Mint curve · shadowpaper Docs

SPAPER is minted at a flat 100 per USDT of loss while the LP is below 2M USDT, then along a decaying curve driven by cumulative tail losses.

The mint curve determines how much SPAPER a realised loss or liquidation produces. It has a flat segment and a decaying tail.

Inputs#

gMint basis of this loss: the realised loss net of any LP-side fee

trackedNet LP balance at the moment of settlement; may be negative

HCumulative mint basis minted in the tail segment; only increases

Constants: threshold 2,000,000 USDT · flat rate 100 SPAPER per USDT · decay scale 120,000,000 USDT. Governance can change them only through the 24-hour Timelock.

Computation#

flat  = min(g, max(0, 2,000,000 − tracked))
tail  = g − flat
mint  = flat × 100
if tail > 0:
  start = 120M / (120M + H)
  end   = 120M / (120M + H + tail)
  mint += tail × 100 × start × end
H += tail

← Scroll sideways for long formulas

All arithmetic is integer and rounds down. The order of settlements within a block can change how a loss near the 2,000,000 USDT threshold is split.

Curve shape#

The marginal mint rate in the tail is 100 × (120M ÷ (120M + H))² SPAPER per USDT.

Marginal SPAPER per USDT vs. cumulative tail basis H25 / $1 at H = $120M

H $120M

H	SPAPER per USDT
0	100
40M	56.25
120M	25
360M	6.25

There is no exponential term and no bonus multiplier: a mint of m tokens yields a share of m ÷ (supply + m). Because segments are judged on net LP, minting returns to the flat rate whenever the LP falls back below 2,000,000 USDT; H never decreases.

Example#

Alice's liquidation has a mint basis of 98 USDT (100 USDT margin less the 2 USDT LP-side fee). The table compares two moments.

State at settlement	Split	SPAPER minted
tracked = 1,999,950; H = 0	flat 50, tail 48	5,000 + ≈ 4,800 = ≈ 9,800
tracked above 2M; H = 120M	flat 0, tail 98	≈ 2,450

Case 1: flat = min(98, 2,000,000 − 1,999,950) = 50  → 50 × 100 = 5,000
        tail = 48; start = 1; end = 120M/(120M + 48) ≈ 1
        48 × 100 × 1 × ≈1 ≈ 4,800                    → total ≈ 9,800
Case 2: start = 120M/240M = 0.5; end ≈ 0.5
        98 × 100 × 0.5 × 0.5 ≈ 2,450

← Scroll sideways for long formulas

The same 98 USDT loss mints about four times as much SPAPER at launch as it does after 120M USDT of tail losses.