The Deadly Race: When Graceful Recovery Makes Coercion-Resistant Custody Worse Than Useless

This paper contributes a design bar for coercion-resistant custody and a construction that meets
it, motivated by a sharp negative result: custody designs that lack such a bar can be worse than
useless — worse than merely a false sense of security, which would be bad enough — actively
endangering the holder they claim to protect.

Physical-coercion ("wrench") attacks defeat custody schemes that key management and cryptography
treat as out of scope. We give a formal model of coercion against a secret-holder and prove that a
large class of "graceful" recovery designs — those that leave a device seizure holding a
feasible-but-slower path to the secret — are strictly worse than useless: they manufacture a
material incentive to assassinate the victim. We name this the Deadly Race, derive it from a single
impossibility (one cannot prove one has forgotten), and distill a design bar — the No-Gray-Area
Criterion — that any coercion-resistant scheme must clear.

We then present a construction — the Time-Gated Perceptual Oracle (TGPO) — that clears the bar for
the Bitcoin self-custody setting while keeping custody individual, and we locate a shipping
alternative — timelock-rescue vaults — precisely: it clears the same bar by the other available
route, at the cost of a trusted third party. We also classify the most widely shipped consumer
countermeasure — the self-destruct ("wallet-erase") PIN — and find it clears nothing: the vendor's
own documentation presupposes a surviving backup, so the erasure removes the device path while
leaving intact the path that runs through the holder. The framework fixes a bar; it does not claim
TGPO is the unique construction that clears it.

Manuscript in preparation; not peer reviewed.