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Equation 55 · Part 11 · A Reference Frame Becomes Classical by Publishing Its Orientation

=

Rϵ,δ(g)=max⁡{M:F1,…,FM are disjoint,pϵ(Fk)≥1−δ for every k},R_{\epsilon,\delta}(g)= \max\left\{M:\begin{array}{l} F_1,\ldots,F_M\ \text{are disjoint},\\ p_{\epsilon}(F_k)\geq1-\delta\ \text{for every }k \end{array}\right\},
=

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

Now define Rϵ,δ(g)=max⁡{M:F1,…,FM are disjoint,pϵ(Fk)≥1−δ for every k}R_{\epsilon,\delta}(g)= \max\left\{M:\begin{array}{l} F_1,\ldots,F_M\ \text{are disjoint},\\ p_{\epsilon}(F_k)\geq1-\delta\ \text{for every }k \end{array}\right\}. subject to 1-δ\delta>pblind(ϵ)p_{\mathrm{blind}}(\epsilon) and to a fixed rule for which fragment partitions are admissible. The displayed g records the physical parameter of interest; under the Haar-average convention the resulting scalar is independent of its coordinate label. A worst-case definition would retain explicit dependence until the infimum is taken.

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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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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.