Nonexistence of spiral-like blocking strategies below the critical speed

Let $\sigma>0$ be the barrier speed in the isotropic fire problem, and let $\bar\sigma=2.6144\ldots$ denote the critical value obtained from the spectral analysis of the retarded differential equation governing a saturated spiral. A spiral-like strategy is a barrier of the spiral form considered in the source. Spiral blocking conjecture. If $\sigma\leq\bar\sigma$, then no spiral-like strategy blocks the fire. The source explains that saturated spirals block when $\sigma>\bar\sigma$ and motivates this conjecture for general spirals; the asserted nonexistence at and below the critical value remains open.