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Equation 2 · Part 1 · The Jagged Frontier Fallacy: Deconstructing Harvard's Canonical AI Productivity Study

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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.
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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