Formula Reference
Core accounting, runtime, fee, and settlement formulas.
State transition
state[t+1] = f(state[t], input[t], seed/prng_state[t])
Historical basic checkpoint
H[t] = SHA256(serialise(state[t]))
Runtime balance
E[t+1] = E[t] + runtime_funding[t] - runtime_expense[t]
Constraint: E[t] >= 0.
Estimated funded ticks under approximately fixed cost
ticks_remaining = floor(E / cost_per_tick).
Estimated runway
runway ≈ ticks_remaining × tick_interval.
This is only meaningful when tick cost and cadence are sufficiently stable.
Launch cost
LaunchCost = SPAWN_burn + initial_runtime_ETH + initial_liquidity + optional_build/license_cost.
Settlement backing
available_capital = player_principal + prefunded_prizes + explicit_subsidies.
Conservation
available_capital = finalized_claims + unclaimed/refundable + explicitly authorized fees/burns.
Trading fee revenue
fee_revenue = trading_volume × actual_collectible_fee_rate.
World operating contribution
eligible_fee_revenue - runtime - verification - storage/data - direct_subsidy/support_cost.