Bayyinah at-Taʿlīm: Structural Honesty Verification for Educational Fairness Systems, from Primary Schooling to Graduate Research

This application note applies Structural Honesty Verification (SHV) -- the verification of correspondence between a system's surface claims and its actual substrate behavior -- to educational fairness across three tiers: K-12 schooling, undergraduate admissions and assessment, and graduate research. Its central observation is that "fair" and "equitable" are surface claims that usually conceal which mechanism is running, and that the algorithmic-fairness impossibility results (calibration and equalized error rates cannot both hold once base rates differ) make the choice of fairness definition consequential rather than cosmetic. SHV does not choose the definition, remove bias, or adjudicate merit. Its contribution is to make an institution declare which fairness definition its mechanism implements, to make resource and record divergences tamper-evident and regression-gated, and to separate what is genuinely verifiable (funding, provenance, non-deletion, reproduction) from what is not (merit, equity, understanding). The paper presents a three-tier classification of what can and cannot be verified, nine mechanisms across the three educational tiers, and an end-to-end worked example on New York City's Fair Student Funding formula, including a five-school FY2023 recompute that reconstructs the Department of Education's own allocation walkthrough from public data. The work is theoretical with one operational worked example. It has not yet undergone independent cross-instance audit, and its scope limits are stated explicitly. The complete audit trail, per-claim verification provenance, and version history are published separately in the Audit and Provenance Companion (DOI 10.5281/zenodo.21436486).