillator, convert polar (phase, amplitude) to Cartesian (x, y) for grid placement:

radius = amplitude × grid_center × 0.8
x = radius × cos(phase × π/180)
y = radius × sin(phase × π/180)
col = center + x (mapped to grid coordinates)
row = center - y

Heat Map: For each oscillator row and time column, retrieve historical phase value at lookback = (columns - col) × sample_rate, then map phase to color using a hue gradient.

Entanglement Web: Render matrix[j] as table cell with background color opacity = E(i,j).

Field Cloud: Background color = (phi_dom > -90 AND phi_dom < 90) ? green : red, with opacity = mix(min_opacity, max_opacity, CI).

All visual components render only on the last bar (barstate.islast) to minimize computational overhead.

How to Use This Indicator

Step 1: Apply QRFM to your chart. It works on all timeframes and asset classes, though 15-minute to 4-hour timeframes provide the best balance of responsiveness and noise reduction.

Step 2: Enable the dashboard (default: top right) and the circular orbit plot (default: middle left). These are your primary visual feedback tools.

Step 3: Optionally enable the heat map, entanglement web, and field cloud based on your preference. New users may find all visuals overwhelming; start with dashboard + orbit plot.

Step 4: Observe for 50-100 bars to let the indicator establish baseline coherence patterns. Markets have different "normal" CI ranges—some instruments naturally run higher or lower coherence.

Understanding the Circular Orbit Plot
The orbit plot is a polar grid showing oscillator vectors in real-time:

Center point: Neutral (zero phase and amplitude)
Each vector: A line from center to a point on the grid
Vector angle: The oscillator's phase (0° = right/east, 90° = up/north, 180° = left/west, -90° = down/south)
Vector length: The oscillator's amplitude (short = weak signal, long = strong signal)
Vector label: First letter of oscillator name (R = RSI, M = MACD, etc.)
What to watch:

Convergence: When all vectors cluster in one quadrant or sector, CI is rising and coherence is forming. This is your pre-signal warning.
Scatter: When vectors point in random directions (360° spread), CI is low and the market is in a non-trending or transitional regime.
Rotation: When the cluster rotates smoothly around the circle, the ensemble is in coherent oscillation—typically seen during steady trends.
Sudden flips: When the cluster rapidly jumps from one side to the opposite (e.g., +90° to -90°), a phase reversal has occurred—often coinciding with trend reversals.
Example: If you see RSI, MACD, and Stochastic all pointing toward 45° (northeast) with long vectors, while CCI, TSI, and ROC point toward 40-50° as well, coherence is high and dominant phase is bullish. Expect an ignition signal if CI crosses threshold.

Reading Dashboard Metrics
The dashboard provides numerical confirmation of what the orbit plot shows visually:

CI: Displays as 0-100%. Above 70% = high coherence (strong regime), 40-70% = moderate, below 40% = low (poor conditions for trend entries).
Dom Phase: Angle in degrees with directional arrow. ⬆ = bullish bias, ⬇ = bearish bias, ⬌ = neutral.
Field Strength: CI weighted by amplitude. High values (> 0.6) indicate not just alignment but strong alignment.
Entangled Pairs: Count of oscillator pairs with E > threshold. Higher = more confirmation. If minimum is set to 4, you need at least 4 pairs entangled for signals.
Phase Lock: 🔒 YES (all oscillators within tolerance) or 🔓 NO (spread too wide).
State: Real-time classification:
🚀 IGNITION: CI just crossed threshold with phase-lock
⚡ COHERENT: CI is high and stable
💥 COLLAPSE: CI has dropped sharply
🌀 CHAOS: Low CI, scattered phases
Collapse Risk: 0-100% scale based on recent CI change. Above 50% warns of imminent breakdown.
Interpreting Signals
Long Ignition (Blue Triangle Below Price):

Occurs when CI crosses above threshold (e.g., 0.80)
Dominant phase is in bullish range (-90° to +90°)
All oscillators are phase-locked (within tolerance)
Minimum entangled pairs requirement met
Interpretation: The oscillator ensemble has transitioned from disorder to coherent bullish alignment. This is a high-probability long entry point. The multi-layer confirmation (CI + phase direction + lock + entanglement) ensures this is not a single-oscillator whipsaw.

Short Ignition (Red Triangle Above Price):

Same conditions as long, but dominant phase is in bearish range (< -90° or > +90°)
Interpretation: Coherent bearish alignment has formed. High-probability short entry.

