S_total
= total SOPH supplyS_staked
= total SOPH stakedR_max
= maximum reward pool per periodR_actual
= actual rewards emitted per periodx = S_staked / S_total
R_actual = R_max * sqrt(x)
x = 0.25
, then sqrt(0.25) = 0.5 → 50.00%
of R_max
is emittedx = 0.5
, then sqrt(0.5) ≈ 0.7071 → 70.71%
of R_max
is emittedx = 0.75
, then sqrt(0.75) ≈ 0.8660 → 86.60%
of R_max
is emitted