BTC - Power Law 1.5: Dynamic 50/50 Decay

OVERVIEW
Most Bitcoin models treat the asset as if it exists in a vacuum of infinite exponential growth. The classical Power Law (v1.0) was a groundbreaking start, but as Bitcoin matures into a multi-trillion dollar institutional asset, our models must account for the laws of physics and liquidity. The Power Law 1.5: Dynamic 50/50 Decay is a second-generation structural engine. It doesn't just draw a line; it calculates the structural "Center of Gravity" of Bitcoin’s adoption curve while accounting for the natural maturation (decay) of the network’s growth speed.

THE MATHEMATICAL BACKBONE: QUANTILE MEDIAN CALCULATION
The "Fair Value" line (blue) is derived using a Log-Log Linear Regression focused on the 50th percentile (Median). The script first transforms the price and the time (days since the Genesis Block) into a logarithmic scale. It then calculates a power-law constant by finding the Absolute Least Deviation across the entire historical dataset since 2011. Specifically, it uses the formula: Price = 10^(Intercept + Slope * log10(Days)). To ensure the line is a true median, the script calculates the Median Offset of every historical price point from the raw regression line. By shifting the intercept by this median value, we guarantee that exactly 50% of all weekly bars fall above the curve and 50% fall below it, creating a robust, non-biased structural center.

THE ALPHA SHADOW: DYNAMIC EXPONENT PROJECTION
Unlike standard power-law projections that rely on a static slope, the "Alpha Shadow" (the projection extending from the blue backbone) utilizes a Time-Varying Exponent Model. The model acknowledges that Bitcoin's growth speed—the exponent 'b'—is a decaying function of time, reflecting the diminishing returns of a maturing asset. The script recalculated the Instantaneous Slope on every single bar using the formula: Future_Slope = Initial_Slope - (Decay_Rate * log10(Total_Days_from_Genesis)). While the Decay Rate (default 0.045) serves as a structural sensitivity constant, its application ensures the growth speed is a dynamic variable rather than a fixed number. Each segment of the dashed green "Shadow" is a unique power-law arc calculated for its specific future time window. This ensures the projection isn't just a straight line drawn on a log chart, but a mathematically tethered curve that "feels" the weight of increasing market capitalization and respects the reality of global liquidity constraints as we approach 2029.

HOW TO READ THE CHART
• The Backbone (Solid Blue): This is the 50/50 Fair Value. When price is below this line, Bitcoin is structurally "cheap." When price is far above it, the asset is in a state of cyclical expansion.
• The Alpha Shadow (Green): This is the mathematical projection of the current curve into 2029. It shows the path of "Fair Value" as the network continues to mature.
• The Regime Audit (Dashboard): A real-time table in the middle-right of your chart provides an audit of the model's integrity, including the current slope (b) and the projected Fair Price for Jan 1, 2029.

WHY THIS IS "FRESH"
Most open-source Power Law scripts on TradingView utilize a Static Linear Regression—calculating a single constant slope that is applied equally to 2011 and 2029. Furthermore, common community models often rely on "Outer Band" fitting (connecting historical cycle peaks to cycle lows). While visually appealing, these methods can be highly sensitive to "Black Swan" outliers and often assume Bitcoin’s growth velocity is a permanent constant.

This script stands out by introducing a Maturation Framework. Instead of fitting to volatile extremes, we anchor the logic to a 50/50 Quantile Median, creating a backbone that is mathematically centered regardless of cyclical noise. By then applying a Dynamic Decay Factor to the growth exponent, we move away from the "static bands" approach and toward a model that respects the physical reality of a maturing, multi-trillion-dollar asset class. This provides a structurally grounded, institutional-grade view of Bitcoin’s trajectory that accounts for the diminishing returns inherent in global adoption.

DISCLAIMER
This script is for educational and macro-analytical purposes only. It does not constitute financial advice. The 2029 projection is a mathematical extrapolation based on historical data and decay constants; it is not a guarantee of future price action.

TAGS
bitcoin, powerlaw, macro, regression, fairvalue, btc, projection, quantitative, math, structural, Rob Maths, robmaths, Rob_Maths