Collapse (Circles Above and Below Price):

CI has dropped by more than the collapse threshold (e.g., 0.55) over a 5-bar window
CI was previously above 0.6 (collapsing from coherent state)
Interpretation: Phase coherence has broken down. If you are in a position, this is an exit warning. If looking to enter, stand aside—regime is transitioning.

Phase-Time Heat Map Patterns
Enable the heat map and position it at bottom right. The rows represent individual oscillators, columns represent time bins (most recent on left).

Pattern: Horizontal Color Bands

If a row (e.g., RSI) shows consistent color across columns (say, green for several bins), that oscillator has maintained stable phase over time. If all rows show horizontal bands of similar color, the entire ensemble has been phase-locked for an extended period—this is a strong trending regime.

Pattern: Vertical Color Bands

If a column (single time bin) shows all cells with the same or very similar color, that moment in time had high coherence. These vertical bands often align with ignition signals or major price pivots.

Pattern: Rainbow Chaos

If cells are random colors (red, green, yellow mixed with no pattern), coherence is low. The ensemble is scattered. Avoid trading during these periods unless you have external confirmation.

Pattern: Color Transition

If you see a row transition from red to green (or vice versa) sharply, that oscillator has phase-flipped. If multiple rows do this simultaneously, a regime change is underway.

Entanglement Web Analysis
Enable the web matrix (default: opposite corner from heat map). It shows an N×N grid where N = number of active oscillators.

Bright Yellow/Gold Cells: High pairwise entanglement. For example, if the RSI-MACD cell is bright gold, those two oscillators are moving in phase. If the RSI-Stochastic cell is bright, they are entangled as well.

Dark Gray Cells: Low entanglement. Oscillators are decorrelated or in quadrature.

Diagonal: Always marked with "—" because an oscillator is always perfectly entangled with itself.

How to use:

Scan for clustering: If most cells are bright, coherence is high across the board. If only a few cells are bright, coherence is driven by a subset (e.g., RSI and MACD are aligned, but nothing else is—weak signal).
Identify laggards: If one row/column is entirely dark, that oscillator is the outlier. You may choose to disable it or monitor for when it joins the group (late confirmation).
Watch for web formation: During low-coherence periods, the matrix is mostly dark. As coherence builds, cells begin lighting up. A sudden "web" of connections forming visually precedes ignition signals.
Trading Workflow
Step 1: Monitor Coherence Level

Check the dashboard CI metric or observe the orbit plot. If CI is below 40% and vectors are scattered, conditions are poor for trend entries. Wait.

Step 2: Detect Coherence Building

When CI begins rising (say, from 30% to 50-60%) and you notice vectors on the orbit plot starting to cluster, coherence is forming. This is your alert phase—do not enter yet, but prepare.

Step 3: Confirm Phase Direction

Check the dominant phase angle and the orbit plot quadrant where clustering is occurring:

Clustering in right half (0° to ±90°): Bullish bias forming
Clustering in left half (±90° to 180°): Bearish bias forming
Verify the dashboard shows the corresponding directional arrow (⬆ or ⬇).

Step 4: Wait for Signal Confirmation

Do not enter based on rising CI alone. Wait for the full ignition signal:

CI crosses above threshold
Phase-lock indicator shows 🔒 YES
Entangled pairs count >= minimum
Directional triangle appears on chart
This ensures all layers have aligned.

Step 5: Execute Entry

Long: Blue triangle below price appears → enter long
Short: Red triangle above price appears → enter short

Step 6: Position Management

Initial Stop: Place stop loss based on your risk management rules (e.g., recent swing low/high, ATR-based buffer).

Monitoring:

Watch the field cloud density. If it remains opaque and colored in your direction, the regime is intact.
Check dashboard collapse risk. If it rises above 50%, prepare for exit.
Monitor the orbit plot. If vectors begin scattering or the cluster flips to the opposite side, coherence is breaking.
Exit Triggers:

Collapse signal fires (circles appear)
Dominant phase flips to opposite half-plane
CI drops below 40% (coherence lost)
Price hits your profit target or trailing stop
Step 7: Post-Exit Analysis

After exiting, observe whether a new ignition forms in the opposite direction (reversal) or if CI remains low (transition to range). Use this to decide whether to re-enter, reverse, or stand aside.

