Exact State-Ranked Array-RQMC: Representations and Shared Work

Repeated states in state-ranked Array-RQMC receive rank-specific inputs. We execute the reranked population without visiting every particle when complete states repeat and transitions admit short finite-word interval partitions. Primal image-basis and dual constraint counters preserve the realized histogram path and supported readouts. Fixed suffix dependencies survive triangular scrambles; syndrome-prefix diversity determines exact conditional demand for shared dual transformations. A sharp finite-sum bound and rank-boundary geometry connect demand to execution cost. Six compiled executors share repair and tandem tapes and return every step histogram and readout. With eight seeds per cell on one non-isolated host, median within-seed timing ratios favor direct basis over the other non-enumerating methods in all 17 cells. With 2^20 particles, it outpaces compact rank streaming by about 41-57 times for repair and 10 for tandem. Dual coefficient retention improves on matched reconstruction; fixed-workload diagnostics characterize the remaining work. This record contains the 20-page author manuscript and 6-page reader supplement, version 20261005-estimator. This is an author preprint; it has not yet been peer reviewed or accepted for publication. Code and reproduction data. The fixed public companion exact-state-ranked-array-rqmc-v1.0.0 provides the measured source, all 4,080 original timings, saved trajectories, corrected executors, and table, figure and PDF reproduction. Download array-rqmc-repro-20261006.zip and follow its README. It is the public counterpart of array-rqmc-review-20261005-estimator.zip named in the paper; its provenance file identifies the unchanged scientific inputs and the omission of private editorial material. Code and the layout template use MPL-2.0; author publication materials and saved data use CC BY 4.0. Dependencies retain their own licenses. The two PDFs deposited here remain unchanged.