Vector Radius PBR Scaling

Vector Radius PBR Scaling — √Price Geometric Chart Calibration

WHAT THIS INDICATOR DOES

This indicator calculates a theoretically derived PBR (Points Per Bar) scaling value based on the concept of √price space geometry. You select a swing high and low using date inputs, and it outputs PBR values that can be used with TradingView's chart scaling for experimental geometric analysis with circle and arc tools.

It is designed for students and researchers of geometric market theory who want to explore how √price transformations affect chart scaling and circle geometry.

THE CONCEPT

Standard PBR divides the price range by the number of bars. This treats all price levels equally — a $100 move at $50 is handled the same as a $100 move at $50,000.

This indicator explores an alternative approach: what if price is better understood as a radial distance from zero? In this theoretical framework, √Price represents the radius — the distance from zero to any price level. The difference √H - √L represents the distance a move covers in this curved space, which is not the same as taking the square root of the range √(H-L). The velocity through this space, measured per bar, produces a scaling factor that accounts for the absolute price level of the instrument.

The formula explored is:

PBR = ((√H - √L) / B) × Radius

Where H is the high price, L is the low price, B is the number of bars, and Radius is either √H or √Mid depending on the mode selected.

TWO MODES

Impulse (× √H) scales by the outer radius, which is the maximum price reached during the swing. The theory suggests this may suit trending or impulsive market conditions where the high represents peak energy expression.

Equilibrium (× √Mid) scales by the midpoint radius, where Mid = (H + L) / 2. The theory suggests this may suit ranging or consolidating conditions where balance around the centre of the move matters more than its extremes.

WHY √H IS USED FOR BOTH UP AND DOWN LEGS

In this geometric framework, √H represents the outer boundary of the swing regardless of direction. Whether price moved up to a high or down from a high, the maximum price level defines the largest radius of the system. This is analogous to how a pendulum's behaviour is governed by its maximum displacement, not its direction of travel.

WHAT THIS DOES NOT DO

This indicator does not predict where price will go. It does not identify support or resistance levels. It does not generate trading signals. It does not guarantee that circles or arcs will align with future price action. It does not replace proper risk management or trading discipline.

Any observed alignments between geometric projections and actual price behaviour may be coincidental. Markets are influenced by fundamentals, sentiment, liquidity, and countless other factors that no geometric formula can fully capture.

HOW TO USE (FOR RESEARCH)

Add the indicator to your chart. Select start and end dates around a swing you want to study. Read the PBR values from the table. Experiment with entering the PBR into your chart scaling settings. Draw circles or arcs and observe. Do not treat any observations as predictive.

TABLE OUTPUT

The indicator displays the high, low, and mid prices of the selected range, the price range and bar count, the √H, √L, and √Mid values, the root speed (√H - √L) / B, and the final PBR for both Impulse and Equilibrium modes.

WHO THIS IS FOR

This is for researchers and students of geometric market analysis who want a tool to quickly calculate √price-based scaling values. It assumes familiarity with PBR scaling, square-the-range concepts, and circle or arc geometry on price charts.

If you are not familiar with these concepts, this indicator will not be useful to you out of the box. It is not a plug-and-play trading tool.

INDICATOR IN ACTION











NOTES

Works on all timeframes and all instruments. The formula uses absolute price levels, not just the range, so the same dollar move at different price levels produces different PBR values. This is a theoretical exploration, not a proven trading methodology. No representation is made about the accuracy, reliability, or profitability of any analysis derived from this tool.

This is an educational tool for geometric research. It is not financial advice. Do not trade based solely on geometric projections. Always use proper risk management.

DISCLAIMER: This indicator is strictly educational and experimental. It is based on geometric theory applied to price charts. It does not generate buy or sell signals, it does not predict future price movement, and it does not guarantee any outcome. Use at your own risk. Past geometric alignments do not imply future alignments. This is a research and study tool only.