Best Practices
Use Price Structure as Context

QRFM identifies when coherence forms but does not specify where price will go. Combine ignition signals with support/resistance levels, trendlines, or chart patterns. For example:

Long ignition near a major support level after a pullback: high-probability bounce
Long ignition in the middle of a range with no structure: lower probability
Multi-Timeframe Confirmation

Open QRFM on two timeframes simultaneously:

Higher timeframe (e.g., 4-hour): Use CI level to determine regime bias. If 4H CI is above 60% and dominant phase is bullish, the market is in a bullish regime.
Lower timeframe (e.g., 15-minute): Execute entries on ignition signals that align with the higher timeframe bias.
This prevents counter-trend trades and increases win rate.

Distinguish Between Regime Types

High CI, stable dominant phase (State: Coherent): Trending market. Ignitions are continuation signals; collapses are profit-taking or reversal warnings.
Low CI, erratic dominant phase (State: Chaos): Ranging or choppy market. Avoid ignition signals or reduce position size. Wait for coherence to establish.
Moderate CI with frequent collapses: Whipsaw environment. Use wider stops or stand aside.
Adjust Parameters to Instrument and Timeframe

Crypto/Forex (high volatility): Lower ignition threshold (0.65-0.75), lower CI smoothing (2-3), shorter oscillator lengths (7-10).
Stocks/Indices (moderate volatility): Standard settings (threshold 0.75-0.85, smoothing 5-7, oscillator lengths 14).
Lower timeframes (5-15 min): Reduce phase sample rate to 1-2 for responsiveness.
Higher timeframes (daily+): Increase CI smoothing and oscillator lengths for noise reduction.
Use Entanglement Count as Conviction Filter

The minimum entangled pairs setting controls signal strictness:

Low (1-2): More signals, lower quality (acceptable if you have other confirmation)
Medium (3-5): Balanced (recommended for most traders)
High (6+): Very strict, fewer signals, highest quality
Adjust based on your trade frequency preference and risk tolerance.

Monitor Oscillator Contribution

Use the entanglement web to see which oscillators are driving coherence. If certain oscillators are consistently dark (low E with all others), they may be adding noise. Consider disabling them. For example:

On low-volume instruments, MFI may be unreliable → disable MFI
On strongly trending instruments, mean-reversion oscillators (Stochastic, RSI) may lag → reduce weight or disable
Respect the Collapse Signal

Collapse events are early warnings. Price may continue in the original direction for several bars after collapse fires, but the underlying regime has weakened. Best practice:

If in profit: Take partial or full profit on collapse
If at breakeven/small loss: Exit immediately
If collapse occurs shortly after entry: Likely a false ignition; exit to avoid drawdown
Collapses do not guarantee immediate reversals—they signal uncertainty.

Combine with Volume Analysis

If your instrument has reliable volume:

Ignitions with expanding volume: Higher conviction
Ignitions with declining volume: Weaker, possibly false
Collapses with volume spikes: Strong reversal signal
Collapses with low volume: May just be consolidation
Volume is not built into QRFM (except via MFI), so add it as external confirmation.

Observe the Phase Spiral

The spiral provides a quick visual cue for rotation consistency:

Tight, smooth spiral: Ensemble is rotating coherently (trending)
Loose, erratic spiral: Phase is jumping around (ranging or transitional)
If the spiral tightens, coherence is building. If it loosens, coherence is dissolving.

Do Not Overtrade Low-Coherence Periods

When CI is persistently below 40% and the state is "Chaos," the market is not in a regime where phase analysis is predictive. During these times:

Reduce position size
Widen stops
Wait for coherence to return
QRFM's strength is regime detection. If there is no regime, the tool correctly signals "stand aside."

Use Alerts Strategically

Set alerts for:

Long Ignition
Short Ignition
Collapse
Phase Lock (optional)
Configure alerts to "Once per bar close" to avoid intrabar repainting and noise. When an alert fires, manually verify:

Orbit plot shows clustering
Dashboard confirms all conditions
Price structure supports the trade
Do not blindly trade alerts—use them as prompts for analysis.

