You control an artifact that can tap to produce at least .
Master Transmuter does not have summoning sickness.

Activate any artifact you control by tapping it, adding at least .
Activate Master Transmuter by paying , tapping it and returning Myr Battlesphere from the battlefield to your hand, putting Myr Battlesphere from your hand onto the battlefield.
Myr Battlesphere enters the battlefield, creating four 1/1 Myr artifact creature tokens.
Activate Clock of Omens twice by tapping four Myr tokens, untapping the mana-producing artifact and Master Transmuter.
Repeat.

Master Transmuter does not have summoning sickness.

Cast Ugin's Nexus by paying .
Ugin's Nexus enters the battlefield, triggering Mirrorworks, causing you to pay to create a copy of Ugin's Nexus.
Exile the token copy of Ugin's Nexus due to the legend rule, causing you to take an extra turn after this one.
Activate Master Transmuter by paying , tapping it, and returning Ugin's Nexus to your hand, choosing not to put an artifact card from your hand onto the battlefield.
Repeat each turn.

Master Transmuter does not have summoning sickness.

Activate Seat of the Synod by tapping it, adding .
Activate Master Transmuter by paying , tapping it and returning Seat of the Synod from the battlefield to your hand, putting Seat of the Synod from your hand onto the battlefield.
Retreat to Coralhelm triggers, untapping Master Transmuter.
Repeat.

Master Transmuter does not have summoning sickness.

At the beginning of your combat phase, Mishra triggers, creating a token copy of Ugin's Nexus that is a 4/4 Construct artifact creature named Mishra's Warform in addition to its other types.
Activate Master Transmuter by paying , tapping it and returning Ugin's Nexus to hand, choosing not to put an artifact onto the battlefield.
At the beginning of your end step, Mishra triggers, causing you to exile Mishra's Warform and take an extra turn after this one.
Move to your next turn.
Cast Ugin's Nexus by paying .
Repeat.

Master Transmuter does not have summoning sickness.
You have not copied a spell with Jin-Gitaxias this turn.

Cast Ugin's Nexus by paying .
Jin-Gitaxias triggers, copying the Ugin's Nexus spell.
Resolve the copied Ugin's Nexus.
Resolve the Ugin's Nexus from step 1, exiling the token copy of Ugin's Nexus due to the legend rule and taking an extra turn after this one.
Activate Master Transmuter by paying , tapping it, and returning Ugin's Nexus to your hand, choosing not to put an artifact card from your hand onto the battlefield.
Repeat each turn.

Master Transmuter does not have summoning sickness.

Activate Chromatic Orrery's first ability by tapping it, adding .
Activate Master Transmuter by paying , tapping it and returning Corridor Monitor to your hand, putting Corridor Monitor from your hand onto the battlefield.
Corridor Monitor enters the battlefield, triggering itself and Mirrorworks.
Resolve the Mirrorworks trigger, causing you to pay to create a token copy of Corridor Monitor.
The Corridor Monitor token enters the battlefield, untapping Master Transmuter.
Activate Master Transmuter by paying , tapping it and returning Chromatic Orrery to your hand, putting Chromatic Orrery from your hand onto the battlefield.
Chromatic Orrery enters the battlefield, triggering Mirrorworks; choose not to pay for the trigger.
Resolve the Corridor Monitor trigger from step 3, untapping Master Transmuter.
Repeat.

Master Transmuter does not have summoning sickness.

Activate Master Transmuter by paying , tapping it and returning Breya from the battlefield to your hand, putting Breya onto the battlefield from your hand.
Breya enters the battlefield, creating two 1/1 Thopter artifact creature tokens.
Activate Clock of Omens by tapping the Thopters, untapping Master Transmuter.
Activate Phyrexian Altar by sacrificing a Thopter, adding .
Repeat.
Once you have infinite creature tokens and infinite colored mana, you may activate Breya's ability infinite times.

Master Transmuter does not have summoning sickness.

Cast Ugin's Nexus by paying .
Ugin's Nexus enters the battlefield, triggering Replication Specialist, causing you to pay to create a copy of Ugin's Nexus.
Exile the token copy of Ugin's Nexus due to the legend rule, causing you to take an extra turn after this one.
Activate Master Transmuter by paying , tapping it, and returning Ugin's Nexus to your hand, choosing not to put an artifact card from your hand onto the battlefield.
Repeat each turn.

Master Transmuter does not have summoning sickness.

Cast Aeon Engine by paying .
Aeon Engine enters the battlefield, triggering Mirrorworks, causing you to pay to create a copy of Aeon Engine.
Activate Master Transmuter by paying and tapping it, returning Aeon Engine to your hand.
Pass the turn.
Untap all permanents you control during each opponent's untap step due to Unwinding Clock.
Activate the token copy of Aeon Engine by tapping and exiling it, reversing the game order.
On your turn, repeat from step 1.

