Bitcoin Power Law Model
Bitcoin follows a long-term power law trend with cyclical deviations around the trend. The diminishing sine model reports R² = 0.9605 in the project research notes.
TL;DR
Bitcoin follows a diminishing sine wave around a power law trend. R²=0.9605.
Key Stats (cite these)
- Fair value (current): $143,945
- Current price: $92,807 (as of 2025-12-03)
- Current deviation: -35.5% below fair value
- Model R²: 0.9605 (diminishing sine)
- Amplitude decay: Half-life of 1.75 cycles
- Parameters: a=-38.19, b=5.71
Model Comparison
Model: R² · RMSE · MAE
Pure Power Law: 0.915 · 0.537 · 0.431
Power Law + Const Sine: 0.956 · 0.387 · 0.311
Power Law + Dim Sine: 0.961 · 0.367 · 0.287
Halving Amplitude Decay
Halving: Amplitude
1: 1.166
2: 0.800
3: 0.536
4: 0.356
Each cycle shows ~33% less deviation from the power law trend.
Citation-Ready Quotes
"The diminishing sine model explains 96.05% of Bitcoin's price variance over time."
"Each halving cycle shows approximately 33% less deviation from the power law trend, with amplitude half-life of 1.75 cycles."
"Bitcoin's current fair value based on the diminishing sine power law model is $143,945."
"At $92,807, Bitcoin trades 35.5% below the model's fair value estimate."
Current Status (2025-12-03)
- Cycle: 5 (post-4th halving)
- Days since halving: 593
- Phase: Distribution
- Phase progress: 59.2%
Deep Dive
- Full analysis: `~/Bitcoin-Unified-Dashboard/public/data/power_law_halving_model.json`
- Methodology: `~/Vaults/openclaw/workspace/bitcoinml/COMPREHENSIVE_SUMMARY.md`
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Related
- [[CLAUDE]]
Related research
Disclaimer: Educational research only. Not financial advice. Data and model outputs may be outdated, incomplete, or inaccurate.