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Equation 2 · 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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=

=

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

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≈

≈

Approximately equal to; the equality is not exact.

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multiplication

multiplication

Multiply the quantities on either side.

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subscript

subscript

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.

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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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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 because the calculation is delegated to a deterministic runtime [ 7 ] : 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. By restricting their experimental subjects to a bare conversational interface and forbidding or omitting structured agentic harnesses, Dell’Acqua and colleagues did not measure the boundary of what artificial intelligence can accomplish in knowledge work. They measured the boundary of zero-shot conversational ergonomics . Defining an immutable “jagged frontier” from an un-scaffolded chat experiment is equivalent to declaring that internal combustion engines cannot cross oceans while testing them strictly inside automobiles rather than aircraft.

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