I don't think recognizing yourself in a mirror is the type of intelligence we're talking about here. But they are a little smarter than some animals obviously.
I think it is one valid method to determine "self-awareness, but perhaps not the ONLY valid way to test for such a trait. FYI, I've seen videos of crows creating and using 'tools' to retrieve food. I've seen MANY instances of clear signs of intelligence in MANY forms of life. Humans may currently be at the top of the intelligence scale, but considering the fact the evolution continues here on Earth, that may not be true for all time. What then? It's also possible we may find more intelligent examples of life in space based on DNA offshoots never seen on Earth for all I know.
I guess you are saying the paint on my car is aware because it responds to environmental factors like the sun... It peals and fades when it is 'aware' of sunlight! Amazing!
That's not even a good strawman. Chemistry alone never defined "life", nor is your paint based on "DNA".
All those capacities you listed are observed in things that we wouldn't consider 'alive'. Memory can be stored in molecules and some molecules can even self-replicate.
You're ignoring the whole basis of the conversation now (DNA). What can I say. IMO the whole universe is "alive", so....
Hey, what a great example of "intelligent design", using the basic building blocks of life.
I appreciate that... Most creationists wouldn't dare even attempt it. Though I think you are trying to twist what the article was saying about intelligence into meaning what you want it to.
From my perspective I've gone out of my way NOT to try to define 'intelligence' so I wasn't twisting their words, or meaning. I can't help it that two people can "interpret" a paper differently. I've seen that happen plenty often in debate. At least I've tried to provide actual scientific substance to the conversation.
Well now you are assuming that the laws of math and physics couldn't arise without an intelligence. You are going to have to prove that this can't happen which is obviously impossible.
I'm not even clear why you feel that's a 'requirement' in the first place. In a purely "random" and "dead" universe, the laws of physics might still create the EXACT same layout of matter, yet no life might exist in it. I'm fine with that concept, but that isn't the universe that we actually live in.
We have no reason to believe math is the product of an intelligence.
Again, I'm not even arguing that point to begin with, and then again, you can't demonstrate math would exist in the absence of preexisting intelligence either.

It's a push, either way you look at it.
To answer this question you'd have to be able to exist outside of this universe.
I'm not even claiming God technically exists "outside of" this universe, rather God exists AS this physical universe, and everything in this universe is a part of God.
You'd have to look at all the other universes that exist and then say "nope, math doesn't exist here, it does exists here though, oh but this one doesn't have math!"
Once you've established a probability for math to exist, then you can decide if you want to slap a "goddidit" label on it. Of course no one can do this...
None of that is really related to the DNA debate IMO.
If you subscribe to the "many worlds" hypothesis, then you would count yourself lucky to live in a universe with physical constants conducive to life.
You'd have to first demonstrate that life happened on "change", or as a stroke of "luck" rather than any other way. Good luck with that.
Here ya go:
Double-Stranded DNA Can Wrap Around Itself to Form Supercoiled Structures - Biochemistry - NCBI Bookshelf
and another just in case:
ScienceDirect.com - Molecular Cell - Spontaneous Sharp Bending of Double-Stranded DNA
Summary:
"The explanation normally given for these phenomena is that such sharp DNA bending is achieved in vivo by specific proteins that overwhelm the DNA's inherent inflexibility with large force. In this view, proteins dictate how and when the loops will form, while the DNA follows passively."
Um, none of that material (AFAIK) claimed that life formed "accidentally". All it seems to claim is how DNA is affected by environmental factors. I have no doubt that DNA follows many rules of physics. That was never in debate.
Of course you are probably just going to move the goalpost back again.
You say "life can't diversify by itself!" then come evolution so then you say...
Um, I never said any such thing by the way. This seems to be another example of you tilting and windmills and strawmen of your own design, rather than having anything to do with me or this conversation.
"Ah ha, well life can't begin by itself!" then comes abiogenesis so then you say...
"Well organic chemistry can't begin by itself!" then you see it in a lab so then you say...
FYI, all I said was that DNA did not form "accidentally", rather it was "intelligently designed' to house and facilitate the expression of awareness and intelligence at the microscopic level for relatively short intervals.
"Well... uh... then the PHYSICAL LAWS OF THE UNIVERSE can't begin by themselves!"
I didn't personally make that claim by the way. FYI, it's not always easy to see each 'atheist' as a unique individual, nor is it easy to see each 'Christian' as a unique individual with unique beliefs. It's not fair to accuse me of claims I never made.
So I wonder... once they've completed quantum theory, where then will you shove your 'intelligence' argument?
By the time scientists finally get there and can put it altogether, I'm sure they will have figured out that:
A) The universe we live in is "electromagnetic" in nature and chemically active just as our bodies are "electric" and chemically active.
B) "Awareness" and 'Intelligence' are quantum effects associated with electro-chemical systems.
C) The universe itself is one such aware and intelligent electro-chemical system.