-Increasing the awareness of cults and ruinous influences. It exists
here, so why not provide simple training on how to behave when a friend invites you to an odd group, or what to watch out for when your family member starts acting weird.
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Mandatory check ups, for everyone. Sure, there are a
lot of people, but even a partial implementation makes it harder for an obvious cultist to hide.
-Increasing welfare and support for poorest, jobless, those who lost their families in a single night due to wildlife attacks, etc. Again- pathological families are more likely to fall to chaos. A healthy mind has fever cracks for literal evil to slip through.
1. Already done. In fact its been done for ages.
2. That seems counter productive to therapy and even then there's not much we can do. I'd be very surprised if there wasn't incentives to make people go and those that really need it are made to go nor do I think avernites are so prideful that they wouldn't especially when it was created and sponsored by the Govenor. However, I think you're not noticing the possible back fire of a cultist infecting his pysician who goes on to infect more psychologists. Its a risk now of course though.
3. Dude avernus is the best save Muspelheim in terms of social security nets. Poor as shit for us is middle class by midgard standards. the poorest have free good quality food as a standard every day, their children are educated to the highest levels with excellent scholarships again for free, there is no unemployment as between their education and the constant death rate there's always options somewhere and of course there's the military and our orphanages and health care is the beyond the best. There are very few practical ways we can improve our social security more than it already is, we have a universal basic income IIRC and more.
I honestly don't think that's the case with behavior. I mean:
-Wouldn't spiritually inclined people in hopeless situations seek support in faith?
-Wouldn't chronically ill, hypochondriac or severely wounded people more often (subconsciously) seek protection from Nurgle?
-Wouldn't people heavily involved fighting circles far to Khorne more easily than a lonely housewife?
-Doesn't a crime-ridden neighborhood invite drug dealers, which mainly follow Slaneesh?
-Creative people in competitive environments (e.g. high-technology businesses) sound like perfect Tzeentch followers.
Sure, there are many varied characteristics, but that far in the future, statistical tools and computing power should be enough to find out correlations that can be actually applied, if people bothered to find them.
We already have tools which allow some impressive characterization of massive communities now. 40k years in the future, in a near-totalitarian state? Should have plenty of data to work with.
How about their holy numbers and symbols? Image recognition to find things similar enough to tainted symbols, and basic search engines to find large quantities of a singular tainted number.
Especially considering that we have hordes of magical superhumans trying to find those people. At this point their experience alone could work as a practical basis for making of theoretical models.
But, none of those are indicative of anything.
A person who seeks support in faith is usually just seeking support in that especially on Avernus where people are very pious. If Avernus still had drug dealers then they can just be drug dealers, they're not always slaaneshi. If they're involved in fighting then they're not automatically Khorn bait, they could just be doing it to blow of steam.
The gods embody certain characteristics, but people possessing them is not indicative of them falling to that god. You can draw plenty of correlations me and my friends did. Bite us in the backside hard.
If we applied theoretical models of behaviour of possible chaos infection on such vague characteristics and behaviours then our potential cultists suddenly is the entire human population of the galaxy and that clearly isn't right.
There are much more specific things we look for, but they're not perfect either for instance
Abomination: Deference to authority, unthinking.
Khorne: More irrational anger and rage.
Nurgle: Jolliness and at a hidden stage very good health (Nurgle can sneak extremely well its actually among the best at it)
Tzeench: Extreme optimism, always has a plan
Slaanesh: Overly perfectionist/over indulgent.
More specific, but still not great. And of course then add in Chaos Undivided.
Basically there's things to watch out for and there are correlations that can be drawn, but they're for things that should not be relied upon (all the examples I gave can just be normal regular people and in every 100,000 times they are just that.)
As for the other two
1. The image recognition is an old trick, though whether we have to do it manually or whether our systems are well enough protected that we can work without them I dunno.
2. We don't have search engines. We don't even have an internet. It'd be infected irreparably an hour. Still if I get what you mean looking for concentrations of things like the number 6, I'd be surprised if that wasn't done automatically and places that have lots of a god's special number are certainly monitored.