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Equation 95 · Part 4 · A Reference Frame Becomes Classical by Publishing Its Orientation

=

ρF(g)=ρF(e)\rho_F(g)=\rho_F(e)
=

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

Orientation-blind access. “An isotropic bath cannot publish orientation” is too broad if it means only that the incoming probes are unpolarized. An asymmetric rotor can transfer orientation to initially isotropic carriers through a covariant interaction. The correct zero-record condition is operational: if the accessible channel satisfies ρF(g)\rho_F(g)=ρF(e)\rho_F(e) for all g —for example because a complete group twirl erases directional dependence—then no fragment beats the Haar-prior baseline.

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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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