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

This working paper proposes a superlinear-feedback, tangent-based geometric model for Bitcoin's historical price trajectory, developed as an exploratory alternative to standard Power Law approaches. Using an empirically defined tangency-and-non-crossing methodology, the model is calibrated against seven historical support nodes and shown to track the observed data with a measurably lower error than the best available Power Law fit on the same nodes (Section 6). The paper's central argument, however, moves beyond curve-fitting. Two independent exclusions are derived mathematically: a linear contraction of Bitcoin's own liquid supply, and ordinary exponential demand growth, are each shown to produce only a weak logarithmic price divergence on their own — insufficient to account for the sharper, superlinear acceleration the data exhibits (Sections 3.1-3.2). This leads to the paper's key structural claim: the mechanism responsible for that acceleration is most likely external to Bitcoin's own supply dynamics, with Bitcoin's fixed supply acting as a necessary precondition rather than the complete explanation. Considerable attention is given to the model's own limitations: parameter instability under refitting, the weak falsifiability of the general functional family versus the fragility of any specific parameterization, and an explicit boundary analysis distinguishing what the model's mathematics can and cannot support. The paper concludes that its most durable contribution may lie less in the specific price curve than in its potential use as a measurement instrument — a fixed, verifiable reference point against which the dynamics of an external, otherwise difficult-to-observe system might be studied indirectly. This is an exploratory, self-critical working paper, not a price-prediction tool or financial advice. It does not forecast any literal future price and takes no position on macroeconomic or monetary questions beyond what is mathematically necessary to state its argument.