Enhance

Enhance consumes other equipment and/or Colossus Fragments as fuel, together with gold, to raise an item up to its rarity cap. Each fragment gives one fuel unit. Equipment gives a rarity-weighted unit plus 80% of the fuel already invested in it, weighted by the gap between the target rarity and the consumed item's rarity. Same-or-higher-rarity fuel has weight 1; one/two/three-or-more rarity steps below use ×0.25, ×0.063, ×0.016.

Fuel advances deterministically; the operation has no success roll or downgrade. Partial fuel remains as enhancement XP. Fuel beyond the rarity cap is wasted, and consumed equipment is removed. Locked items cannot be fuel, and an item cannot consume itself. Gold is proportional to the fuel applied in each step, item level and rarity, with a minimum cost basis of item level 10. A full step uses fuel units × 0.25 × the level-cost curve × 1.25 raised to rarity tier; the default step-to-step gold ratio is 1. Partial steps pay their proportional share and the total action cost is rounded once, with a minimum of one gold. The table uses item level 10 and complete steps. Reaching a milestone creates a sleeping bonus that must be activated at Awaken.