The Geometry of Bitcoin: Superlinear-Feedback Asymptotic Model and Finite-Time Singularity

Conventional forecasting models, particularly those assuming permanent diminishing returns, may not necessarily account for Bitcoin's absolute, fixed supply cap of 21 million coins. Standard growth functions often lack an intrinsic mathematical mechanism that responds to the structural break imposed by an exhausting supply, which frequently leads to continuous recalibration across different market eras. As an alternative theoretical framework, this paper proposes a tangent-based model and documents a measurable geometric divergence between it and the best possible fit of the standard Power Law — the mathematical formulation of the diminishing-returns principle referenced above, in which price is assumed to grow as a fixed power of time, P(x) = A · xn — on the same historical data. This divergence is confirmed statistically in Section 6, not merely asserted here.