Ideal Market Conditions
Best Performance
Instruments:

Liquid, actively traded markets (major forex pairs, large-cap stocks, major indices, top-tier crypto)
Instruments with clear cyclical oscillator behavior (avoid extremely illiquid or manipulated markets)
Timeframes:

15-minute to 4-hour: Optimal balance of noise reduction and responsiveness
1-hour to daily: Slower, higher-conviction signals; good for swing trading
5-minute: Acceptable for scalping if parameters are tightened and you accept more noise
Market Regimes:

Trending markets with periodic retracements (where oscillators cycle through phases predictably)
Breakout environments (coherence forms before/during breakout; collapse occurs at exhaustion)
Rotational markets with clear swings (oscillators phase-lock at turning points)
Volatility:

Moderate to high volatility (oscillators have room to move through their ranges)
Stable volatility regimes (sudden VIX spikes or flash crashes may create false collapses)
Challenging Conditions
Instruments:

Very low liquidity markets (erratic price action creates unstable oscillator phases)
Heavily news-driven instruments (fundamentals may override technical coherence)
Highly correlated instruments (oscillators may all reflect the same underlying factor, reducing independence)
Market Regimes:

Deep, prolonged consolidation (oscillators remain near neutral, CI is chronically low, few signals fire)
Extreme chop with no directional bias (oscillators whipsaw, coherence never establishes)
Gap-driven markets (large overnight gaps create phase discontinuities)
Timeframes:

Sub-5-minute charts: Noise dominates; oscillators flip rapidly; coherence is fleeting and unreliable
Weekly/monthly: Oscillators move extremely slowly; signals are rare; better suited for long-term positioning than active trading
Special Cases:

During major economic releases or earnings: Oscillators may lag price or become decorrelated as fundamentals overwhelm technicals. Reduce position size or stand aside.
In extremely low-volatility environments (e.g., holiday periods): Oscillators compress to neutral, CI may be artificially high due to lack of movement, but signals lack follow-through.
Adaptive Behavior
QRFM is designed to self-adapt to poor conditions:

When coherence is genuinely absent, CI remains low and signals do not fire
When only a subset of oscillators aligns, entangled pairs count stays below threshold and signals are filtered out
When phase-lock cannot be achieved (oscillators too scattered), the lock filter prevents signals
This means the indicator will naturally produce fewer (or zero) signals during unfavorable conditions, rather than generating false signals. This is a feature—it keeps you out of low-probability trades.

Parameter Optimization by Trading Style
Scalping (5-15 Minute Charts)
Goal: Maximum responsiveness, accept higher noise

Oscillator Lengths:

RSI: 7-10
MACD: 8/17/6
Stochastic: 8-10, smooth 2-3
CCI: 14-16
Others: 8-12
Coherence Settings:

CI Smoothing Window: 2-3 bars (fast reaction)
Phase Sample Rate: 1 (every bar)
Ignition Threshold: 0.65-0.75 (lower for more signals)
Collapse Threshold: 0.40-0.50 (earlier exit warnings)
Confirmation:

Phase Lock Tolerance: 40-50° (looser, easier to achieve)
Min Entangled Pairs: 2-3 (fewer oscillators required)
Visuals:

Orbit Plot + Dashboard only (reduce screen clutter for fast decisions)
Disable heavy visuals (heat map, web) for performance
Alerts:

Enable all ignition and collapse alerts
Set to "Once per bar close"
Day Trading (15-Minute to 1-Hour Charts)
Goal: Balance between responsiveness and reliability

Oscillator Lengths:

RSI: 14 (standard)
MACD: 12/26/9 (standard)
Stochastic: 14, smooth 3
CCI: 20
Others: 10-14
Coherence Settings:

CI Smoothing Window: 3-5 bars (balanced)
Phase Sample Rate: 2-3
Ignition Threshold: 0.75-0.85 (moderate selectivity)
Collapse Threshold: 0.50-0.55 (balanced exit timing)
Confirmation:

Phase Lock Tolerance: 30-40° (moderate tightness)
Min Entangled Pairs: 4-5 (reasonable confirmation)
Visuals:

Orbit Plot + Dashboard + Heat Map or Web (choose one)
Field Cloud for regime backdrop
Alerts:

Ignition and collapse alerts
Optional phase-lock alert for advance warning
Swing Trading (4-Hour to Daily Charts)
Goal: High-conviction signals, minimal noise, fewer trades

Oscillator Lengths:

RSI: 14-21
MACD: 12/26/9 or 19/39/9 (longer variant)
Stochastic: 14-21, smooth 3-5
CCI: 20-30
Others: 14-20
Coherence Settings:

