Density Zones (GM Crossing Clusters) + QHO Spin Flips

INDICATOR NAME
Density Zones (GM Crossing Clusters) + QHO Spin Flips

OVERVIEW
This indicator combines two complementary ideas into a single overlay: *this combines my earlier Geometric Mean Indicator with the Quantum Harmonic Oscillator (Overlay) with additional enhancements*

1) Density Zones (GM Crossing Clusters)
A “Density Zone” is detected when price repeatedly crosses a Geometric Mean equilibrium line (GM) within a rolling lookback window. Conceptually, this identifies regions where the market is repeatedly “snapping” across an equilibrium boundary—high churn, high decision pressure, and repeated re-selection of direction.

2) QHO Spin Flips (Regression-Residual σ Breaches)
A “Spin Flip” is detected when price deviates beyond a configurable σ-threshold (κ) from a regression-based equilibrium, using normalized residuals. Conceptually, this marks excursions into extreme states (decoherence / expansion), which often precede a reversion toward equilibrium and/or a regime re-scaling.

These two systems are related but not identical:
- Density Zones identify where equilibrium crossings cluster (a “singularity”/anchor behavior around GM).
- Spin Flips identify when price exceeds statistically extreme displacement from the regression equilibrium (LSR), indicating expansion beyond typical variance.

CORE CONCEPTS AND FORMULAS

SECTION A — GEOMETRIC MEAN EQUILIBRIUM (GM)
We define two moving averages:

(1) MA1_t = SMA(close_t, L1)
(2) MA2_t = SMA(close_t, L2)

We define the equilibrium anchor as the geometric mean of MA1 and MA2:

(3) GM_t = sqrt( MA1_t * MA2_t )

This GM line acts as an equilibrium boundary. Repeated crossings are interpreted as high “equilibrium churn.”

SECTION B — CROSS EVENTS (UP/DOWN)
A “cross event” is registered when the sign of (close - GM) changes:

Define a sign function s_t:

(4) s_t =
+1 if close_t > GM_t
-1 if close_t < GM_t
s_{t-1} if close_t == GM_t (tie-breaker to avoid false flips)

Then define the crossing event indicator:

(5) crossEvent_t = 1 if s_t != s_{t-1}
0 otherwise

Additionally, the indicator plots explicit cross markers:
- Cross Above GM: crossover(close, GM)
- Cross Below GM: crossunder(close, GM)

These provide directional visual cues and match the original Geometric Mean Indicator behavior.

SECTION C — DENSITY MEASURE (CROSSING CLUSTER COUNT)
A Density Zone is based on the number of cross events occurring in the last W bars:

(6) D_t = Σ_{i=0..W-1} crossEvent_{t-i}

This is a “crossing density” score: how many times price has toggled across GM recently.

The script implements this efficiently using a cumulative sum identity:

Let x_t = crossEvent_t.

(7) cumX_t = Σ_{j=0..t} x_j

Then:

(8) D_t = cumX_t - cumX_{t-W} (for t >= W)
cumX_t (for t < W)

SECTION D — DENSITY ZONE TRIGGER
We define a Density Zone state:

(9) isDZ_t = ( D_t >= θ )

where:
- θ (theta) is the user-selected crossing threshold.

Zone edges:
(10) dzStart_t = isDZ_t AND NOT isDZ_{t-1}
(11) dzEnd_t = NOT isDZ_t AND isDZ_{t-1}

SECTION E — DENSITY ZONE BOUNDS
While inside a Density Zone, we track the running high/low to display zone bounds:

(12) dzHi_t = max(dzHi_{t-1}, high_t) if isDZ_t
(13) dzLo_t = min(dzLo_{t-1}, low_t) if isDZ_t

On dzStart:
(14) dzHi_t := high_t
(15) dzLo_t := low_t

Outside zones, bounds are reset to NA.

These bounds visually bracket the “singularity span” (the churn envelope) during each density episode.

SECTION F — QHO EQUILIBRIUM (REGRESSION CENTERLINE)
Define the regression equilibrium (LSR):

(16) m_t = linreg(close_t, L, 0)

This is the “centerline” the QHO system uses as equilibrium.

SECTION G — RESIDUAL AND σ (FIELD WIDTH)
Residual:

(17) r_t = close_t - m_t

Rolling standard deviation of residuals:

(18) σ_t = stdev(r_t, L)

This σ_t is the local volatility/width of the residual field around the regression equilibrium.

SECTION H — NORMALIZED DISPLACEMENT AND SPIN FLIP
Define the standardized displacement:

(19) Y_t = (close_t - m_t) / σ_t

(If σ_t = 0, the script safely treats Y_t = 0.)

Spin Flip trigger uses a user threshold κ:

(20) spinFlip_t = ( |Y_t| > κ )

Directional spin flips:
(21) spinUp_t = ( Y_t > +κ )
(22) spinDn_t = ( Y_t < -κ )

The default κ=3.0 corresponds to “3σ excursions,” which are statistically extreme under a normal residual assumption (even though real markets are not perfectly normal).

SECTION I — QHO BANDS (OPTIONAL VISUALIZATION)
The indicator optionally draws the standard σ-bands around the regression equilibrium:

(23) 1σ bands: m_t ± 1·σ_t
(24) 2σ bands: m_t ± 2·σ_t
(25) 3σ bands: m_t ± 3·σ_t

These provide immediate context for the Spin Flip events.

