Can Execution Disclosures Reveal Harm to Retail Traders? Accounting Gaps, Sample Selection, and Sharp Bounds

This preprint audits twelve legacy Rule 605 execution-quality reports from Citadel Securities and Virtu for January–June 2026. It measures how exact price-class reconciliation changes sample coverage, weighted spreads, and common-support comparisons. Price-class deficits totaling 36,239 shares occur in Citadel market-order cells representing 58.21% of that family’s reported execution exposure. An exact screen therefore removes far more exposure than the accounting gap itself. The paper separates this analyst-induced selection from evidence of institutional misconduct or customer harm. Elementary counting bounds and explicit whole-share allocations show what venue-wide totals can and cannot establish about an unidentified customer group. The contribution is a documented disclosure audit and a reporting-specific application of established bounds, not a new general identification theorem or a causal finding against either institution.

The manuscript uses finite sums, weighted averages, fractions, and algebraic inequalities. It includes empirical tables, three figures, proofs, sensitivity analyses, and eighteen references.

First draft: March 2026 · Completed: August 2026 · Final revision: October 2026. This is a research preprint and has not been peer-reviewed.