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The Magus archetype Greensting Slayer modifies their Arcane Pool in this way:

At 1st level, a greensting slayer can expend 1 point from his arcane pool as a swift action to add 1d6 points of sneak attack damage to his next melee attack that round. The attack must meet all of the usual prerequisites for making a sneak attack, as the rogue class feature. For every 4 levels beyond 1st, the amount of sneak attack damage dealt by this ability increases by 1d6 (to a maximum of 5d6 at 17th level). If a greensting slayer gets a sneak attack from another source, the bonuses on damage stack.

Does Greensting Slayer Magus 5 have Sneak Attack 2d6, specifically, (assuming skill ranks are met and they chose Mage Hand as a Cantrip) would they qualify for the Arcane Trickster Prestige Class?

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A greensting slayer magus has no sneak attack until the magus spends a point from his arcane pool

Just like a creature that can cast an enlarge person to become size Large does not mean the creature meets size Large requirements and prerequisites, being able to gain sneak attack under certain circumstances does not typically count as having sneak attack now.

A strict GM may allow such a creature to take its first level in the prestige class arcane trickster if the creature would advance a level between sessions if the session ends during a melee round in which the ability sneak attack is gained from the magus's arcane pool if the creature also met the class's other requirements, but that's complicated and likely unreliable unless worked out first with the GM.

But a more generous GM may allow such a greensting slayer magus to meet the sneak attack requirements for the prestige class arcane trickster anyway—despite technically lacking sneak attack upon advancing a level—without feeling as though this will break the game. (Many Pathfinder prestige classes like the arcane trickster are usually less optimized than its core classes.)

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