so if you're saying that the 3D systems is main cause for all these declined transactions
No, I'm saying it is a likely explanation for what you are describing: 1) you attempt to use your card, but get some kind of "failure" message back; 2) you contact your credit card issuer who tells you that they have not declined any charges and they are not/will not block the charge. At least that's what I thought you described.
You've linked threads of folks with Capital One issues, yet I haven't experienced any (so far) with my card.
Don't be too focused on the credit card brand, instead find out who is blocking the charge (at what point in the transaction). Some people have reported they could not get charges through a Capital One card, other people have reported no problems. A report of "success" is hard to ascribe, and many people conflate details (read the threads I linked to carefully, you will see otherwise well-informed people repeating over and over "it's just a fraud-detection system, it happens all the time, just call your bank and they will OK it" - and that completely missed what's going on). Personally, I don't have a Capital One card (do not like the company for other reasons). I do have credit cards issued by pretty much every other major card company. Every one of them failed for me, due to the 3-D Secure system (eventually confirmed to me by the vendor). I'm not going to continue explaining it endlessly - it's well documented in the threads I linked to.
my declined transaction receipt states...(stuff)
I have no idea what that means and it probably means nothing.
This info also matches the pending amount deducted and deposited on my Chase app. Which means there is a log with Chase about the declined transaction.
but...
I've contacted the Chase Support and I don't think the folks that were trying to help me know what is going on...let alone the 3-D Secure system. They just kept insisting that I was doing something wrong and that they don't see any declined transactions on their end, even though I told them that I can provide the receipts that stated "declined" and "abandon debit".
If the Chase employee says they see no declined transactions, I would be inclined to believe them. Whatever some point-of-sale machine spits out on piece of paper (with technical details probably lost in translation) does not matter. I would not put a lot of faith in the literal text strings of that print out, which is basically telling you what you already know: "your purchase failed. you were not charged". You've probably seen dumb error messages on computer screens before, right? This could be one.
That said...
This info also matches the pending amount deducted and deposited on my Chase app. Which means there is a log with Chase about the declined transaction.
If that is the case, you should indeed call Chase and ask them WTH is going on, and why one of their systems (the app) says there was an attempt to charge your account (subsequently reversed), but the, system that the CS agent looked at said there were no attempted charges.
The other thing that's (extra) odd about what you are reporting is that in your case it was not an automated, unattended machine running the charge. I've only heard of 3-D Secure being used for online transactions and at unattended POS systems (gas stations and train stations are the examples always mentioned). This is the first time I've heard of anyone having the problem at a restaurant (presumably that restaurant had live human staff).
But the bottom line is this: you need to figure out at which end of the transaction the purchase process was interrupted. If it's 3-D Secure intervening, your bank will have no record of the transaction. If Chase says they have no record of any attempted charge that was declined, I'd suspect 3-D Secure as the cause. But if it depends on who you ask at Chase...beats me.