The Bitcoin Spiral: A Cycle-Based Framework for Price Dynamics and Statistical Inference

Abstract

This paper proposes a polar-coordinate framework for Bitcoin prices around the halving cycle, where each revolution is one halving epoch and radial distance represents log price. This alignment reveals recurring patterns conventional time-series charts obscure. We develop five statistics, spanning seasonality amplitude, phase concentration, intercycle repeatability, radial growth, and bull-bear asymmetry, each paired with an explicit null hypothesis and, given the small number of completed cycles, block-bootstrap or randomization inference. To test whether the structure is specific to Bitcoin's supply schedule, we apply the identical clock to Ethereum and the S&P 500 as placebo assets. Bitcoin shows significant halving-phase seasonality (p