arXiv:2611.14576v1 Announce Type: new Abstract: Gu\'erin, Laulin, Raschel, and Simon conjectured that the initial biases giving the superdiffusive elephant random walk a bimodal limit law form an interval centered at one half, and they described the problem as challenging. We prove this. For every superdiffusive memory, strongly biased starts are unimodal, and the limit density has two local maxima exactly when the bias lies in a proper open interval. Outside it, including its endpoints, the density has a unique local maximum. The interval is nonempty exactly above a single memory threshold, numerically about $0.6688$, whose uniqueness follows from a positive-weight integral for the central curvature of the fair-start density. We control sign changes in the finite walk's first and second differences, including those created at the boundary, and pass them to the limit. The bias boundary is continuous and tends to zero at least quadratically fast as memory tends to one.
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