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Equation 35 · Part 3 · The Bend an Elevator Cannot Fake

subscript

BϕtrueB\phi_{\rm true}
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

Weighted least squares achieves zero residual on any data that lie exactly in the range of B . If y truly equals Bϕtrue\phi_{\rm true} for some vector ϕtrue\phi_{\rm true} — meaning a genuine, single-valued scalar potential sits at every node, however violently curved the spacetime that produced it — then ϕtrue\phi_{\rm true} itself drives the weighted sum of squares to exactly zero, which is the smallest value the nonnegative objective can take, so the fitted values equal y exactly and r ≡\equiv 0 . This holds independent of how strongly ϕ\phi varies from node to node, independent of C , and independent of the graph’s shape, because it is a fact about linear regression, not about gravity: any closed loop of…

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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.

Open the illustrated subscripts: which member of a family? guide →

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