CI Smoothing Window: 5-10 bars (very smooth)
Phase Sample Rate: 3-5
Ignition Threshold: 0.80-0.90 (high bar for entry)
Collapse Threshold: 0.55-0.65 (only significant breakdowns)
Confirmation:

Phase Lock Tolerance: 20-30° (tight clustering required)
Min Entangled Pairs: 5-7 (strong confirmation)
Visuals:

All modules enabled (you have time to analyze)
Heat Map for multi-bar pattern recognition
Web for deep confirmation analysis
Alerts:

Ignition and collapse
Review manually before entering (no rush)
Position/Long-Term Trading (Daily to Weekly Charts)
Goal: Rare, very high-conviction regime shifts

Oscillator Lengths:

RSI: 21-30
MACD: 19/39/9 or 26/52/12
Stochastic: 21, smooth 5
CCI: 30-50
Others: 20-30
Coherence Settings:

CI Smoothing Window: 10-14 bars
Phase Sample Rate: 5 (every 5th bar to reduce computation)
Ignition Threshold: 0.85-0.95 (only extreme alignment)
Collapse Threshold: 0.60-0.70 (major regime breaks only)
Confirmation:

Phase Lock Tolerance: 15-25° (very tight)
Min Entangled Pairs: 6+ (broad consensus required)
Visuals:

Dashboard + Orbit Plot for quick checks
Heat Map to study historical coherence patterns
Web to verify deep entanglement
Alerts:

Ignition only (collapses are less critical on long timeframes)
Manual review with fundamental analysis overlay
Performance Optimization (Low-End Systems)
If you experience lag or slow rendering:

Reduce Visual Load:

Orbit Grid Size: 8-10 (instead of 12+)
Heat Map Time Bins: 5-8 (instead of 10+)
Disable Web Matrix entirely if not needed
Disable Field Cloud and Phase Spiral
Reduce Calculation Frequency:

Phase Sample Rate: 5-10 (calculate every 5-10 bars)
Max History Depth: 100-200 (instead of 500+)
Disable Unused Oscillators:

If you only want RSI, MACD, and Stochastic, disable the other five. Fewer oscillators = smaller matrices, faster loops.
Simplify Dashboard:

Choose "Small" dashboard size
Reduce number of metrics displayed
These settings will not significantly degrade signal quality (signals are based on bar-close calculations, which remain accurate), but will improve chart responsiveness.

Important Disclaimers
This indicator is a technical analysis tool designed to identify periods of phase coherence across an ensemble of oscillators. It is not a standalone trading system and does not guarantee profitable trades. The Coherence Index, dominant phase, and entanglement metrics are mathematical calculations applied to historical price data—they measure past oscillator behavior and do not predict future price movements with certainty.

No Predictive Guarantee: High coherence indicates that oscillators are currently aligned, which historically has coincided with trending or directional price movement. However, past alignment does not guarantee future trends. Markets can remain coherent while prices consolidate, or lose coherence suddenly due to news, liquidity changes, or other factors not captured by oscillator mathematics.

Signal Confirmation is Probabilistic: The multi-layer confirmation system (CI threshold + dominant phase + phase-lock + entanglement) is designed to filter out low-probability setups. This increases the proportion of valid signals relative to false signals, but does not eliminate false signals entirely. Users should combine QRFM with additional analysis—support and resistance levels, volume confirmation, multi-timeframe alignment, and fundamental context—before executing trades.

Collapse Signals are Warnings, Not Reversals: A coherence collapse indicates that the oscillator ensemble has lost alignment. This often precedes trend exhaustion or reversals, but can also occur during healthy pullbacks or consolidations. Price may continue in the original direction after a collapse. Use collapses as risk management cues (tighten stops, take partial profits) rather than automatic reversal entries.

Market Regime Dependency: QRFM performs best in markets where oscillators exhibit cyclical, mean-reverting behavior and where trends are punctuated by retracements. In markets dominated by fundamental shocks, gap openings, or extreme low-liquidity conditions, oscillator coherence may be less reliable. During such periods, reduce position size or stand aside.

Risk Management is Essential: All trading involves risk of loss. Use appropriate stop losses, position sizing, and risk-per-trade limits. The indicator does not specify stop loss or take profit levels—these must be determined by the user based on their risk tolerance and account size. Never risk more than you can afford to lose.

