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

Does this card's <All Turns> effect prevent me from playing a Digimon card with 6000 DP or less when my opponent has this Digimon while I have 1 or more memory?
Yes, it can't be played. If your opponent has this Digimon, "While your opponent has 1 or more memory" from your opponent's perspective means while you have 1 or more memory.
Ruled Mar 28, 2024
Does this card's <All Turns> effect prevent playing a Digimon card with 6000 DP or less even from effects that play a card?
Yes, it can't be played.
Ruled Mar 28, 2024
Does this card's <All Turns> effect also prevent playing a token that is treated as a Digimon card with 6000 DP or less?
Yes, it can't be played.
Ruled Mar 28, 2024
If I have a Digimon card with an original DP of 6000 or less and its DP would increase to more than 6000 by an effect upon playing it into the battle area, does this card's <All Turns> effect allow that card to be played?
Yes, it can't be played.
Ruled Mar 28, 2024
Does this card's <All Turns> effect allow me to play a Digimon card with 6000 DP or less if paying the play cost would cause the memory to change to 0 or 1 or more on my opponent's side when my opponent has this Digimon?
No, it can't be played. At the timing of the play declaration, if "While your opponent has 1 or more memory" from your opponent's perspective applies (in other words, if you have 1 or more memory), this card's <All Turns> effect doesn't allow you to play such Digimon.
Ruled Mar 28, 2024
When my opponent has this Digimon, does this card's <All Turns> effect allow me to just pay the play cost for a Digimon card with 6000 DP or less without playing it while I have 1 memory or more?
No, it doesn't. You aren't allowed to declare playing a 6000 DP or lower Digimon card.
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.