Not loot. Each one opens exactly one arena door: clear the cave for the artifact, put it in an obelisk or terminal, and it generates the portal.

The Beta list is what Beta costs, not Gamma plus extra. Two exceptions say so on their own pages — the King Titan wants the previous tier's own trophy, and the Overseer's tribute is spent opening a door and is not consumed.

Genesis: Part 1 and Part 2 have no obelisks and no artifacts — their bosses are missions, gated on mission count and Mutagen. Aberration keeps artifacts but hides them behind radiation.

Tribute tables are read off each boss's own article. Where no value is on record — a minimum level, an arena coordinate — this site shows no value rather than a guess.