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Equation 2 · Part 4 · The Jagged Frontier Fallacy: Deconstructing Harvard's Canonical AI Productivity Study

subscript

Errorsystem=Errorsemantic extraction×Errordeterministic runtime≈Errorsemantic extraction×0=0.\text{Error}_{\text{system}} = \text{Error}_{\text{semantic extraction}} \times \text{Error}_{\text{deterministic runtime}} \approx \text{Error}_{\text{semantic extraction}} \times 0 = 0.
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

Similarly, the ReAct framework developed by Yao and colleagues at Princeton and Google demonstrates that interleaving reasoning traces with external execution actions (such as querying an API, executing Python code in a sandboxed interpreter, or retrieving verified database records) transforms the error surface [ 6 ] . Consider the multi-step failure task in the Harvard BCG study: a brand performance evaluation across different business units where financial figures were distributed across text and tables. When this class of problem is routed through a tool-augmented harness (such as Toolformer or an agentic code execution sandbox), the probability of arithmetic hallucination drops to zero…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.