The Token

Emissions & Gauge Weighting

Community emissions are the single largest bucket of $MRN supply (50%). This page derives the exponential curve, the gauge system, and the per-user boost multiplier.

Weekly emission (baseline)

E_w = E_0 · e^(−λ · w)

E_0 = 1,850,000    (MRN week 1)
λ   = ln(2) / 200  = 0.003465736 per week

Half-life:  200 weeks  ≈  3.84 years
Total emitted over 520 weeks (10 years):
   ∫  E_0 · e^(−λw) dw  ≈  E_0 / λ · (1 − e^(−520λ))
                       ≈  5.00 × 10⁸  MRN

Emissions sample table

Week	E_w (MRN)	Cumulative	% of 500M
1	1,850,000	1,850,000	0.37%
26 (6 mo)	1,693,441	45,732,183	9.15%
52 (1 yr)	1,548,979	88,441,024	17.69%
104 (2 yr)	1,297,205	160,220,900	32.04%
200 (half-life)	925,000	250,000,000	50.00%
260 (5 yr)	751,890	300,047,150	60.01%
520 (10 yr)	305,432	499,940,282	99.99%

Gauge weighting

Each basket has a gauge. veMRN holders vote weekly to allocate the emission across gauges. If gauge g receives vote weight w_g, its share of week-w emissions is:

E_w,g  =  E_w  ·  w_g / Σ_j w_j

Vote weight of a locker at time t on gauge g:
   w_i,g(t)  =  bal_i(t) · s_i,g

with:
   bal_i(t) = amount_i · ( T_end,i − t ) / T_max
   T_max    = 48 months   (max lock)

Locker boost multiplier

Within a gauge, emissions are distributed pro-rata to basket-share holders, but each user's claim is boosted by their own veMRN position. The boost formula (adapted from Curve gauge math) is:

b_i  =  min ( 1  +  1.5 · ( ve_i / ve_total ) · ( S_total / s_i ) , 2.5 )

where:
  ve_i     = user i's veMRN balance
  ve_total = total veMRN supply
  s_i      = user i's basket shares in the gauge
  S_total  = total basket shares in the gauge

b_i is a user's boost multiplier; capped at 2.5×.

Worked example

Alice holds 10,000 basket shares (0.5% of a 2M-share gauge).
She locks 50,000 MRN for 24 months → veMRN = 25,000 (half of max weight).
Total veMRN supply = 40,000,000. So ve_i/ve_total = 0.000625.

b_Alice = 1  +  1.5 · 0.000625 · (2,000,000 / 10,000)
        = 1  +  1.5 · 0.000625 · 200
        = 1  +  0.1875
        = 1.1875 ×

Alice's boosted share of gauge emissions per week:
   0.005 · b_Alice · E_w,g  =  0.005938 · E_w,g

Why cap at 2.5×

Without a cap, a whale locking the entire $MRN supply for 48 months would capture arbitrarily large shares of gauges they hold tiny positions in. The 2.5× cap makes it impossible for a locker to steal more than 60% of the emission stream they wouldn't otherwise be entitled to.

← Previous

$MRN Tokenomics

Stock Baskets