Master Transmuter does not have summoning sickness.

Activate Chromatic Orrery's first ability by tapping it, adding .
Activate Master Transmuter by paying , tapping it and returning Corridor Monitor to your hand, putting Corridor Monitor from your hand onto the battlefield.
Corridor Monitor enters the battlefield, triggering its ability twice.
Resolve the first Corridor Monitor trigger, untapping Master Transmuter.
Activate Master Transmuter by paying , tapping it and returning Chromatic Orrery to your hand, putting Chromatic Orrery from your hand onto the battlefield.
Resolve the remaining Corridor Monitor trigger from step 3, untapping Master Transmuter.
Repeat.

Master Transmuter does not have summoning sickness.

Activate Master Transmuter by paying , tapping it and returning Breya from the battlefield to your hand, putting Breya onto the battlefield from your hand.
Breya enters the battlefield, triggering itself and Intruder Alarm.
Resolve the Breya trigger, creating two 1/1 Thopter artifact creature tokens.
The Thopters enter the battlefield, triggering Intruder Alarm twice.
Resolve all Intruder Alarm triggers, untapping all creatures.
Activate Phyrexian Altar by sacrificing a Thopter, adding .
Repeat.
Once you have infinite creature tokens and infinite colored mana, you may activate Breya's ability infinite times.

Master Transmuter does not have summoning sickness.

Activate Chromatic Orrery's first ability by tapping it, adding .
Activate Master Transmuter by paying , tapping it and returning Corridor Monitor to your hand, putting Corridor Monitor from your hand onto the battlefield.
Corridor Monitor enters the battlefield, triggering its ability twice.
Resolve the first Corridor Monitor trigger, untapping Master Transmuter.
Activate Master Transmuter by paying , tapping it and returning Chromatic Orrery to your hand, putting Chromatic Orrery from your hand onto the battlefield.
Resolve the remaining Corridor Monitor trigger from step 3, untapping Master Transmuter.
Repeat.

Master Transmuter does not have summoning sickness.
"Construct" chosen with Molten Echoes.

Activate Chromatic Orrery's first ability by tapping it, adding .
Activate Master Transmuter by paying , tapping it and returning Corridor Monitor to your hand, putting Corridor Monitor from your hand onto the battlefield.
Corridor Monitor enters the battlefield, triggering itself and Molten Echoes.
Resolve the Molten Echoes trigger, creating a token copy of Corridor Monitor with haste.
The Corridor Monitor token enters the battlefield, untapping Master Transmuter.
Activate Master Transmuter by paying , tapping it and returning Chromatic Orrery to your hand, putting Chromatic Orrery from your hand onto the battlefield.
Resolve the Corridor Monitor trigger from step 3, untapping Master Transmuter.
Repeat.

Master Transmuter and Xenic Poltergeist do not have summoning sickness.

Activate Xenic Poltergeist by tapping it, causing Ugin's Nexus to become an artifact creature until end of turn.
At the beginning of your end step, Athreos' second ability triggers, putting a coin counter on Ugin's Nexus.
Activate Krark-Clan Ironworks by sacrificing Ugin's Nexus, adding .
Ugin's Nexus is exiled instead of being put into your graveyard, causing you to take an extra turn after this one.
Athreos' third ability triggers, causing you to return Ugin's Nexus from exile to the battlefield.
Activate Master Transmuter by paying , tapping it and returning Ugin's Nexus to your hand, choosing to not put an artifact onto the battlefield.
Move to your extra turn.
Cast Ugin's Nexus by paying .
Repeat.

Master Transmuter and Xenic Poltergeist do not have summoning sickness.

Activate Xenic Poltergeist by tapping it, causing Ugin's Nexus to become an artifact creature until end of turn.
At the beginning of your end step, Athreos' second ability triggers, putting a coin counter on Ugin's Nexus.
Activate Ashnod's Altar by sacrificing Ugin's Nexus, adding .
Ugin's Nexus is exiled instead of being put into your graveyard, causing you to take an extra turn after this one.
Athreos' third ability triggers, causing you to return Ugin's Nexus from exile to the battlefield.
Activate Master Transmuter by paying , tapping it and returning Ugin's Nexus to your hand, choosing to not put an artifact onto the battlefield.
Move to your extra turn.
Cast Ugin's Nexus by paying .
Repeat.

Master Transmuter and Xenic Poltergeist do not have summoning sickness.

Activate Xenic Poltergeist by tapping it, causing Ugin's Nexus to become an artifact creature until end of turn.
At the beginning of your end step, Athreos' second ability triggers, putting a coin counter on Ugin's Nexus.
Activate Phyrexian Altar by sacrificing Ugin's Nexus, adding .
Ugin's Nexus is exiled instead of being put into your graveyard, causing you to take an extra turn after this one.
Athreos' third ability triggers, causing you to return Ugin's Nexus from exile to the battlefield.
Activate Master Transmuter by paying , tapping it and returning Ugin's Nexus to your hand, choosing to not put an artifact onto the battlefield.
Move to your extra turn.
Cast Ugin's Nexus by paying .
Repeat.

