arXiv:2610.31531v1 Announce Type: new Abstract: For full-length Reed--Solomon codes, every received word whose interpolation polynomial has degree equal to the code dimension is a deep hole. The Cheng--Murray conjecture asserts that these are the only deep holes in dimensions $3\le k\le q-2$, except when $q$ is even and $k=q-3$. Earlier results settled the conjecture over odd prime fields and in the high-dimensional range. We resolve the remaining cases $3\le k\le\lfloor q/2\rfloor$ over every finite field $\F_q$, thereby completing the classification in all nonexceptional dimensions. Our proof combines two complementary approaches. The tangent envelope of a marked arc yields differential constraints that settle the even-characteristic range $3\le k\le q/2$ and the odd-characteristic range $3\le k\le q/3$. In the remaining odd-characteristic range, local syndrome compatibility and combinatorial counting rule out additional deep holes.