Scroll down to page 7 for a more obvious display of the same data but without the giant red labels of each flare and you can read "The solar flare at ~21:37 EST on 12 December is clearly visible, along with the precursor count-rate decline that precedes it.
Ok I was looking at the 41 hour difference starting from 21h37 EST, but you are correct there was a 40 hour early detection until 21h37 EST as well.
I haven't got muon data from Purdue for that particular 40 hour early warning, it appears that Purdue itself did not produce muon figures over that same period. But muon detection is one of the most favored methods in solar event early warning systems (CMEs) , so there is some logic behind muons relating to early warning drops in decay rates:
"The information about primary ion type and energy is mostly smeared during
its successive interactions with atmospheric nuclei, therefore, only coherent measurements of all
secondary fluxes (neutrons, muons, and electrons), along with their correlations, can help to make
unambiguous forecasts and estimate the energy spectra of the upcoming dangerous flux. "
There are other events that occur before a solar flare. Sunspots show a cycle before flaring up. The only way to detect if there is about to be a flare is to analyze the fastest particles that burst out before the solar flare.
Your argument requires time travel since solar protons (must travel at less than c) can't arrive before x rays (must travel at c) from the same event
About 1/3 of the way down the article it points out what I've already told you. The data used was not gathered by those institutions which means they have no way to check for periodic affects on the equipment. The article also points out that follow up investigations found no evidence to confirm the effect, so the effect is definitely deniable.
Not deniable, subject to corroboration. The article we are discussing gave the studies significant respect, despite the section you are quoting that refers to the need for further corroboration. I agree, further corroboration is needed.
Cosmic rays are basically fast protons, solar wind is slow protons and other light atomic nuclei.
I've bolded a very important sentence that actually contradicts your entire position. I want you to consider the effects of your sentence compared with your claim. Your claim is that muons affect decay rates and that changes in quantities of muons result in changes in decay rates. Now go back to the sentence in bold and please answer this question, is the number of muons that impact/affect a radioactive element on a probe moving away from earth greater than, less than, or equal to the number of muons that impact/affect a radioactive element on earth?
If the number of muons is different then the decay rate on a probe should be different or your claim is wrong (we know the decay rate on the Cassinni probe isn't different).
If the number of muons isn't different then your bolded sentence has some serious problems since there's no atmosphere around the probe
To answer your question, I would say the muon effect is less on a probe, and so decay rates should be less on earth and faster in space, and be consistent once in space no matter what the solar distance (as the Cassini probe confirms).