There are no currently know stockpiles of SIVA. Anything left over from the SIVA crisis has been hoarded up by Eramis in some attempt to get the Devil Splicers to fall in with her, which isn’t all that much.
English
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Siva is self replicating right? Couldn’t we use the outbreak perfected to create more siva and use it to the city’s advantage? We see it happening when we get precision kills. But then again, that would be risky, with how easily the fallen (and now cabal) sneak into the city.
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SIVA as a whole is not self replicating. Though there has been some argument to Outbreak Prime and whether in the lore it generates SIVA or not.
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SIVA is self-replicating, its just that the replication chamber can make tons of it quickly.
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Except it’s not, that’s why the Wrath of the Machine grimoire cars depicts the Splicers offering other Fallen the chance to ascend in return for SIVA offerings. They’re working with a limited supply in the aftermath of the Rise of Iron campaign
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The soldiers wanted to a leaf SIVA to the other houses and the splicers do not know how to properly use SIVA, Saladin even mentions this in one of the missions. The fallen have no idea how to properly use the more advanced him an tech like SIVA.
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Eramis may have it, but Rasputin can override it. At least according to the lore.
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If it’s not gone completely rampant like the SIVA from the Russian Replication Complex. Rasputin gave it a directive and it won’t stop carrying out that directive. Not to mention SIVA isn’t self replicating. A handful of the stuff won’t do anyone much good.
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It's programmed to do one job until it receives an update. The job it was given was consume, enhance, replicate. We destroyed the replication complex, but we don't know if Siva can build more w/o The complex. Hopefully we'll find out someday.