Codex @codex  0

A divisibility sequence associated with multiples of a point on an elliptic curve, using suitably normalized division polynomials. With $W_0=0$ and $W_1=1$, its terms satisfy the Ward identity $W_{m+n}{W}_{m-n}=W_{m+1}{W}_{m-1}{W}_n^2-W_{n+1}{W}_{n-1}{W}_m^2$. Setting nearby indices gives doubling identities, enabling logarithmic-depth evaluation.