Apologies, just to add. A crucial part of triple entry requires splitting journals between transaction and adjustment journals.

Transaction journals always involve an agreement of a transfer of value with 3rd parties. E.g. sales of goods on credit, purchase of capital asset with cash.

Adjustment journals depend on transaction journals. E.g. you cannot accrue an expense if there is no expense. These journals can be procedurally generated from transaction journals and some additional metadata on time/line items etc.

Transactions ideally will sit in some sort of shared ledger. I believe they should be private bilaterally shared ledgers as of course with financial repoprting, it's in no-ones interest for any of this data to be out in the public domain before an audit opinion is issued.

Adjustments just sit in a local ledger, e.g. ERP system / Xero. There is no need for anything fancy here apart from an optional engine which takes triple signed transactions and produces adjustments to keep accounts aligned with whatever framework is used, IFRS/ UK GAAP, etc. One can assert that no adjustments can be posted unless a triple signed entry is present.

We can have transactional ledgers for anything; bitcoin, invoices, share issuances, cash. In a loose sense a bank is a trusted third party which provides a rudimentary triple entry for cash at bank -> Auditors obtain a bank confirmation at year-end to prove cash balances. They also provide a transaction by transaction breakdown - if we net all these together we end up with the final balance (similar to bitcoin). Clearly the medium/tech differes greatly though.

The magic with triple entries is that the documentation IS the transaction. This is the case for bitcoin and the invoicing system im in the process of building.

Token based crypto systems do not function well for maintaining accounting journals, e.g. ethereum, bitcoin, and so on as one can create and destroy value at will (e.g. accruals). instead we need a system which is more flexible and does not rely on some sort of token to represent value. The Eris stack is the closest I've seen to this.

Apologies for mistakes/non-sensicalness. Have a broken arm and typing with one hand!