ASQ: Query Sensitivity Analysis — Citability in generative AI engines as a function of prompt design

This study formalizes and expands the concept of Query Sensitivity Analysis (QSA): an entity's citability in generative AI engines is not a stable attribute of its content, but a function of three independent variables — the entity, the engine, and the query formulation. Across two experiments (108 responses in Foz do Iguacu; 5,544 responses on 82 entities in hospitality and ERP, collected on Gemini, GPT-4o, and Claude), QSA is confirmed at multi-vertical scale, and sensitivity is shown to be a property of the engine x vertical pair: the engines' robustness ranking inverts across verticals. The branded vs. discovery distinction is the determining axis; the discovery query subtype produces a marginal effect. No entity is Invisible in branded queries. Version 2 (erratum and methodological update). This version corrects and strengthens v1 after re-analyzing the data: ASQ typology regenerated by a reproducible script (compute_pp3.py): v1 contained outdated, manually hardcoded values. A fourth type is introduced, Marginal (0 < branded < 0.5), which separates "insufficient recognition" from "Fragmented". Reclassifications in the ERP vertical: Senior Sistemas corrected from Fragmented to Consolidated (Consolidated 6→7); System Sistemas reclassified as Marginal (Fragmented 25→23, plus 1 Marginal); extreme cases 17→18. Corrected an incorrect v1 claim that "all entities have a branded rate above 0.96". Experiment 1 aligned with the Foz do Iguacu study (unidirectional query effect); ERP corpus rebaselined from 1,490 to 2,790 responses. Copy-editing revision. Declaration of AI use added, for methodological transparency. The hospitality vertical remains unchanged. The central thesis (citability = entity x engine x query formulation) remains and is reinforced. Version 3 (submission revision). Language and metadata revision for journal submission: author name format corrected in document properties; copy-editing revision.