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

What does this equation mean?

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\},

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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Rϵ,δR_{\epsilon,\delta}

Symbol R_epsilon,delta

ReR_epsilon,delta is the quantity selected or evaluated by the optimization written on the right.

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gg

Symbol g

g is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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MM

Symbol M

M appears in the objective or constraint used by the optimization on the right.

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ll

Symbol l

l appears in the objective or constraint used by the optimization on the right.

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F1F_1

Symbol F_1

F1F_1 appears in the objective or constraint used by the optimization on the right.

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FMF_M

Symbol F_M

FMF_M appears in the objective or constraint used by the optimization on the right.

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pϵp_{\epsilon}

Symbol p_epsilon

pep_epsilon appears in the objective or constraint used by the optimization on the right.

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FkF_k

Symbol F_k

FkF_k appears in the objective or constraint used by the optimization on the right.

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δ\delta

Symbol delta

delta is the quantity selected or evaluated by the optimization written on the right.

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kk

Symbol k

k appears in the objective or constraint used by the optimization on the right.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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subscript

subscript

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.

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How to interpret it

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What the article says around this equation

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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