= Solution
In the ideal unscattered coincidence model, let a <positron annihilation> occur at position $s$ on a <coincidence line of response> connecting detectors $A$ and $B$. Its two oppositely directed <photons> must both survive. Their independent attenuation factors multiply:
$$
P_{\rm coinc}(s)=\exp\left[-\int_A^s\mu(\ell)\,d\ell\right]\exp\left[-\int_s^B\mu(\ell)\,d\ell\right]=\boxed{\exp\left[-\int_A^B\mu(\ell)\,d\ell\right].}
$$
The source position cancels because the complementary path integrals span the whole chord. In a uniform slab of chord length $L$, the same argument is $e^{-\mu s}e^{-\mu(L-s)}=e^{-\mu L}$. Therefore attenuation correction requires the full <linear attenuation coefficient> map along the chord, but not the depth of the particular annihilation along that chord. This argument addresses attenuation of true <PET coincidences>; scatter, random coincidences and detector efficiency need their own corrections.
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