The Bounded-Dilution Proof

What is the worst case the GCSR can produce, and is it bounded?

43.75% deficit in the joint failure scenario. Bounded. Convergent.

Under the joint failure scenario where (a) the price of SZK goes to zero, (b) every other piece of exogenous collateral simultaneously loses 50% of its value, and (c) the dilution mechanism runs to its bounded limit at the 15% cap, the maximum deficit relative to outstanding szUSD supply is 43.75%.

Bounded. Convergent. Survivable. Equivalently, 56.25% recovery on szUSD in the worst joint scenario.

In summary: the protocol's loss-absorption capacity is the sum of the exogenous collateral surplus above 100%, the bonded szBOND supply, and the dilutive capacity of SZK up to the cap. Each term has a worst-case lower bound. The sum of those lower bounds, expressed as a fraction of outstanding szUSD, is 1 − 0.5625 = 43.75% deficit.

The proof depends on assumptions:

• Exogenous collateral does not lose more than 50% of its value simultaneously.
• szBOND holders absorb in priority before szUSD.
• The resolution waterfall executes in code without governance intervention.

The full long-form proof — including the per-term derivations and the scenario analysis outside the stated assumptions — is published from the canonical version of this chapter on sultanismyname.com and from the GitHub repository.

• § 4.2 · The 15% Cap — without it, the proof is unbounded
• § 4.3 · The 130% Floor — the other half of the worst-case-bound construction
• § 4.5 · Phased Launch — how the protocol stages exposure to this worst case