We revisit the single-machine problem $1\mid\mid\sum U_j$ through Moore's shortest-processing-time insertion rule: scan jobs from shortest to longest and accept a job whenever the accepted set remains feasible. Direct implementation checks every affected deadline prefix and takes quadratic time. For job set $Y$, let ${\rm Slack}(Y)$ be its least deadline-prefix gap in isolation. A candidate $(p,d)$ is addable to accepted set $X$ if and only if $$ \mathrm{Proc}(X_{<d})+p \leq \min{d, {\rm Slack}(X_{\geq d})}. $$ An augmented balanced search tree stores total work and intrinsic slack per subtree, composing under an associative ordered-block product. A read-only query follows a root-to-leaf path: right turns accumulate work due before $d$; left turns certify $d$ and a skipped suffix. With $q$ stored deadlines, queries and point updates take $O(\log(q+2))$ worst-case time. The scan runs in $O(n\log(k+2))$ time ($k$ output distinct deadlines) and $O(n\log n)$ overall. Matching algebraic computation-tree lower bounds show $O(n\log n)$ is optimal, persisting when $p_j=1$ under a given SPT order. Preprocessed $q$-key states still require $Ω(\log q)$ per query. For every attainable cardinality, acceptance prefixes over all tie orders are precisely minimum-work feasible sets with componentwise-minimum sorted processing-time vectors. Equal-processing-time choices form canonical chain-presented laminar matroids; their direct sum describes all complete greedy outputs, and their ordered sum describes all optimal prefixes. Finally, a linear-size flow network defines a scheduling polymatroid rank whose contracted, scaled increments recover the complete rank functions of the tier matroids.

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