Master Transmuter does not have summoning sickness.

Activate Karn by paying , causing Ugin's Nexus to become an artifact creature until end of turn.
At the beginning of your end step, Athreos' second ability triggers, putting a coin counter on Ugin's Nexus.
Activate Krark-Clan Ironworks by sacrificing Ugin's Nexus, adding .
Ugin's Nexus is exiled instead of being put into your graveyard, causing you to take an extra turn after this one.
Athreos' third ability triggers, causing you to return Ugin's Nexus from exile to the battlefield.
Activate Master Transmuter by paying , tapping it and returning Ugin's Nexus to your hand, choosing to not put an artifact onto the battlefield.
Move to your extra turn.
Cast Ugin's Nexus by paying .
Repeat.

Master Transmuter does not have summoning sickness.

Activate Karn by paying , causing Ugin's Nexus to become an artifact creature until end of turn.
At the beginning of your end step, Athreos' second ability triggers, putting a coin counter on Ugin's Nexus.
Activate Ashnod's Altar by sacrificing Ugin's Nexus, adding .
Ugin's Nexus is exiled instead of being put into your graveyard, causing you to take an extra turn after this one.
Athreos' third ability triggers, causing you to return Ugin's Nexus from exile to the battlefield.
Activate Master Transmuter by paying , tapping it and returning Ugin's Nexus to your hand, choosing to not put an artifact onto the battlefield.
Move to your extra turn.
Cast Ugin's Nexus by paying .
Repeat.

Master Transmuter does not have summoning sickness.

Activate Karn by paying , causing Ugin's Nexus to become an artifact creature until end of turn.
At the beginning of your end step, Athreos' second ability triggers, putting a coin counter on Ugin's Nexus.
Activate Phyrexian Altar by sacrificing Ugin's Nexus, adding .
Ugin's Nexus is exiled instead of being put into your graveyard, causing you to take an extra turn after this one.
Athreos' third ability triggers, causing you to return Ugin's Nexus from exile to the battlefield.
Activate Master Transmuter by paying , tapping it and returning Ugin's Nexus to your hand, choosing to not put an artifact onto the battlefield.
Move to your extra turn.
Cast Ugin's Nexus by paying .
Repeat.

Master Transmuter does not have summoning sickness.

Activate Karn's first loyalty ability by putting a loyalty counter on it, causing Ugin's Nexus to become an artifact creature until end of turn.
At the beginning of your end step, Athreos' second ability triggers, putting a coin counter on Ugin's Nexus.
Activate Krark-Clan Ironworks by sacrificing Ugin's Nexus, adding .
Ugin's Nexus is exiled instead of being put into your graveyard, causing you to take an extra turn after this one.
Athreos' third ability triggers, causing you to return Ugin's Nexus from exile to the battlefield.
Activate Master Transmuter by paying , tapping it and returning Ugin's Nexus to your hand, choosing to not put an artifact onto the battlefield.
Move to your extra turn.
Cast Ugin's Nexus by paying .
Repeat.

Master Transmuter does not have summoning sickness.

Activate Karn's first loyalty ability by putting a loyalty counter on it, causing Ugin's Nexus to become an artifact creature until end of turn.
At the beginning of your end step, Athreos' second ability triggers, putting a coin counter on Ugin's Nexus.
Activate Ashnod's Altar by sacrificing Ugin's Nexus, adding .
Ugin's Nexus is exiled instead of being put into your graveyard, causing you to take an extra turn after this one.
Athreos' third ability triggers, causing you to return Ugin's Nexus from exile to the battlefield.
Activate Master Transmuter by paying , tapping it and returning Ugin's Nexus to your hand, choosing to not put an artifact onto the battlefield.
Move to your extra turn.
Cast Ugin's Nexus by paying .
Repeat.

Master Transmuter does not have summoning sickness.

Activate Karn's first loyalty ability by putting a loyalty counter on it, causing Ugin's Nexus to become an artifact creature until end of turn.
At the beginning of your end step, Athreos' second ability triggers, putting a coin counter on Ugin's Nexus.
Activate Phyrexian Altar by sacrificing Ugin's Nexus, adding .
Ugin's Nexus is exiled instead of being put into your graveyard, causing you to take an extra turn after this one.
Athreos' third ability triggers, causing you to return Ugin's Nexus from exile to the battlefield.
Activate Master Transmuter by paying , tapping it and returning Ugin's Nexus to your hand, choosing to not put an artifact onto the battlefield.
Move to your extra turn.
Cast Ugin's Nexus by paying .
Repeat.