The Geometry of Bitcoin: Superlinear Feedback and the Finite-Time Singularity Problem

Standard growth descriptions of Bitcoin's price history, particularly those built on permanent diminishing returns, contain no superlinear, self-reinforcing term, and they are typically recalibrated as new market eras arrive. This paper asks a narrower question: whether a self-reinforcing feedback loop can be detected at all, using Bitcoin's absolute, fixed supply cap of 21 million coins as a reference point. To this end, it compares a tangent-based model, which contains a superlinear feedback term, with the best possible fit of the standard Power Law on the same historical data. The Power Law is the mathematical formulation of the diminishing-returns principle, in which price is assumed to grow as a fixed power of time, P(x) = A · xn. From this comparison, the paper then estimates an effective feedback exponent for the observed stretch (Section 3.3.1). The geometric divergence between the two models is documented statistically in Section 6, not merely asserted here.