This document serves as the formal mathematical guarantee for the Stream-Scholar protocol's absolute solvency, as required by Institutional Issue #200.

The contract guarantees that at any given ledger sequence, the following fixed-point math invariant strictly holds:

Total_Deposited == Total_Streamed + Total_Remaining + Protocol_Fees

• Precision Limits: All values utilize a highly controlled 1-stroop base precision. Fixed-point fractional rounding (e.g. 10% taxes on a 1 stroop withdrawal) operates via the mathematical DustSweeper module, ensuring that microscopic fractions are natively swept to the protocol treasury rather than causing mathematical leakage or an underflow state.
• Non-Negative Supply: Streams and claims are strictly bounded using saturating_sub, preventing any state where internal timeline calculations regress (Total_Remaining < 0).
• No Thin-Air Value: Protocol deductions are explicitly derived from fractional deductibles of Total_Remaining and directly credited to global variables, maintaining the zero-sum integrity of the architecture.

The formal invariant is strictly verified via Soroban SDK fuzz testing (test_tvl_invariant_fuzz and test_time_drift_fuzz), covering over thousands of randomized high-frequency actions simulating extreme network loads, malicious micro-match attackers, and arbitrary epoch time-drifts.

Under no mathematical circumstances can this equation be bypassed or violated.