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Build works by focusing on alt-quality of 
Gemling Legionnaire's 
Advanced Thaumaturgy.
Despair gives -100% reduced mana cost (including the cost from 
Archmage) making it free to cast.
Blink gives more than DOUBLE blink distance.
Alchemist's Boon gives cast speed during any mana flask effect (
Lavianga's Spirits)
Mana Remnants gives mana regeneration rate (more on that later)
Blasphemy + 
Temporal Chains has insane slow values
The highest end of builds. Makes 4 blinks per second blood mage look like they're standing still.
This tree focuses on 
The Adorned for rare jewels.
Do not use this tree without The Adorned.
Do not use this version without 
Dueling Wand.
Temporalis is obviously required as it's a tempo build.
Solar Amulet gives us a nice amount of spirit. Can be replaced with 
Twisted Amulet noting spirit constraints. You want +4 Spells, Cast Speed, and +5% quality on the suffix. Prefix wants the spirit roll as well as mana.
Pearl Ring or 
Mnemonic Ring are both good choices. The Pearl Ring gives more speed and is my choice. Mnemonic Ring for more mana gives more damage and survivability. Obviously you're aiming for cast speed and +1 spell. Prefixes are mana and mana%. Alternatively use a 
Gold Ring. I have both a Pearl Ring and Gold Ring for free mirror service this league.
Sapphire Goal here is to get spell damage on prefix, along with crit+crit+cast speed on the suffix. Mix and match the critical chance vs critical damage bonus on the suffixes based on your actual numbers.
Dueling Wand is not a requirement. Can run 
Runemastered Runic Fork or any other wand base really. On a budget with 
Aldur's Legacy theRunic Fork gives an extra +1 level which helps with damage, as well as just being able to slot in more 
Iron Rune for more spell damage. Between these two you'll get sigificantly more spell damage on fork, but at the expense of a huge chunk of cast speed.
Tasalian Focus is a standard es+es%+spell / crit chance + cast speed +2 setup.
Sirenscale Gloves are explicitly 1 socket gloves converted to a jewel socket. Normal arcane surge gloves otherwise.
Sekhema Sandals with quad resists to help cap resists.
The 
Runeforged Grinning Mask is not strictly required, however, it opens up to using 
Powered by Verisium on the Dueling Wand. If you don't want to go this route, skip Powered by Verisium later.
Between 
Raven-Touched Shard + 
Megalomaniac + Solar Amulet you need the following notables: 
Infusion of Power OR 
Thaumaturgic Generator, Zarokh's Gift, and 
Paragon.
Mageblood can be replaced with any other belt. I personally use 2x Legacy of Diamond and 2x Legacy of Silver
Sources of quality (required to reduce mana costs):
Corruption 23%, Paragon (5%), 
Fox Idol (5%), Solar Amulet (desecrated mod 5%), Gemling Legionnaire ascend (6%), comes out to 44%. Dialla's Desire on a single skill, in our case Blink, for another 5%.
OPTIONAL 
Split Personality is not required. It allows us to pickup a lot more skill speed on the monk side. You can also start with the sorceress start to get more spell damage + crit. Or just skip the Split Personality entirely and use the jewel socket.
No Longer need 
Grip of Kulemak
Support Gem Requirements:
Str 25
Dex 15
Int 80
Virtuous Barrier
Spellslinger
Level 7
Blasphemy
Level 18
Alchemist's Boon
Level 15
Charge Regulation
Mana Remnants
Level 18
Blink
Siphon Elements
Spark
Level 20
Frost Bomb
Combat Frenzy
Spark because this is the spark version of the build. Vilenta's Propulsion is interchangeable with Projectile Acceleration III, the latter having less projectile speed but more damage.
Arc is similar in supports to Spark. Arc technically does tons of damage and the chaining feels great. Feel free to completely ignore Spark and only use Arc. I personally use Spark for main mapping as it spreads out without needing to aim, and Arc for single target, especially if I have a lingering spark anyway. Sione's Temper is not required and can be replaced with another damage support.
Spellslinger is integral to the build now and can no longer be replaced with 
Runeseeker's Call for this version of the build. Here we can pseudo automate 
Frost Wall for Verglas procs. 
Comet is used for two reasons. One is to guarantee that something will land on the Frost Wall and destroy it. Another is for bossing purposes to just open the fight with some comets. Glacier buffs the life of the Frost Wall which in turn gives added Gain as Cold to both Spark and Arc.
Frost Bomb to kickstart your infusions as needed.
Blink obviously for a blink build. If you are not at level 40 Blink, consider dropping Cooldown Recovery II for Uhtred's Augury.
Alchemist's Boon for cast speed.
Charge Regulation for multiplicative critical hit chance.
Mana Remnants to recover mana in mapping after taking hits to overflow mana. Also provides mana regeneration rate.
Siphon Elements is new to this version of the build. Useful for maintaining cold infusions for Spark.
Blasphemy is the most important spirit gem here. The 
Enfeeble + Temporal Chains combo is your main survivability vector. We also use this to set our life to low life using Atziri's Communion. Note that you need to use a 20% quality, not a 23%, for low life.
Blink to move
Spark for mapping
Arc for more direct single target damage
Usually start maps with Frost Bomb just to generate the first few infusions.
For the Speedy version you will need to regularly press Spellslinger to generate the Verglas buff. This is handled automatically with 
Cast on Critical for the Dreamer version. Verglas is not used in the Despair version.
Changed Crit Damage on Runeforged Grinning Mask to Spirit Reservation Efficiency. This allows the speed version to run 
Combat Frenzy for MORE SPEED and the Dreamer version to run 
Explosive Transmutation
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Mercenary
Gemling Legionnaire
