Sufficient Statistics
B_H values horizon progress, B_F values reliability in unforgiving environments, and C measures the value mass where both constraints bind.
Horizon, forgiveness, and dynamic AI competition. The paper studies why AI firms race on different technologies across task regions.
AI progress is not one scalar quality ladder. Tasks fail for different reasons. Some tasks require long chains of coordinated action. Other tasks can be short but unforgiving because a local error is costly or irreversible. The model turns that distinction into sufficient statistics for valuing frontier movement and firm races.
B_H values horizon progress, B_F values reliability in unforgiving environments, and C measures the value mass where both constraints bind.
The same economy can race on runtime in one task region and on base reliability in another. The regional ratio B_H^R/B_F^R determines the direction.
Deployment scale creates productive tipping only when served tasks produce usable traces that move the scarce boundary. Otherwise scale can be pure lock-in.
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