Burn Progression

Burning more $BAG raises an Ape's weight, permanently, on a diminishing-returns curve with no ceiling on the Ape's own record.

Every $BAG burned into an Ape is destroyed forever and counted forever — the Ape's Lifetime $BAG Burned figure only ever goes up. Burn Progression converts that figure into a boost added on top of the Ape's Base Rarity Weight:

burnBoost = √(netBurned ÷ 4,250)
effectiveWeight = baseRarityWeight + burnBoost

Total $BAG burned	Burn boost
5,000	1.0×
20,000	2.0×
45,000	3.0×
80,000	4.0×
500,000	10.0×

A common Ape can out-earn a rare one

There is no rule saying a common Ape can't eventually surpass a naturally rare one — that's intentional. A 1.00x Ape that burns 500,000 $BAG reaches a 10.0x boost; a 5.50x Ape that only activates stays at 1.0x boost. Rarity gives the head start; burning determines how far an owner takes it.

The network-wide ceiling

There's one important catch: how much of an Ape's burn boost actually counts right now is capped by a ceiling that rises as the whole collection burns more, together — not by what any single Ape does on its own.

$BAG burned network-wide	Ceiling
< 5,555,000	1.0×
≥ 5,555,000	2.0×
≥ 13,332,000	3.0×
≥ 22,220,000	4.0×
≥ 33,330,000	Uncapped

A burn that would push an Ape's boost past the current ceiling simply isn't accepted — the transaction fails before any tokens are taken, rather than silently burning them for no effect. As more of the collection activates and burns, the ceiling rises for everyone at once, unlocking previously-blocked burning automatically.

Full activation of every single Ape in the collection burns 9,443,500 $BAG — 21.25% of total supply. That crosses the first ceiling but not the second, so reaching further stages genuinely needs the community to keep burning beyond just activating.

Diminishing returns

Progression is continuous, never tiered — 25,001 burned always beats 25,000, no flat plateau.
Each additional increment produces a smaller marginal gain than the last — the square-root curve is what makes this diminishing by design.
The permanent record (Lifetime $BAG Burned) is never rewritten, even while the ceiling temporarily limits what counts.