The sign of the Cayley--Dickson basis product coincides with the explicit twist function of Ren and Zhao(Theorem~1 for the standard algebras; Theorem~2 for the split relation)~\cite{RenZhao2023}.This paper gives an independent treatment of that sign law from thecomputational side. We prove the block sign rules (the ``OPMT sign law'')directly from the Cayley--Dickson doubling formula, introduce a holographic descent algorithm whose correctness we prove against these rules, andcollapse the descent into a strictly table-free word-RAM evaluatorusing three trailing-zero counts, one maximum comparison, and one populationcount. We prove that the evaluator computes exactly the twist functionof~\cite{RenZhao2023}, and that our split variant implements theirTheorem~2. The structural-break descent, the constant-time collapse, and theequivalence theorem are new; the sign function itself is dueto~\cite{RenZhao2023}, building on Albuquerque--Majid~\cite{AlbuquerqueMajid1999}and the Cayley--Dickson process of Schafer~\cite{Schafer1954}.We extend the framework to the dual family, provingproving proving , and to tensor products via a signcomposition principle. We further present an empirically validated countingformula for a class of zero-divisor pairs, stated explicitly as a conjecture.Three implementations are provided and cross-verified: a full table builder,and and single-product evaluators.