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Published equation contexts

BϕtrueB\phi_{\rm true}

Why this formula appears here

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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BB

Symbol B

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ϕtrue\phi_{\rm true}

Symbol phi_rm true

phiri_rm true is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Published contexts (1)

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BϕtrueB\phi_{\rm true}

Equation 35 · Evolutionary Physics

The Bend an Elevator Cannot Fake

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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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