Supply and Allocation

MORPH is an ERC-20 token used for payments, staking, governance, and fees.

• Genesis supply: S0 = 10,000,000 (ten million)

• Protocol fee: ϕ = f · payout → partially burned, partially sent to treasury

• Emissions: Finite and front-loaded if enabled, for bootstrapping

Staking and Access Tiers

Operators stake s to reach tiers Tj with (r(j)min, s(j)min).

• Higher tiers allow higher job ceilings P(j)max and faster settlement

• Slashing multipliers σ(j)r increase with tier to price fraud risk

Payout Function and Properties

Let P be job price, q̂ aggregated quality, r reputation, and f fee rate.

Define:

η(q̂, r) = γ + αq̂ + βr

Where:

• α, β ≥ 0

• γ = 1 − α − β

• η ∈ [0,1]

Robot receipt:

R = P · η(q̂, r) · (1 − f)

Properties:

• Monotonicity: R increases with q̂ and r

• Upper bound: R ≤ P(1−f)

• Continuity: Small scoring differences → smooth payout changes, reducing disputes

If a challenge succeeds:

• Slash robot stake by σrs

• Slash oracle stake by σos

• Slashes distributed to poster, challenger, and burn

Finite Emission Support

If enabled by governance:

• Finite bootstrap emission Et = E0 e^(−λt) at epoch t

• Allocated to verified jobs by weight:

wi = q̂i · log(1 + si

• Constraint: Σt Et ≤ I0 (initial incentive pool)

• Emissions optional and time-limited

Worked Example

Given:

• P = 1000

• f = 0.02

• α = 0.5

• β = 0.3

• γ = 0.2

• q̂ = 0.85

• r = 0.70

Calculation:

η = 0.2 + 0.5·0.85 + 0.3·0.70
   = 0.2 + 0.425 + 0.21
   = 0.835

R = 1000 · 0.835 · 0.98 ≈ 818.3 MORPH

Fee ϕ ≈ 16.7 MORPH; burn = bϕ.