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Equation 1 · Part 9 · The Jagged Frontier Fallacy: Deconstructing Harvard's Canonical AI Productivity Study

subscript

P(Y∣X)=∏t=1TP(yt∣y<t,X).P(Y \mid X) = \prod_{t=1}^{T} P(y_t \mid y_{<t}, X).
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

When a knowledge worker asks a bare conversational model to analyze a multi-variable spreadsheet with interdependent business constraints, the model must perform several disjoint cognitive operations within a single autoregressive forward pass: P(Y∣X)=∏t=1TP(yt∣y<t,X)P(Y \mid X) = \prod_{t=1}^{T} P(y_t \mid y_{<t}, X). Because token generation is strictly left-to-right and causal, any early latent error in intermediate arithmetic or structural interpretation compounds multiplicatively across subsequent tokens. If the prompt lacks an explicit scratchpad, state harness, or programmatic tool-execution loop, the model cannot pause, verify an invariant, execute a deterministic calculation, or revise an earlier premise [ 6 , 7 ] .

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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 article section

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