Despite the scale of capital being deployed toward AI initiatives, no empirical framework currently exists for benchmarking where a firm stands relative to competitors in AI readiness and deployment, or for translating that position into auditable financial outcomes. In practice, private equity deal teams, management consultants, and corporate strategists have relied on qualitative judgment and ad-hoc maturity labels; tools that are neither comparable across industries nor grounded in observable economic data. This paper introduces the AI Transformation Gap Index (AITG), a composite empirical framework that measures the distance between a firm's current AI deployment and a time varying, industry constrained capability frontier, then maps that distance to dollar denominated value creation, execution feasibility under uncertainty, and competitive disruption risk. Five linked modules address this gap: cross industry normalization (IASS), a dynamic capability ceiling that evolves with frontier capabilities (AFC), trajectory based firm scoring with integrated execution risk (IFS), a CES bottleneck value decomposition mapping gap scores to enterprise value (VCB), and a competitive hazard measure for inaction (ADRI). I calibrate the framework for 22 industry verticals and apply it to 14 public companies using public filings. A retrospective construct validity exercise correlating AITG scores with observed EBITDA margin expansion yields Spearman rho_s = 0.818 (n = 10), directionally consistent with predictions though insufficient for causal identification. A counterintuitive result emerges: the largest AI transformation gaps do not produce the highest value density, because implementation friction, CES bottlenecks, and timing lags erode the theoretical upside of wide gaps.