Case Analysis

Normal Scenario

• Assuming $T=0.5$,

1. If $r = 0.5$ (VRT Reserve is excessive)

   • $f(r) = 0.6$

   • $P_{VRT} = P_{ex} \times 0.6$

   • If VRT is traded at $10 on the exchange, the value of VRT within the Reserve is calculated as $6.

   • An RP holder with $300 worth of RP can convert RP → VRT to receive 50 VRT, which can then be sold on the exchange for $500 (arbitrage opportunity).

   • This reduces the quantity of VRT in the Reserve, moving $r$ closer to 0.

2. If $r = -0.5$ (VRT Reserve is insufficient)

   • $f(r) = 1.667$

   • $P_{VRT} = P_{ex} \times 1.667$

   • If VRT is traded at $10 on the exchange, the value of VRT within the Reserve is calculated as $16.67.

   • A VRT holder with $300 worth of VRT (30 tokens) can purchase from the exchange and convert VRT → RP to obtain RP worth $500.1 (arbitrage opportunity).

   • This increases the quantity of VRT in the Reserve, moving $r$ closer to 0.

Worst Case Scenario

• Assuming $T=0.5$,

  • Worst Case

    1. If VRT cannot fully meet the demand for RP ($r<0$)

       • $r=-0.9$ (Scenario in which 90% of the Reserve’s VRT is extracted through an exploit)

         • $(r,f(r)) = (-0.9, 11.270)$

         • $\int_{-0.9}^{0} f(r)\, dr = 2.198$

         • Initial Reserve VRT = 300,000,000, assuming 1 VRT=$1

           • Scenario would require a temporary inflow of $659.4M worth of RP → VRT.

       • $r=-0.99$ (Scenario in which 99% of the Reserve’s VRT is extracted while maintaining T)

         • $(r,f(r)) = (-0.99, 120.486)$

         • $\int_{-0.99}^{0} f(r)\, dr = 5.439$

         • Initial Reserve VRT = 300,000,000, assuming 1 VRT=$1

           • Scenario would require a temporary inflow of $1.631B worth of RP → VRT.

       • However, the amount of RP an individual can hold per partner is limited. For initial service stability, Vacas plans to implement daily limits on RP → VRT swaps to mitigate such risks.

    2. If demand for VRT → RP is excessively high ($r>0$)

       • Centralized RP has inherently low transaction value, making it difficult to exploit for profit through vulnerabilities.

       • Moreover, when T≥0.5, an attacker would need to monopolize nearly all circulating VRT in order to mount such an attack—an impractical requirement given supply constraints.

The VRT ↔ RP exchange mechanism resembles that of a traditional AMM model but has a critical distinction: due to the centralized nature and low transaction value of RP, conventional DEX-style exploits are impractical. Furthermore, RP cannot be liquidated or exchanged outside its intended context, greatly reducing risks associated with liquidity-based attacks. These characteristics make the VRT–RP exchange system inherently more stable and resistant to vulnerabilities compared to traditional decentralized exchanges.