The Prismatic Piper Combos

Infinite Mana
Peregrine Drake + Archaeomancer + Displace/Ghostly Flicker
High Tide + Archaeomancer + Displace/Ghostly Flicker + Cloud of Faeries

Untapper Combos
Battered Golem + Banishing Knack/Retraction Helix + Everflowing Chalice/Fountain of Youth + Golem Foundry = infinite 3/3s, storm count
Battered Golem + Banishing Knack/Retraction Helix + Fountain of Youth + infinite mana = infinite life
Battered Golem + Banishing Knack/Retraction Helix + infinite mana + any artifact = infinite untaps

Other Combos
Infinite storm count + Temporal Fissure = Infinite bounce
Infinite blue creature ETBs + Sage’s Row Denizen = Infinite mill
Infinite mana + Capsize = Infinite bounce
Infinite mana + Whispers of the Muse = Infinite draw
Infinite mana + Secret Door = Infinite dungeon crawls

Redundant Cards
Archaeomancer can be replaced with Mnemonic Wall, Salvager of Secrets, or Scrivener for flicker combos
Battered Golem can be replaced with Mirran Spy or Zephyr Scribe for artifact bounce combos

Tutors
Drift of Phantasms: Battered Golem, Capsize, Displace, Ghostly Flicker, Golem Foundry, Sage’s Row Denizen, Trinket Mage
Merchant Scroll: Banishing Knack, Capsize, Displace, Ghostly Flicker, High Tide, Retraction Helix, Snap, Whispers of the Muse
Trinket Mage: Everflowing Chalice, Fountain of Youth, Secret Door
Vedalken Aethermage/Step Through: Archaeomancer, Mnemonic Wall, Sage’s Row Denizen, Salvager of Secrets, Scrivener, Trinket Mage