The 7 Equations

Every mechanism in the SVRN economy is governed by a mathematical equation. No admin keys. No governance overrides. Just math.

1

Bridge Rate

One-Way Bridge Conversion
UCU=USDCbasket_price_USD\text{UCU} = \frac{\text{USDC}}{\text{basket\_price\_USD}}

The bridge converts fiat (USDC) into UCU at the current compute basket price. As compute gets cheaper (Wright's Law), each dollar buys more UCU — making the currency deflationary relative to compute costs.

Variables

  • UCUUCUUnified Compute Units received
  • USDCUSDCUS dollars deposited
  • basket_price_USDbasket\_price\_USDCurrent price of 1 compute unit in USD
Contract:OneWayBridge

Bridge Rate Calculator

$10,000
$0.50
UCU Received20,000
2

Creator Grant Curve

Log-Quadratic Grant Scaling
G(n)=10−0.798+0.690⋅log⁡10(n)−0.026⋅(log⁡10(n))2G(n) = 10^{-0.798 + 0.690 \cdot \log_{10}(n) - 0.026 \cdot (\log_{10}(n))^2}

Creator grants follow a log-quadratic curve that rewards early growth more than linear scaling but prevents runaway grants at massive scale. The quadratic term provides gentle compression.

Variables

  • G(n)G(n)Grant multiplier for n followers/users
  • nnNumber of followers or active users
  • −0.798-0.798Intercept coefficient (\alpha)
  • 0.6900.690Linear log coefficient (\beta)
  • −0.026-0.026Quadratic compression coefficient (\gamma)
Contract:CreatorGrantOracle

Creator Grant Calculator

1,000
Grant Multiplier G(n)10.9144
3

UBC Constraint

Universal Basic Compute Floor
Ncitizens×UBCmin⁡≤CdistributableN_{\text{citizens}} \times \text{UBC}_{\min} \leq C_{\text{distributable}}

The hard constraint ensuring the system can always honor its UBC commitments. The number of active citizens multiplied by the minimum annual allocation must never exceed distributable capacity. If it would, new citizens go to a FIFO waitlist.

Variables

  • NcitizensN_{\text{citizens}}Number of active UBC recipients
  • UBCmin⁡\text{UBC}_{\min}Minimum UCU per citizen per year (87,600)
  • CdistributableC_{\text{distributable}}Total distributable compute capacity
Contract:UBCDistributor

UBC Constraint Calculator

1,000
10.0M UCU
UBC minimum: 87,600 UCU/year
Required Capacity87.60M UCU
Utilization876.0%
ConstraintVIOLATED
4

Bonfire Burn

Revenue Overflow Destruction
Bonfire(t)=max⁡(0,R(t)−D(t))\text{Bonfire}(t) = \max(0, R(t) - D(t))

When protocol revenue exceeds compute distribution in an epoch, the surplus is permanently burned. This creates deflationary pressure proportional to economic activity — more usage means more burning.

Variables

  • Bonfire(t)\text{Bonfire}(t)UCU burned in epoch t
  • R(t)R(t)Total revenue received in epoch t
  • D(t)D(t)Total compute distributed in epoch t
Contract:Bonfire

Bonfire Burn Calculator

500,000 UCU
300,000 UCU
Burn Amount200,000 UCU
5

Quadratic Voting

Square Root Voting Power
power=tokens_staked\text{power} = \sqrt{\text{tokens\_staked}}

Voting power is the square root of staked tokens. This prevents plutocratic capture: 1 token = 1 vote, but 100 tokens = 10 votes (not 100). Concentrating wealth gives diminishing governance returns.

Variables

  • power\text{power}Voting power (in votes)
  • tokens_staked\text{tokens\_staked}UCU tokens staked for governance
Contract:QuadraticVoting

Quadratic Voting Calculator

10,000
Voting Power100.00
vs. Linear (1:1)10,000
Reduction Factor99.0%
6

Conviction Weighting

Time-Locked Commitment Multiplier
weight=power×(1+ln⁡(1+days30))\text{weight} = \text{power} \times \left(1 + \ln\left(1 + \frac{\text{days}}{30}\right)\right)

Conviction weighting rewards long-term commitment. Staking for 30 days doubles your voting weight. The logarithmic curve means early commitment is heavily rewarded but returns diminish over time.

Variables

  • weight\text{weight}Conviction-weighted voting power
  • power\text{power}Base quadratic voting power
  • days\text{days}Days tokens have been staked
Contract:ConvictionWeighting

Conviction Weighting Calculator

100
30 days
Conviction Weight169.31
Multiplier1.693x
7

Sovereignty Index

Patron Dependency Scoring
S(a)=1−max⁡(value_to_patrontotal_value)S(a) = 1 - \max\left(\frac{\text{value\_to\_patron}}{\text{total\_value}}\right)

Measures how independent a citizen is from any single patron. A score of 1.0 means fully sovereign (no single entity dominates their income). Citizens below 80% threshold are flagged as patron-dependent.

Variables

  • S(a)S(a)Sovereignty score for address a (0-1)
  • value_to_patron\text{value\_to\_patron}Value received from largest patron
  • total_value\text{total\_value}Total value received from all sources
Contract:SovereigntyIndex

Sovereignty Index Calculator

15,000 UCU
100,000 UCU
Sovereignty Score S(a)0.8500
StatusSOVEREIGN
ThresholdS(a) ≥ 0.80