The ladder
Rarity was never assigned. Every trait was counted over the finished set, each monk scored as the sum of the inverse frequencies of its traits, and the ranking that fell out cut the collection into these five pools. The pools were then packed three bits per token and sealed on-chain in the same transaction as the provenance hash, so the distribution below can be counted from the chain rather than taken on trust.
Your answer decides which pool you draw from. It never decides which monk.
Satori
13 of 888 · 1.5% · score 88+Thirteen of these exist.
Bamboo
45 of 888 · 5.1% · score 75-87A pebble struck bamboo and you heard it.
Still Water
110 of 888 · 12.4% · score 60-74You stopped performing and said the thing.
Dust
220 of 888 · 24.8% · score 45-59A real position, held loosely.
Clouded
500 of 888 · 56.3% · score 0-44You answered. Something answered, anyway.
If a pool runs out
The gate falls DOWN the ladder, never up. If you earn Bamboo and all forty-five Bamboo monks are gone, you are handed a Still Water. You are never handed something rarer than you earned, because the entire point of the gate is that rarity cannot be obtained by waiting for the right moment.
Sit with the koan