Activity-Based Costing of the "Non-Creation of Records": Cross-Subsidization, 3E Audit Failure, and Withholding Tax Leakage Under Endogenous Intake Filtering

Prior studies (Miyazawa, 2026a, 2026b) modelled the legal boundary conditions at the initial intake stage of Japan’s public sector, such as the non-binding instruction under Article 14 of the Whistleblower Protection Act and the discretion to reserve acceptance under Article 65 of the Criminal Investigation Norms, and showed with a partial differential equation (PDE) model that optimal intake control is bang-bang with a critical complexity threshold x*, under which, in the model, high-complexity cases (x ≥ x*) are left unrecorded.This paper, the third of a trilogy, projects this endogenous intake filtering onto Activity-Based Costing (ABC; Drury & Tayles, 2024), the 3E (economy, efficiency, effectiveness) audit standard and withholding income tax theory. Decomposing counter work into statutory investigation and reserved-acceptance consultation handling, we prove the 3E Impossibility and Cross-Subsidization Theorem: within the model, when a lower cutoff compresses real output and formal records, an organization keeping a fixed budget would face either a collapse of efficiency, the unit cost of statutory work diverging without bound, or cross-subsidization, budgets approved for statutory work being effectively reallocated to gatekeeping.We also prove the Withholding Tax Leakage Theorem: within the model, if non-taxable allowances were disbursed by budget inertia without verification against actual investigation, payments lacking the substance of reimbursement (Income Tax Act, Articles 9(1)(iv) and 28) would rise monotonically as the threshold falls, implying a structural risk of withholding-tax leakage at the withholding agent (Article 183). Calibration on National Police Agency statistics (2001–2024) shows the formal recording share contracting from 74.62% to 21.71%; under the stated assumptions, this implies a 1.89-fold unit cost per cleared case (3.71-fold per recorded offense) and a cross-subsidy share of up to 78.29%. No budget, payroll or tax data are analysed, and no finding is made about any body. Declarations (printed on the PDF; for reference) Conflict of interest statement:The author is the addressee of the two official replies reproduced in the Evidence Bundle (Ex. 17 and Ex. 50), which were first produced for the prior studies (Miyazawa, 2026a, 2026b), and is a party to related administrative procedures, and therefore has a direct procedural interest in those matters. Those procedures have resulted in no finding of any kind, and this paper makes no allegation concerning any organ or official involved in them, and attributes no intention, bad faith or unlawful conduct to any organ, officeholder or official. Declaration of generative AI and AI-assisted technologies in the writing process:During the preparation of this work the author used Claude Opus 5.5 (Anthropic), through the Claude Code tool, solely to improve the readability and language of the English text, to assist with translation of the author’s Japanese manuscript into English, and to adjust the LaTeX formatting of the manuscript, including the typesetting of its equations and table. Generative AI was not used for data analysis, for deriving the conclusions, or for any other core research task: the research question, the activity-based costing model, the definitions, the theorems and their proofs, the selection and calibration of the official statistics, the reading of the statutes and official documents, and the conclusions are the author’s own, and no AI tool was used to create or alter any data, result or image. After using this tool, the author, as a human, reviewed and edited the output as needed and takes full responsibility for the final content of this publication, including its accuracy and safety. Data availability:The macroeconomic data analysed in the empirical calibration are publicly available in the White Paper on Police (Keisatsu Hakusho) and the Criminal Statistics published by the National Police Agency of Japan, cited in the references. The two redacted official documents referred to in this paper (Ex. 17 and Ex. 50) are reproduced in the Evidence Bundle and described in the Schedule of Exhibits; both are deposited as separate files in Zenodo under the DOI 10.5281/zenodo.23640727, which cites all versions of the deposit and resolves to the latest one. This preprint itself is published as a separate Zenodo record, independent of that deposit, under the concept DOI 10.5281/zenodo.23830592 (all versions; version v1: 10.5281/zenodo.23830593; version v2: 10.5281/zenodo.23831360). The first prior study of the trilogy is available on SSRN under the DOI 10.2139/ssrn.7554559, and the second as SSRN preprint 7635698.