Turn Pili-Pala into a blue creature using Architect's first ability.
Tap Pili-Pala, generating {2} using Architect's second ability.
Pay {2} to untap Pili-Pala, generating {U}.
Repeat until you have infinite {U} mana.
Activate Memnarch's ability to turn every permanent into an artifact, then use Memnarch's second ability to gain control of every permanent.

Gain control of all permanents

Infinite colored mana

Memnarch

Pili-Pala

Grand Architect

Activate Memnarch's first ability by paying {1}{U}{U}, causing Teferi to become an artifact.
Activate Vorel by paying {G}{U} and tapping it, doubling the number of loyalty counters on Teferi.
Activate Teferi's third loyalty ability by removing ten loyalty counters from it, causing you to take two extra turns after this one.
Move to your first extra turn.
Activate Teferi's first loyalty ability by putting a loyalty counter on it, causing you to loot.
Activate Vorel by paying {G}{U} and tapping it, doubling the number of loyalty counters on Teferi.
Move to your second extra turn.
Repeat from step 2.

Infinite turns

Vorel of the Hull Clade

Teferi, Master of Time

Activate Memnarch's first ability by paying {1}{U}{U}, causing Mu Yanling to become an artifact.
Activate Vorel by paying {G}{U} and tapping it, doubling the number of loyalty counters on Mu Yanling.
Activate Mu Yanling's third loyalty ability by removing ten loyalty counters from it, causing you to take an extra turn after this one.
Repeat from step 2 each turn.

Mu Yanling

Activate Memnarch's first ability by paying {1}{U}{U}, causing Kitsa to become an artifact.
Cast Blinkmoth Infusion by paiyng {12}{U}{U}, minus {1} for each artifact you control.
Kitsa's prowess ability triggers, giving it +1/+1 until end of turn.
Holding priority, activate any number of mana-producing artifacts you control, adding at least {2}.
Activate Kitsa's second ability by paying {2} and tapping it, copying Blinkmoth Infusion.
Resolve the copy of Blinkmoth Infusion, untapping all artifacts you control.
Repeat from step 4.

Infinite mana artifacts you control can produce

Infinite magecraft triggers

Infinite untap of artifacts you control

Kitsa, Otterball Elite

Blinkmoth Infusion

Activate Memnarch's first ability by paying {1}{U}{U}, causing Biovisionary to become an artifact.
Cast Echo Storm by paying {3}{U}{U}, targeting Biovisionary.
Echo Storm triggers, copying it for each time you've cast from the command zone this game, with each copy targeting Biovisionary.
Resolve all Echo Storms, creating that  make copies of Biovisionary.
At the beginning of your end step, each Biovisionary triggers.
Resolve the first trigger, causing you to win the game.

Win the game

Biovisionary

Echo Storm

Activate Memnarch's first ability by paying {1}{U}{U}, causing Sphinx's Disciple to become an artifact.
Cast Idris either from your hand or from the command zone by paying {1}{U}{R} and commander tax, if applicable.
When Idris enters the battlefield, its imprint ability triggers, targeting Sphinx's Disciple.
Holding priority, activate Lithoform Engine's first ability by paying {2} and tapping it, copying Idris' trigger, targeting Basalt Monolith.
Resolve both Idris triggers, exiling Basalt Monolith and Sphinx's Disciple.
During your next turn, activate Idris using Basalt Monolith's first ability by tapping it, adding {C}{C}{C}.
Activate Idris using Basalt Monolith's second ability by paying {3}, untapping it.
Sphinx's Disciple triggers, causing you to draw a card.
Repeat from step 6.

Infinite card draw

Infinite draw triggers

Idris, Soul of the TARDIS

Lithoform Engine

Basalt Monolith

Sphinx's Disciple

Activate Memnarch's first ability by paying {1}{U}{U}, causing Sphinx's Disciple to become an artifact.
Cast Idris either from your hand or from the command zone by paying {1}{U}{R} and commander tax, if applicable.
When Idris enters the battlefield, its imprint ability triggers, targeting Sphinx's Disciple.
Holding priority, activate Strionic Resonator by paying {2} and tapping it, copying Idris' trigger, targeting Basalt Monolith.
Resolve both Idris triggers, exiling Basalt Monolith and Sphinx's Disciple.
During your next turn, activate Idris using Basalt Monolith's first ability by tapping it, adding {C}{C}{C}.
Activate Idris using Basalt Monolith's second ability by paying {3}, untapping it.
Sphinx's Disciple triggers, causing you to draw a card.
Repeat from step 6.

Strionic Resonator

Activate Memnarch's first ability by paying {1}{U}{U}, causing Medomai the Ageless to become an artifact.
Deal combat damage to an opponent using Medomai the Ageless.
Medomai the Ageless triggers, causing you to take an extra turn after this one.
Cast Idris by paying {1}{U}{R}.
When Idris enters the battlefield, it triggers, exiling Medomai the Ageless until Idris leaves the battlefield.
Move to your extra turn.
At the beginning of your upkeep, Idris's vanishing ability triggers, removing a time counter from it.
Deal combat damage to an opponent using Idris and Thrummingbird.
Idris and Thrummingbird trigger.
Resolve the Idris trigger, causing you to take an extra turn after this one.
Resolve the Thrummingbird trigger, putting a time counter on Idris.
Repeat from step 6.

Medomai the Ageless

Thrummingbird

Activate Memnarch's first ability by paying {1}{U}{U}, causing Medomai the Ageless to become an artifact.
Deal combat damage to an opponent using Medomai the Ageless.
Medomai the Ageless triggers, causing you to take an extra turn after this one.
Cast Idris by paying {1}{U}{R}.
When Idris enters the battlefield, it triggers, exiling Medomai the Ageless until Idris leaves the battlefield.
Move to your extra turn.
At the beginning of your upkeep, Idris's vanishing ability triggers, removing a time counter from it.
Activate Karn's Bastion's second ability by paying {4} and tapping it, putting a time counter on Idris.
Deal combat damage to an opponent using Idris.
Idris triggers, causing you to take an extra turn after this one.
Repeat from step 6.

Karn's Bastion

Activate Memnarch's first ability by paying {1}{U}{U}, causing Medomai the Ageless to become an artifact.
Deal combat damage to an opponent using Medomai the Ageless.
Medomai the Ageless triggers, causing you to take an extra turn after this one.
Cast Idris by paying {1}{U}{R}.
When Idris enters the battlefield, it triggers, exiling Medomai the Ageless until Idris leaves the battlefield.
Activate Jhoira's Timebug by tapping it, putting a time counter on Idris.
Move to your extra turn.
At the beginning of your upkeep, Idris's vanishing ability triggers, removing a time counter from it.
Deal combat damage to an opponent using Idris.
Idris triggers, causing you to take an extra turn after this one.
Repeat from step 6.

Combos with "Memnarch"