Parameter Sensitivity: The indicator's behavior changes with input parameters. Aggressive settings (low thresholds, loose tolerances) produce more signals with lower average quality. Conservative settings (high thresholds, tight tolerances) produce fewer signals with higher average quality. Users should backtest and forward-test parameter sets on their specific instruments and timeframes before committing real capital.

No Repainting by Design: All signal conditions are evaluated on bar close using bar-close values. However, the visual components (orbit plot, heat map, dashboard) update in real-time during bar formation for monitoring purposes. For trade execution, rely on the confirmed signals (triangles and circles) that appear only after the bar closes.

Computational Load: QRFM performs extensive calculations, including nested loops for entanglement matrices and real-time table rendering. On lower-powered devices or when running multiple indicators simultaneously, users may experience lag. Use the performance optimization settings (reduce visual complexity, increase phase sample rate, disable unused oscillators) to improve responsiveness.

This system is most effective when used as one component within a broader trading methodology that includes sound risk management, multi-timeframe analysis, market context awareness, and disciplined execution. It is a tool for regime detection and signal confirmation, not a substitute for comprehensive trade planning.

Technical Notes
Calculation Timing: All signal logic (ignition, collapse) is evaluated using bar-close values. The barstate.isconfirmed or implicit bar-close behavior ensures signals do not repaint. Visual components (tables, plots) render on every tick for real-time feedback but do not affect signal generation.

Phase Wrapping: Phase angles are calculated in the range -180° to +180° using atan2. Angular distance calculations account for wrapping (e.g., the distance between +170° and -170° is 20°, not 340°). This ensures phase-lock detection works correctly across the ±180° boundary.

Array Management: The indicator uses fixed-size arrays for oscillator phases, amplitudes, and the entanglement matrix. The maximum number of oscillators is 8. If fewer oscillators are enabled, array sizes shrink accordingly (only active oscillators are processed).

Matrix Indexing: The entanglement matrix is stored as a flat array with size N×N, where N is the number of active oscillators. Index mapping: index(row, col) = row × N + col. Symmetric pairs (i,j) and (j,i) are stored identically.

Normalization Stability: Oscillators are normalized to [-1, 1] using fixed reference levels (e.g., RSI overbought/oversold at 70/30). For unbounded oscillators (MACD, ROC, TSI), statistical normalization (division by rolling standard deviation) is used, with clamping to prevent extreme outliers from distorting phase calculations.

Smoothing and Lag: The CI smoothing window (SMA) introduces lag proportional to the window size. This is intentional—it filters out single-bar noise spikes in coherence. Users requiring faster reaction can reduce the smoothing window to 1-2 bars, at the cost of increased sensitivity to noise.

Complex Number Representation: Pine Script does not have native complex number types. Complex arithmetic is implemented using separate real and imaginary accumulators (sum_cos, sum_sin) and manual calculation of magnitude (sqrt(real² + imag²)) and argument (atan2(imag, real)).

Lookback Limits: The indicator respects Pine Script's maximum lookback constraints. Historical phase and amplitude values are accessed using the [offset] operator, with lookback limited to the chart's available bar history (max_bars_back=5000 declared).

Visual Rendering Performance: Tables (orbit plot, heat map, web, dashboard) are conditionally deleted and recreated on each update using table.delete() and table.new(). This prevents memory leaks but incurs redraw overhead. Rendering is restricted to barstate.islast (last bar) to minimize computational load—historical bars do not render visuals.

Alert Condition Triggers: alertcondition() functions evaluate on bar close when their boolean conditions transition from false to true. Alerts do not fire repeatedly while a condition remains true (e.g., CI stays above threshold for 10 bars fires only once on the initial cross).

Color Gradient Functions: The phaseColor() function maps phase angles to RGB hues using sine waves offset by 120° (red, green, blue channels). This creates a continuous spectrum where -180° to +180° spans the full color wheel. The amplitudeColor() function maps amplitude to grayscale intensity. The coherenceColor() function uses cos(phase) to map contribution to CI (positive = green, negative = red).

No External Data Requests: QRFM operates entirely on the chart's symbol and timeframe. It does not use request.security() or access external data sources. All calculations are self-contained, avoiding lookahead bias from higher-timeframe requests.

Deterministic Behavior: Given identical input parameters and price data, QRFM produces identical outputs. There are no random elements, probabilistic sampling, or time-of-day dependencies.

— Dskyz, Engineering precision. Trading coherence.