It's a solidified unit of Seithr and the Boundary’s energy, giving them their name. A Seithr Core, unlike a Boundary Fragment, contains much more concentrated energies due to the melded souls inside its body and have a significant effect at refining power of the ones who use them, such has been seen with people like Nex. This effect is only ever temporary.
They are something of an enigma but their incredible power led to their development being stopped and banned regarded as “objects of destruction”. Even though it only contains small amounts, exposure to one can eventually become fatal due to the Boundary's power. Certain people with affinity to the Boundary's power and Seithr have been shown to be able to harness energy of the core, though the energy burns itself away quickly, as its very low quality and quantity.
Akuhei has said they could be considered the catalyst of the Third War of Armagus, as a result of humanity's curiosity with the Boundary. According to him, they were the versatile lynchpin of developments humanity made such as weapons and even artificial life—and suggests there are different kinds of Seithr Core.
It exists in a form of a spherical and inorganic black mass of highly concentrated Seithr and it is also packed with energy of souls, making it similar to the core of a Nox. In appearance, the Seithr Core look like a metallic-black sphere with blue photon energy rushing through its body and sometimes are covered in glyphs suggesting their existence is magical in nature.
Not a lot is known about the Seithr Cores, though in comments dropped by Zaezel nearing the end of Verse 1, they were objects that dated back to before the Third War and were part of the unforgiven sins of humanity. They were used, harnessed, and refined over time to design incredible innovations.
At some point after the Third War of Armagus, the Seithr Cores were officially banned from development by the NOS's decree and were deemed "Objects of Destruction". However, it's clear they're still around, as they're seen in story.
Though not much is known about the Seithr Core, they are a highly important item in the universe and plot of Control Sequence.
The Seithr Cores were left in the dark throughout Verse 1, mentioned only a few times. The first time was when Akuhei sent a strange crimson shard over to Lukain who mentioned that it was true that a real Red Core could be made again. Nothing was exactly said about that, but the Seithr core resurfaces toward the end of Verse 1 when Zaezel mentions that the cores were part of how humanity committed their unforgivable sins. While Reiga and Siegfried explained that it didn't justify killing the people of the present for a mistake in the past, Zaezel retorted that the cores were very much still being used and created.
In the ending of the Verse, a core was utilized by Zaezel and empowered the Norai Stigma he had with the help of the Proto Harvester suggesting that beings such as Zaezel have direct ties to the core or at least are capable of using their abilities.
How the Seithr Cores are being designed and how they resurfaced is a mystery in current story that plagues even Nex.
The Cores play a more important and direct role in Verse 2 of Control Sequence.
Red Seithr Core - Experimental variety.