Cast Spellseeker, stacking Inalla's trigger under Spellseeker's ETB trigger.
Tutor Culling the Weak to hand with Spellseeker's ability.
Cast Culling the Weak, sacrificing Spellseeker and adding {B}{B}{B}{B}.
Resolve and pay for the Inalla trigger from earlier, creating a token copy of Spellseeker and leaving {B}{B}{B} floating.
When the token ETBs, tutor Unearth to your hand.
Unearth Spellseeker, leaving {B}{B} floating.
Shortcut resolving both Inalla's trigger and Spellseeker's ETB, tutoring for Burnt Offering and Finale of Promise, leaving {B} floating.
Cast Burnt Offering, sacrificing Spellseeker and adding {B}{R}{R}.
Use that mana to cast Finale of Promise with X=1 targeting Unearth and Culling the Weak.
Sacrifice a Spellseeker token to Culling the Weak for {B}{B}{B}{B} and Unearth Spellseeker.
Resolve Spellseeker's ETB and Inalla's trigger, tutoring Entomb and Reanimate into hand.
Entomb and then Reanimate Archaeomancer, leaving {B} floating.
Resolve Archaeomancer's ETB, returning Burnt Offering from your graveyard to your hand.
Cast Burnt Offering on Archaeomancer, adding {B}{B}{B}{B}.
Resolve the Inalla trigger from when Archaeomancer ETB'd and return Reanimate to your hand, leaving {B}{B}{B} floating.
Reanimate Archaeomancer and resolve the Inalla trigger, retrieving Burnt Offering and FInale of promise, {B} floating.
Sacrifice Archaeomancer to Burnt Offering, adding {R}{R}{B}{B}.
Cast Finale of Promise with X=1 targeting Entomb and Reanimate.
Entomb Shallow Grave and Reanimate Archaeomancer, {B} floating.
Resolve the Archaeomancer trigger returning Burnt Offering from your graveyard to your hand.
Sacrifice Archaeomancer to Burnt Offering, adding {B}{B}{B}{B}.
Resolve the Inalla trigger, making a token copy of Archaeomancer with haste and leaving {B}{B}{B} floating.
Return Shallow Grave with the token copy's ETB.
Cast Shallow Grave targeting Archaeomancer, leaving {B} floating.
Repeat steps 20-24 for infinite hasty Archaeomancers.

Infinite lifeloss

Infinite magecraft triggers

Infinite storm count

Infinite creature tokens with haste

Infinite death triggers

Infinite creature ETB

Infinite creature LTB

Infinite creature sacrifice triggers

Inalla, Archmage Ritualist

Spellseeker

Culling the Weak

Shallow Grave

Burnt Offering

Finale of Promise

Reanimate

Entomb

Archaeomancer

Unearth

Activate Timestream Navigator by paying {2}{U}{U}, tapping it and putting it from the battlefield onto the bottom of your library, causing you to take an extra turn after this one.
Activate Isochron Scepter by paying {2} and tapping it, casting a copy of Entomb without paying its mana cost.
Resolve Entomb, searching your library for Timestream Navigator and putting it into your graveyard.
Cast Timestream Navigator from your graveyard by paying {1}{U}.
Repeat each turn.

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