WHAT YOU SEE ON THE CHART

1) MA1 / MA2 / GM lines (optional)
- MA1 (blue), MA2 (red), GM (green).
- GM is the equilibrium anchor for Density Zones and cross markers.

2) GM Cross Markers (optional)
- “GM↑” label markers appear on bars where close crosses above GM.
- “GM↓” label markers appear on bars where close crosses below GM.

3) Density Zone Shading (optional)
- Background shading appears while isDZ_t = true.
- This is the period where the crossing density D_t is above θ.

4) Density Zone High/Low Bounds (optional)
- Two lines (dzHi / dzLo) are drawn only while in-zone.
- These bounds bracket the full churn envelope during the density episode.

5) QHO Bands (optional)
- 1σ, 2σ, 3σ shaded zones around regression equilibrium.
- These visualize the current variance field.

6) Regression Equilibrium (LSR Centerline)
- The white centerline is the regression equilibrium m_t.

7) Spin Flip Markers
- A circle is plotted when |Y_t| > κ (beyond your chosen σ-threshold).
- Marker size is user-controlled (tiny → huge).

HOW TO USE IT

Step 1 — Pick the equilibrium anchor (GM)
- L1 and L2 define MA1 and MA2.
- GM = sqrt(MA1 * MA2) becomes your equilibrium boundary.
Typical choices:
- Faster equilibrium: L1=20, L2=50 (default-like).
- Slower equilibrium: L1=50, L2=200 (macro anchor).

Interpretation:
- GM acts like a “center of mass” between two moving averages.
- Crosses show when price flips from one side of equilibrium to the other.

Step 2 — Tune Density Zones (W and θ)
- W controls the time window measured (how far back you count crossings).
- θ controls how many crossings qualify as a “density/singularity episode.”

Guideline:
- Larger W = slower, broader density detection.
- Higher θ = only the most intense churn is labeled as a Density Zone.

Interpretation:
- A Density Zone is not “bullish” or “bearish” by itself.
- It is a condition: repeated equilibrium toggling (high churn / high compression).
- These often precede expansions, but direction is not implied by the zone alone.

Step 3 — Tune the QHO spin flip sensitivity (L and κ)
- L controls regression memory and σ estimation length.
- κ controls how extreme the displacement must be to trigger a spin flip.

Guideline:
- Smaller L = more reactive centerline and σ.
- Larger L = smoother, slower “field” definition.
- κ=3.0 = strong extreme filter.
- κ=2.0 = more frequent flips.

Interpretation:
- Spin flips mark when price exits the “normal” residual field.
- In your model language: a moment of decoherence/expansion that is statistically extreme relative to recent equilibrium.

Step 4 — Read the combined behavior (your key thesis)
A) Density Zone forms (GM churn clusters):
- Market repeatedly crosses equilibrium (GM), compressing into a bounded churn envelope.
- dzHi/dzLo show the envelope range.

B) Expansion occurs:
- Price can release away from the density envelope (up or down).
- If it expands far enough relative to regression equilibrium, a Spin Flip triggers (|Y| > κ).

C) Re-coherence:
- After a spin flip, price often returns toward equilibrium structures:
- toward the regression centerline m_t
- and/or back toward the density envelope (dzHi/dzLo) depending on regime behavior.
- The indicator does not guarantee return, but it highlights the condition where return-to-field is statistically likely in many regimes.

IMPORTANT NOTES / DISCLAIMERS
- This indicator is an analytical overlay. It does not provide financial advice.
- Density Zones are condition states derived from GM crossing frequency; they do not predict direction.
- Spin Flips are statistical excursions based on regression residuals and rolling σ; markets have fat tails and non-stationarity, so σ-based thresholds are contextual, not absolute.
- All parameters (L1, L2, W, θ, L, κ) should be tuned per asset, timeframe, and volatility regime.

PARAMETER SUMMARY

Geometric Mean / Density Zones:
- L1: MA1 length
- L2: MA2 length
- GM_t = sqrt(SMA(L1)*SMA(L2))
- W: crossing-count lookback window
- θ: crossing density threshold
- D_t = Σ crossEvent_{t-i} over W
- isDZ_t = (D_t >= θ)
- dzHi/dzLo track envelope bounds while isDZ is true

QHO / Spin Flips:
- L: regression + residual σ length
- m_t = linreg(close, L, 0)
- r_t = close_t - m_t
- σ_t = stdev(r_t, L)
- Y_t = r_t / σ_t
- spinFlip_t = (|Y_t| > κ)

Visual Controls:
- toggles for GM lines, cross markers, zone shading, bounds, QHO bands
- marker size options for GM crosses and spin flips

ALERTS INCLUDED
- Density Zone START / END
- Spin Flip UP / DOWN
- Cross Above GM / Cross Below GM

SUMMARY
This indicator treats the Geometric Mean as an equilibrium boundary and identifies “Density Zones” when price repeatedly crosses that equilibrium within a rolling window, forming a bounded churn envelope (dzHi/dzLo). It also models a regression-based equilibrium field and triggers “Spin Flips” when price makes statistically extreme σ-excursions from that field. Used together, Density Zones highlight compression/decision regions (equilibrium churn), while Spin Flips highlight extreme expansion states (σ-breaches), allowing the user to visualize how price compresses around equilibrium, releases outward, and often re-stabilizes around equilibrium structures over time.