Replication Package: JFAR 294

This release provides the executable replication materials for “Separated Duties, Shared Exposure: Coalition Containment and Feasible Redesign.” It implements a probability-free assessment of the amount accessible to cooperating employees when each payment already satisfies a different-preparer/different-reviewer rule. The outputs are the complete coalition-exposure spectrum, the minimum headcount needed to reach a selected tolerance, an exact unrestricted reviewer-change benchmark, eligible repairs, maximizing employee sets, and every coalition size whose exposure worsens.The six-person example shows that two reviewer changes reduce maximum three-person access from three tranches to two without increasing two-person exposure. In the weighted example, eligibility raises the required changes from two to four: the eligible repair meets the $220,000 three-person cap while increasing four-person exposure by $10,000. A twelve-record payment-release reconstruction documents delegated limits, role domains, supplier-owner exclusions, effort budgets, and a complete 144-cell eligibility matrix. Its eligible eight-change repair attains a three-person bound of $234,290 and explicitly reports deterioration at coalition sizes four and ten. An alternative vendor-master route is evaluated as another path to an existing payment, without duplicating that payment’s amount.The package includes constructed input files, assessment and repair programs, expected outputs, generated table sources and figures, input provenance, regression tests, dependency specifications, checksum manifests, and clean-directory reproduction instructions. All employee identities, monetary caps, assignments, and numerical cases are constructed. Public process documentation informs the input schema, not the observations. The release supports exact control-design comparisons; it does not estimate fraud incidence, realized losses, employee dishonesty, or audit materiality.Additional description: MethodsReviewers are represented as balanced permutations with no self-review. For each coalition-size limit, the assessor maximizes jointly accessible, separately capped payment exposure. Equal-weight spectra are checked against the cycle-subset-sum formula, and unrestricted repair counts against the exact cycle-splicing benchmark. Weighted repairs enforce documented eligibility, delegated limits, supplier-owner conflicts, and review-effort budgets. Complete small-system enumeration and independent mixed-integer calculations check selected solutions. The twelve-record application uses exact sparse matching and complete change-distance layers through the first feasible unrestricted layer. Alternative paths are combined by logical union for each monetary record. Probability calculations are separate, explicitly constructed stress laws.Additional description: Technical informationPython 3.11 or later. Tested dependency versions are NumPy 2.3.5, SciPy 1.17.0, Matplotlib 3.10.8, ReportLab 4.4.9, SymPy 1.14.0, and PyMuPDF 1.26.7.Install requirements.txt, then run:python reproduce.py --out ../JFAR_replication_checkThe output directory must be new or empty and outside the package. The runner regenerates numerical results, tables, and graphics without copying released results. The open Tinos font is required for byte-identical figure reproduction; font files are not included. After dependency installation, execution requires no network access, credentials, private dataset, or commercial solver.Current implemented limits are nine employees for complete-permutation repair, sixteen for sparse-mask repair with a node budget, and twenty for employee-set assessment. Interrupted searches do not issue optimality or infeasibility certificates.Additional description: OtherFirst public replication release, corresponding to the manuscript’s v04 scientific content and v05 submission packaging. All cases are constructed. The journal manuscript, title page, cover letter, private correspondence, third-party literature PDFs, and font files are not part of this software/data deposit. Journal acceptance and public DOI activation are not asserted. Copyright remains with the author; the proposed component licenses are MIT for code and CC BY 4.0 for constructed data, outputs, and accompanying documentation.KeywordsForensic accounting; separation of duties; segregation of duties; coalition exposure; internal control; accounts payable; authorization assignments; control redesign; constrained optimization; reproducible research.SubjectsJEL: C61; D81; M41; M42.