Per-Entity Bias Mapping for AI Visibility: Why Brand Mentions Require Entity-Specific Calibration

AI-mediated answer systems increasingly determine how brands and organizations are represented to users. Existing approaches reduce visibility to mention rate or citation frequency. This paper argues that aggregate metrics are insufficient because entities exhibit systematically different AI visibility error profiles. We identify three failure modes: (1) invisibility for underrepresented entities, (2) the Brand Hallucination Paradox — high-salience brands receive more fabricated citations than low-salience brands (T1: 52.69% vs T3: 37.87%, χ²=45.326, p=1.67×10⁻¹¹, Cohen's h=0.299), (3) the CEE Entity Infrastructure Gap — OR=6.77 for Wikipedia/Wikidata presence T1 vs T3 (p=0.0002); English Wikipedia presence reduces fabrication odds by 28% (OR=0.724, p=0.024). A fourth dimension: Parametric-Retrieval Lag Asymmetry. Regulatory-framed queries elevate fabrication to 56.77% vs 37.59% factual baseline (+19.2 pp, FDR q<0.001) — a passive adversarial attack surface requiring no model access. Empirical study: n=100 Hungarian B2B entities, 1,400 probe runs, 2,062 sources, non-AI HTTP+Crossref verification. Platforms: claude-sonnet-4-6 and gpt-4o-2024-08-06. Data collection: 2026-05-22, 07:25–12:16 UTC. Full data released as supplementary materials (CC BY 4.0).