Where this scenario stands
| Quantity | Value | Meaning |
|---|
Balance trajectories
Required income by deadline and newcomer share
LOGOS per newcomer per epoch. These are formal constant-income solutions; † exceeds the pool budget. “No finite rate” means insufficient leadership income. Other inputs follow your current settings.
| Deadline | γ = 100% | 75% | 50% | 25% | 10% |
|---|
Model, symbols & assumptions
This calculator implements our deterministic onboarding model, not the reference panel’s fee-refilled mining controller. It does not simulate random PoS wins or mining claims.
Before pool exhaustion and locked-reward maturity:
mliq = βm; mlock = (1 − β)m
Stot(t) = S₀ + (M + PL)t
g(t) = [1 + (M + PL)t / S₀]PL / (M + PL)
A(t; M) = S₀ + PLt − S₀g(t)
bᵢ(t) = βmt + γ A(t; M) / N
kᵢ(t) = (1 − β)mt
sᵢ(t) = kᵢ(t) + bᵢ(t) = mt + γ A(t; M) / N
R(t) = R₀ − Mt
N: number of tokenless newcomers. m: constant mining income per newcomer. M: total payout to all miners. γ: fraction of payouts received by newcomers. PL: leadership pot per epoch. S₀: initial active stake, including all capitalised participants. R₀: initial mining pool. KB: required unlocked balance. t: epochs since genesis. g: growth factor of genesis-funded stake. A: leadership income generated by mining-funded stake.
β is the fraction of mining rewards that is immediately unlocked, common to all miners; the input is a percentage. For example, enter 0.01 for 0.01% (β = 0.0001). β = 0 recovers the all-locked baseline; β = 100% makes all mining income unlocked. It is not a fee-diversion parameter.
All rewards are reinvested. Both locked and unlocked mining tokens are stakeable; leadership rewards are unlocked. The unlocked balance is part of total stake, not additional to it. At fixed m and γ, changing β does not change total stake or pool depletion. No pool replenishment, claim fees, withdrawals, or minted leadership rewards are included. Mining stops when the pool empties; subsequent leadership income grows linearly because stake shares remain fixed. Qualification tests a balance and does not spend it. Staking unlocked rewards is a behavioural assumption, not an enforced requirement.
Leadership: φ(α) = 1 − (1 − f)α, where α is relative stake and f the active-slot parameter. Normalised expected rewards PLφ(αᵢ)/Σφ(αⱼ) are approximated by PLαᵢ. Outcomes shown here are not success probabilities.
Mining: mᵢ = hᵢ(d/p)w, where hᵢ is attempts per epoch, d/p the win probability, and w the retained claim reward. Constant incomes are imposed here; no actual difficulty controller is simulated. Incumbent initial allocations must remain inside S₀. Their subdivision does not change these newcomer trajectories under the proportional-reward approximation.
Lower bound and approximation: let c = PLT²/(2S₀) and D = βT + c. Then m₀ = KB/D is a necessary lower bound, not a sufficient rate. First correction: m₀[1 + (c/D)(2Nm₀/γ + PL)T/(3S₀)]. The approximation needs ε = (M + PL)T/S₀ ≪ 1. The exact solver includes both direct unlocked mining and leadership income. With β > 0 and γ > 0 there is no leadership-only ceiling, but the pool budget can still make a target unaffordable.
A month is 365/12 days. Horizons are restricted to at most 12 months; the 12-month value is the limit immediately before unlocking. A result exactly at 12 months does not qualify strictly before one year.