# kaal:claim:7322599-012

**Claim.** Making the stake captive closes the release leak but does not rescue the instrument: the surviving capacity slope is still negative in the carry cost because the walk value of the balance cancels through the surplus — the stake never mints a hostage.

**Type.** mechanism  **Support.** argued

**Holds when.**

- misconduct punishable in place with stake seized before any release clock runs

**Source quote.**

> Captivity does not rescue the instrument: when misconduct is punishable in place with the stake seized before any release clock runs, the leak closes, but the surviving slope is −p CF , because the walk value of the balance cancels through the surplus. The stake never mints a hostage.

**From.** Wulf A. Kaal, *Refundable Stake Does Not Expand Deterrent Capacity in Long-Lived Delegation: Collateral, Premia, and Pseudonymous Markets* (2026), 4 The premium principle and the main result, page 7

**Cite as.** Wulf A. Kaal, Refundable Stake Does Not Expand Deterrent Capacity in Long-Lived Delegation: Collateral, Premia, and Pseudonymous Markets (2026). SSRN: https://ssrn.com/abstract=7322599

**Verify.** sha256 of source PDF `130ee4e65fb79a9f3a96f6df22408b40c2de76e9ec8fc2bd1c68f0f6a7104333` at https://raw.githubusercontent.com/wulfkaal/Academic-Papers/main/papers/pdf/Kaal%20-%202026%20-%20Refundable%20Stake%20Does%20Not%20Expand%20Deterrent%20Capacity%20in%20Long-Lived%20Delegation%20Collateral%2C%20Premia%2C%20and%20Pseudonymous%20Markets.pdf

**Topics.** risk-and-incentives, consensus-and-security, economics

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