A Physics-Constrained Multi-Dimensional Revenue Intelligence Algorithm for Explainable Detection of Tax Fraud in the Mining and Petroleum Sectors of Developing Countries
Testing whether production, costs, prices, royalties, and shipments are jointly feasible against physics, geology, statute, and market.
A taxpayer can falsify any single report, but not the joint consistency of all of them with the identities that govern an extractive operation. MDRIA turns six such identities into a label-free, attributable fraud score.
The gap this closes
Audit selection in most resource-rich developing economies still relies on static rule-based registers — "gross margin below sector norm for two years" — where each rule examines a single reporting channel in isolation.
That fragmentation is the vulnerability. A taxpayer who knows the rules can spread evasion across several channels — a few percent off the export price, a few off reported grade, a modest inflation of intercompany fees — so no single indicator crosses its threshold while the aggregate loss is substantial. The datasets that could jointly expose the inconsistency sit in separate institutions: tax, customs, mines, petroleum regulator, utilities, central bank.
A taxpayer can falsify any individual report, but cannot easily falsify the joint consistency of all reports with the physical, geological, statutory, and market constraints that govern an extractive operation.
Ore that is mined must be hauled, crushed, and ground, consuming diesel, power, and water in quantities set by engineering relationships the taxpayer does not control. Metal produced must reconcile with declared tonnage, grade, and recovery. Exports must mass-balance against production and inventory. Each is an identity, not a statistical tendency — so fraud in any channel leaves a residual in at least one identity, and fraud spread across many leaves residuals in many at once.
Headline result
On a synthetic panel of 600 firms over 12 quarters, with five injected fraud typologies at 20% prevalence, MDRIA reaches AUC 0.858 (composite) and 0.869 (Bayesian fusion) — without ever seeing a label. A generic unsupervised baseline on the same raw features manages only 0.643.
AUC aggregates over all thresholds, but an audit office lives at one point on the curve. At 30 audits — 5% of the population — MDRIA's queue is 90–93% fraudulent (composite 0.93, Bayesian 0.90), against 27% for Isolation Forest and 20% for random selection. Supply MDRIA's component scores to a supervised gradient-booster and AUC rises to 0.970.
Six constraints, each independently interpretable
Every taxpayer-period is scored against six families of constraint residuals, normalised robustly onto a common [0,1] scale, then augmented with graph features of the related-party network. Each runs as an independent service — a data outage in one source degrades rather than disables the system.
Production consistency
Metered energy, fuel, and water tie output to declared tonnage, grade, and recovery through engineering identities.
Transfer-pricing deviation
Realised prices tested against quoted references after quality and freight adjustment. AUC 1.00 on its own typology.
Cost inflation
Intercompany fees and operating costs checked against structural norms. AUC 0.97 on cost inflation.
Royalty integrity
Royalties must follow arithmetically from sales at statutory rates. AUC 1.00 on royalty evasion.
Revenue feasibility
Reported revenue tested for joint feasibility against production and price envelopes.
Shipment reconciliation
Exports reconciled with production and inventory; mirror import statistics surface contained-metal gaps.
A petroleum decline agent and a graph agent extend the set — the former enforcing reservoir decline behaviour, the latter surfacing shared directors and payment corridors across related parties.
From residuals to a ranked verdict
The six residuals fuse into one fraud probability by either a transparent weighted composite or sequential Bayesian log-odds pooling with audit-outcome feedback. Weights are published by the administration, not learned — expert-elicited weights are adequate at launch.
Consistent filings — no elevated component; firm stays out of the audit queue.
One or more residuals raised; memo lists each component, its residual, and the periods affected.
Multiple identities violated at once — the spread-thin signature; escalate with a max-component override.
Why not a purely learned model
Labelled ground truth in a low-capacity administration is scarce, delayed, and selection-biased — audits happen where suspicion already fell, so learned coefficients inherit the administration's blind spots. MDRIA's constraint residuals are invariant to legitimate heterogeneity by construction, breaking that circularity while keeping the verdict explainable.
Fusion defeats the spread-thin strategy
Detection decomposed by fraud typology. Each component is sharpest on its own channel; the diagonal is near-perfect, off-diagonal entries sit near chance — clean evidence that each residual measures what it claims.
| Fraud typology | Sharpest component | Component AUC | Under fusion |
|---|---|---|---|
| Transfer mispricing | Transfer pricing | 1.00 | detected |
| Royalty evasion | Royalty integrity | 1.00 | detected |
| Cost inflation | Cost inflation | 0.97 | detected |
| Production under-reporting | Physics (cost 0.92) | 0.87 | detected |
| Spread-thin (multi-channel) | Joint consistency | — | 1.000 |
The key result. Multi-channel "spread-thin" evasion — per-channel intensity θ ≤ 0.12, the strategy that defeats every threshold rule — is the framework's most detectable typology (AUC 1.000 under both fusers), precisely because weak evidence concentrated nowhere becomes strong evidence pooled across identities.
Any reasonable weighting works
Across 2,000 random simplex weight vectors, composite AUC spans 0.70–0.87; defaults hit 0.858.
No precision instruments needed
Sweeping physical-covariate noise from 2% to 25%, Bayesian-fusion AUC stays essentially flat.
As features, they lift learning
MDRIA components feeding a gradient-booster exceed every purely data-driven model.
Explainability and deployment
An audit is contestable — assessments, valuation disputes, and proceedings each open under statute. "Why was this taxpayer selected" is not a courtesy but a ground. MDRIA emits, per firm, a memorandum naming each elevated component, its residual, the data behind it, and the periods affected.
Attributable verdicts
Every elevated case states which constraints are violated and by how much — for audit planning, taxpayer due process, and defensibility in dispute resolution.
Modular, fail-visible architecture
Six independent agents plus graph and petroleum-decline services. A source outage renormalises weights and proceeds — silent degradation, not outage.
Entity resolution is the real cost
Matching one firm across sources with inconsistent identifiers is the largest practical expense, handled by a dedicated layer with human-review queues.
Formally grounded
Boundedness, monotonicity, bounded outlier influence, almost-sure posterior consistency, and a closed-form minimum-detectable-fraud bound are all proved.
Limitations
Constraint residuals catch only fraud that violates a physical, statutory, or market identity — collusive schemes leaving every identity intact are invisible. Linear pooling can dilute a lone alarming component, so a max-component override ("audit if any sⱼ > 0.95") is recommended. Synthetic validation demonstrates mechanical correctness under injected typologies, not field performance against adaptive evaders. Entity resolution and inter-agency data-sharing remain the binding institutional constraints.
Selected references: Daniel, Keen & McPherson (2010) · Otto et al. (2006) · Crivelli, de Mooij & Keen (2016) · Cobham & Janský (2018) · UNCTAD (2020) · Tørsløv, Wier & Zucman (2023) · Readhead (2016) · Guj et al. (2017).
Reproducibility. A synthetic panel of 600 firms over 12 quarters with five injected fraud typologies at 20% prevalence; no live administrative data. Views are the author's and do not represent any revenue administration.