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Here, $\mathbb{E}$ stands for "Extra", as in the extra strands in the tangle outside of the two being paired.

As mentioned in the bottom equation $R_{ab}\mathbin{/\mkern-6mu/}P^{ab}=\infty$, pairing is not always well-defined, neither topologically nor algebraically (as the above describes the dimension of the (infinite-dimensional) algebra).