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Well, I don't mean literally killing the Kryptonian race.

We are told that,

Jor-El, managed to steal the Codex and bond its genetic information with the individual cells of his newborn son Kal-El.

And from the movie we are told that there is 1 billion pieces of DNA stored in the codex. Then in the movie we are shown the bonding process that Jor-El did to Kal-El. We are shown what seems to be DNA code bonded to blood cells.

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Now we know that Superman can bleed from when he was struck in the scout ship and when he was on board General Zod's ship.

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So in effect, when Superman bleeds he is losing not only blood, but valuable Kryptonian DNA data. And there is approximately 5,000,000,000 blood cells in 1 milliliter of blood. Of coarse we are not told what the distribution is, but you could definitely say a lot of information would be lost when there is blood lose trauma.

Is there any info on this, canonical or not?

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    It only makes sense that Kryptonian cells can die too. Considering that, if those pieces of DNA are non-transferable/replicable, then all of the data would have been lost by the time he reached adulthood since all the cells carrying the data should have been dead by then. Logically, those DNA should be transferable/replicable. And if they are, then it's also possible that multiple copies of the data exist by the time he reaches adulthood too. – thegreatjedi May 27 '16 at 6:31
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    Using a homo sapien as an example, however, the human body has an average of 5 liters of blood. By your count, that's 25 trillion blood cells to store 1 billion pieces of data. If there is only exactly 1 copy of every piece of data, we'll on average lose 0.02% of all data per drop of blood lost. – thegreatjedi May 27 '16 at 6:35
  • @thegreatjedi, not my count, I am just going off human data. And that is why I said Of coarse we are not told what the distribution is b/c there a far more blood cells then information. – KyloRen May 27 '16 at 6:56
  • @thegreatjedi, I certainly can entertain the fact that the data may be transferred to the new cells after dying, but that does not account for sudden trauma and blood loss. – KyloRen May 27 '16 at 7:04
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    My guess is that redundancy is built-in. In reality though, that doesn't guarantee zero chance of permanent loss. It only reduces the statistical odds given the same amount of damage dealt to the storage system. You can have every single body cell in Superman store 99% of all genetic data, and by chance kill off all of the exact cells storing the data needed for Kryptonians to have a sense of humour. Statistically, it's a negligible chance but still...The only solution is if every single cell can store 100% of the genetic code - you'd need to kill off Superman for permanent data loss. – thegreatjedi May 27 '16 at 8:13
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The implication seems to be that the information that was stored in the codex isn't just (digitally) encoded into his blood. Jax-Ur happens to be examining some blood cells, but I think we can be reasonably sure that it's in his other cells as well.

“Jor-El took the Codex—the DNA of a billion people— then he bonded it within his son’s individual cells.” Jax-Ur was clearly impressed by this accomplishment, and the ingenuity that lay behind it. “It was a brilliant solution. All of Krypton’s heirs living, hidden, in one refugee’s body.”

He increased the magnification. Digitized information danced through the individual blood cells. The genotypes of future generations—crafted to populate a meticulously designed social order—all waited to be harvested.

That being that case, it seems highly likely that out of the 37 trillion(ish) cells in Kal-El's body, there are multiple overlapping copies of each individual genome along with the data required to repair any missing strands, in much the same way that a par file deals with a broken or damaged download.

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