Proof of stake?

 I suppose that if a group of agents and miners agreed to a contract, and the contract was stable between them, then they and they alone have to agree and record this on the ledger.  ETH uses a public distributed block chain, it catches double spenders quickly.  Bu that function is incorporated in the contract.   All stbl point in the clause exits require knowledge of the ledger state.  So provability would have caught that and required a call to an external trusted miner.

So, the smart card uses the ETH block chain ledger, and also uses local proof of stake. Proof of stake is simply a contract partition, assumed to be closed under the contract.

An aside here. If the kernel is rusted then the contract could specify a spectre kernel will handle the active ledger with a hot wallet.  Participant dump their risk cash in the kernel wallet, then run the contract. The kernel code is considered a trusted miner, it can be verified just like any solidify code.

Escro w officers often want checks written to the escrow bank.  If the kernel is participating, then it already has the necessary currency regimes loaded. Step one, all participant dump all assets into the kernel account, in the instruction cache.  Write the provable contract to have the kernel be paymaster for all bets, never use external ledgers at all.  Participants, all kernels them selves, can receive cash payouts and decide for themselves about ledgers.