6 official rulings from Bandai, last ruled Mar 28, 2024. Straight answers to how this card actually resolves.

When my opponent's Digimon attacks and checks my security, I activate this card's effect to gain 1 memory, moving the memory counter to 1 on my side. Does the attack end, even if my opponent's Digimon has checks remaining from <Security Attack +1>?
No, as long as there are attacks and effects that have triggered but haven't finished resolving yet, the attack continues regardless of the memory gauge's current position.
Ruled Mar 28, 2024
While this Tamer is in my battle area, my opponent's Digimon checks my security stack and flips over [BT1-107]/[Holy Wave]. Its <Security> effect activates, adding a card to my security stack. The number of cards in my security stack remained the same, but can I still suspend this card to gain 1 memory?
Yes, because a card was removed from your security stack.
Ruled Mar 28, 2024
While this Tamer is in my battle area, I use [BT1-087]/[Matt Ishida]'s effect to add a yellow card from my security stack to my hand, triggering and adding a card to my security stack. The number of cards in my security stack remained the same, but can I still suspend this card to gain 1 memory?
Yes, because a card was removed from your security stack.
Ruled Mar 28, 2024
If my opponent uses a card like [BT2-020]/[Gallantmon] to trash a card in my security directly, can I activate this card's effect?
Yes, you can.
Ruled Mar 28, 2024
If I activate an effect like [BT4-104]/[Blinding Ray] to remove cards from my own security stack, can I activate this card's effect?
Yes, you can.
Ruled Mar 28, 2024
If this card is played by its <Security> effect, can I suspend it to gain 1 memory?
"No, you can't. Since this card hasn't been played when it is revealed from your security, the condition for [When a card is removed from your security stack] can't be triggered, so this card's effect can't be activated."
Ruled Mar 28, 2024
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Questions and answers are Bandai's official rulings, collected and translated by the DigimonCardGame Wiki community and reused here under CC BY-SA. Card names and card text are © their respective publishers; Combalo is not affiliated with Bandai.