Bitcoin’s price follows a well-documented power law over long time scales, yet this trend alone is a poor short-term predictor: at horizons of a few months, today’s price outperforms any trend extrapolation. We construct a minimal baseline—a sigmoid blend that transitions from today’s price (short horizons) to the power-law trend (long horizons)—and ask whether more sophisticated models can beat it. Using the autoresearch pattern—autonomous AI agents iteratively designing and testing predictive models—we run 40 experiments at horizons of 1, 3, and 6 months. Agents discover increasingly sophisticated models incorporating price momentum, mean reversion, and horizon-specific feature engineering, achieving up to 50% in-sample improvement. We evaluate all models across five non-overlapping two-year holdout windows spanning distinct market regimes (2016–2026), with all hyperparameters—including those of the baseline—re-optimized on each window’s training data. When models use the aggressive hyperparameters discovered by autoresearch, they degrade severely on held-out data, with in-sample improvement anti-correlated with holdout performance. When hyperparameters are instead re-optimized per window with zero correction included as a candidate, the optimization selects zero in every window, collapsing all models back to the baseline. At 1–6 month horizons, this reflects the dominance of price persistence: the naive component (today’s price) carries nearly all the predictive weight, and no tested correction—whether based on mean reversion, momentum regression, or 18 Bayesian structural time series configurations—can improve upon it across five distinct market regimes.