Vectorizing Going-Concern Capacity Institutional Viability, Collapse Bands, and AI-Era Structural Readout

This technical note develops a computable pathway for converting institutional going-concern capacity from an abstract structural constraint into an operational readout. It introduces FGC = X × Y as a multiplicative viability function built on the premise that institutional survival depends on the joint operation of two orthogonal, non-substitutable capacities. Unlike additive models, the FGC structure prevents apparent strength on one axis from compensating for collapse on the other. Using Lehman Brothers as a negative institutional demonstration, the note reconstructs X as front-end expansion and rolling execution capacity, and Y as back-end absorptive integrity and institutional closure capacity. It then sets out the technical steps required to operationalize the model: scenario translation, variable mapping, standardization into a common interval, axis-specific aggregation, multiplicative computation, threshold logic, collapse bands, and time-series readout. The model distinguishes FGC from related index families such as ITI and IDI: ITI reads institutional tension, IDI reads distortion, while FGC reads joint viability as a going-concern condition. The note further extends the model to AI-era institutional analysis. It argues that future audit, due diligence, compliance review, sovereign-fund governance, and capital-market diagnostics will increasingly be machine-assisted, but that narrative retrieval and ordinary RAG pipelines alone are insufficient. Large language models operate as continuation engines rather than accountability engines; they may smooth unresolved absence, Nil entries, or structural gaps into fluent but premature narrative closure. FGC responds by supplying a pre-judgment structural grammar that preserves unresolved states, separates front-end motion from back-end closure, and converts institutional materials into a machine-readable structural surface before judgment. The contribution of the note is technical and methodological. It demonstrates how FGC can move from conceptual formulation to computable institutional readout, and how collapse-sensitive analysis can be extended from historical demonstration toward current capital-market and AI-mediated institutional monitoring.