Industry ApplicationsFebruary 12, 202638 min read

Evidence Coherence Spectral Analysis: Detecting Fraud Through Eigendecomposition of Audit Evidence

Using spectral methods on evidence correlation matrices to identify inconsistencies, fabrication patterns, and systemic fraud signals

Traditional audit systems often rely on rule-based checks and statistical sampling, which can under-detect coordinated fabrication patterns. This paper introduces Evidence Coherence Spectral Analysis, a framework that treats evidence sets as vector spaces, builds correlation matrices from evidence attributes, and applies eigendecomposition to identify anomalous spectral gaps associated with inconsistency or fabrication risk. We define a coherence score, relate it to false-discovery behavior, and describe integration with MARIA OS Evidence Bundles. In controlled financial-statement audit experiments, spectral analysis detected 94.7% of fabricated evidence sets while maintaining a false-positive rate below 2.3%, with streaming support for near-real-time analysis.

auditspectral-analysisevidence-coherencefraud-detectioneigendecompositionmathematicsgovernance
MathematicsJanuary 20, 202624 min read

Linear Algebra Model for Negative Correlation Detection Across Business Universes

Using eigendecomposition of correlation matrices to identify conflicting objectives across business universes

When business universes optimize in opposing directions, organizations incur both direct conflict cost and wasted optimization effort. This paper develops a linear-algebra framework for detecting negative correlations using correlation matrices, eigendecomposition, and spectral analysis. Negative eigenvalues in inter-universe correlation structures identify conflict clusters that require governance intervention rather than additional local optimization.

linear-algebracorrelation-matrixeigendecompositionconflict-detectionmulti-universespectral-analysis