{"paper":{"title":"The Payment Heterogeneity Index: An Integrated Unsupervised Framework for High-Volume Procurement Oversight and Decision Support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The Payment Heterogeneity Index flags suppliers with atypical payment structures using only unlabeled data.","cross_cats":["cs.LG","q-fin.ST","stat.AP"],"primary_cat":"econ.EM","authors_text":"Kyriakos Christodoulides","submitted_at":"2026-05-09T20:59:29Z","abstract_excerpt":"Public procurement is vulnerable to error, fraud and corruption, yet high transaction volumes overwhelm oversight. While research often focuses on tender-stage anomalies, post-award payments remain underexplored. Since labelled datasets are rare and existing methods such as Benford's Law face restrictive assumptions, there is a need for additional interpretable, unsupervised frameworks that augment oversight and simplify management. This paper introduces the Structural Heterogeneity Index (SHI), a composite statistic for one-dimensional samples defined by four components: modality, asymmetry, "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"PHI functions as an effective discovery tool where no confirmed labels exist, offering a transparent, lightweight screening mechanism for post-award oversight.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the structural signatures captured by the Gaussian Mixture Model components and tail-behaviour measure correspond to financially meaningful deviations (errors, fraud, or corruption) rather than benign differences in legitimate payment practices.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The Payment Heterogeneity Index (PHI) is a new unsupervised metric combining tail sensitivity and Gaussian mixture model-based structural dispersion to identify suppliers with atypical payment regimes in high-volume procurement data.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The Payment Heterogeneity Index flags suppliers with atypical payment structures using only unlabeled data.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"cb2423ad776d2d515a45d3dc5f455cc1b4cc7e285c0d9e0a4b5e9570dbc63dea"},"source":{"id":"2605.12547","kind":"arxiv","version":1},"verdict":{"id":"bf0b477f-1a1a-4c5b-bad3-d52fcdd727c2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T21:50:13.430006Z","strongest_claim":"PHI functions as an effective discovery tool where no confirmed labels exist, offering a transparent, lightweight screening mechanism for post-award oversight.","one_line_summary":"The Payment Heterogeneity Index (PHI) is a new unsupervised metric combining tail sensitivity and Gaussian mixture model-based structural dispersion to identify suppliers with atypical payment regimes in high-volume procurement data.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the structural signatures captured by the Gaussian Mixture Model components and tail-behaviour measure correspond to financially meaningful deviations (errors, fraud, or corruption) rather than benign differences in legitimate payment practices.","pith_extraction_headline":"The Payment Heterogeneity Index flags suppliers with atypical payment structures using only unlabeled data."},"references":{"count":32,"sample":[{"doi":"","year":null,"title":"Fazekas, Mihály and Tóth, István János and King, Lawrence P. , year =. Anatomy of Grand Corruption: A Composite Corruption Risk Index Based on Objective Data , journal =","work_id":"c3f7202a-06ef-4f28-adbc-c7d5442d42d8","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Uncovering High-Level Corruption: Cross-National Objective Corruption Risk Indicators Using Public Procurement Data , journal =","work_id":"036fe58e-bc30-4725-8c57-a4fd912b6db2","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Anomaly Detection: A Survey , journal =","work_id":"9f758630-6b47-4758-aaa2-038f261c1337","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Detecting Fraud in Public Procurement: A","work_id":"c6c4edee-374a-4b60-be73-45cae50bb30b","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Public Procurement Fraud Detection and Artificial Intelligence Techniques: A Literature Review , booktitle =","work_id":"12471dc1-97c8-444a-80dc-32ace26fe249","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":32,"snapshot_sha256":"71d554520580bb18bfb37ed0ec7aebcc782e4a66545eacfac66f8e0fcda6e8e3","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"b2cd7aa858fdf4265507da846b0bad9c682b52eebd8306b55ffd6eec251ca8bd"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}