The best defense is a good offense...

Or something like that.

This [Koumei] build is meant to absolutely abuse Kumihimo and Breach Surge, spreading blind and various statuses to ramp up Arcane Impetus even further than without Breach Surge, because of how these two abilities interact with each other. When casting Breach Surge, it blinds enemies and has a chance to cause Radiation status on those affected, but once Kumihimo is cast on those same enemies, each status inflicted on them causes individual sparks from Breach Surge to spread.
So, in a theoretical situation, Breach Surge blinded enemies getting hit with Kumihimo, proc'ing Cold, Magnetic, and Impact, will spread 3 sparks and take 3 instances of both Surge's spark damage and Kumihimo's status damages.
The same can be said about Bunraku, but with a max of 323% Strength, hardly anything will be alive if you ever need to cast that.

This means that not only do you have great crowd control and a maxed 6.5x damage multiplier, but Koumei will be dealing big damage numbers no matter what status is being applied, making her a great crowd control and/or caster frame.

Archon Shards:

• Tauforged Crimson Shards x2: Ability Duration
  While unnecessary, this is to counter the negative Duration from Transient Fortitude. Very helpful in endurance runs.

• Tauforged Amber Shard x1: Cast Speed
  Typical quality of life shard.

• Tauforged Amber Shard x1: Energy on Spawn
  This is to ensure that you start your crowd control snowballing immediately.

Flex Spot Shard:

• Tauforged Violet Shard x1: Equilibrium
  While you shouldn't have energy issues, endurance runs would like this quality of life shard by using an Equilibrium-adjacent shard to ensure that your Breach Surge -> Kumihimo combo stays nearly infinite in it's loop.

• Tauforged Topaz Shard x1: Ability Damage on enemies affected by Radiation
  With Breach Surge giving us 65% chance to apply Radiation statuses to enemies, this will ensure that your 1 and 4 demolish higher level content with ease.

• Tauforged Emerald Shard x1: Max Corrosive Stacks
  While not entirely necessary, the option for Toxic damage to spread Corrosive and immediately armor strip enemies helps TTK on your abilities.

Alternative Arcanes:

• Arcane Universal Fallout can replace Molt Augmented if you feel like Archon Shards Cast Speed and Energy on Spawn are unnecessary/swap those to Crimson shards for Strength instead, making the optional Equilibrium-adjacent Violet shard give you infinite energy alongside Archon Flow.

• Arcane Double Back can also replace Molt Augmented if you feel the need for more damage reduction.

• Arcane Eruption fits our crowd control theme very well, can replace either for personal preference.

• Arcane Phantasm/Arcane Fury: see below, for preferred weapons for explanation.

Preferred weapons:

While I wasn't initially going to put this section in the guide, I will note that this build did have a specific melee-oriented playstyle in mind, utilizing Zaws and their 2 arcane slots. Mostly utilizing Exodia Contagion to clear out waves that are blinded and/or enemies within the strands of Kumihimo. The melee weapon in mind was a Plague Kripath (build hyperlinked) Melee Influence wave clearing polearm, but Sancti Magistar Incarnon or any other high damage/AOE oriented melee will do just fine. Using the hyperlinked [Plague Kripath] build, Arcane Phantasm will give us free movement speed that we cannot (or did not) use Archon Shards for, while Arcane Fury will make the Contagion-Influence dual explosion nuke level cap enemies.