Triple-entry accounting is the name of two unrelated proposals to extend double-entry bookkeeping, the system in which every transaction is recorded twice, as a debit in one account and a matching credit in another, so that the books balance and an omitted entry shows up. The accounting theorist Yuji Ijiri's version, from 1982, adds a third dimension to what a firm's books measure. The version developed by the accountant Todd Boyle and the financial cryptographer Ian Grigg between about 2000 and 2005 adds a third party to who holds the record: one digitally signed receipt, kept identically by the payer, the payee and the issuer between them.

The second version is the one blockchains are said to realise. Grigg made that case for Bitcoin in 2011. Juan Ignacio Ibañez and his co-authors, who have traced the idea's history, accept that Bitcoin has the triple-entry structure and dispute that it is accounting at all.

Ijiri: a third dimension of measurement

Yuji Ijiri, professor of accounting and economics at Carnegie Mellon University, spent more than 25 years on one question: whether double-entry bookkeeping, which the mathematician Arthur Cayley had called "absolutely perfect", could be extended by logic rather than by adding an arbitrary third column. His answer, in the American Accounting Association monograph Triple-Entry Bookkeeping and Income Momentum (1982), starts from what double entry added to single entry. Single-entry books recorded stocks, the assets and liabilities that make up a firm's wealth. Double entry added flows, the revenues and expenses that explain why wealth changed. A third entry would explain why the flows changed.

A Framework for Triple-Entry Bookkeeping (The Accounting Review, 1986) builds the system. It keeps three layers of accounts, each in its own unit: wealth, in dollars; momentum, the rate at which the firm earns, in dollars per period; and force, the factors that change that rate, in dollars per period per period. Each layer is the rate of change of the one before, and the identity debit = credit becomes debit = credit = trebit. Ijiri's aim was managerial: to direct attention to the causes of a change in earnings, below the level of the wealth and income that double entry reports. He returned to the framework at book length in Momentum Accounting and Triple-Entry Bookkeeping (1989).

The system found few users. Eric Melse's Accounting in three dimensions: a case for momentum (Balance Sheet, 2004) noted that triple-entry and momentum accounting were seldom applied, and argued for them on the grounds that managers and outside stakeholders needed more forward-looking information about a company's trends.

Boyle and Grigg: a third party to the record

The second idea came out of digital payments. Todd Boyle, an accountant building web-based ledgers in Seattle, described a shared transaction repository around 2000. When Alice posts a transaction naming Bob, her software stores it and also submits it to a shared service, which forwards it to Bob, so the two keep pointers to one shared record instead of two private ones. Boyle's three entries were the shared record and a private stub for each party.

Ian Grigg's paper Triple Entry Accounting (Systemics, 2005) reached the same structure from payment systems he and Gary Howland had built since the mid-1990s. Alice signs an instruction to pay Bob; Ivan, the issuer who runs the payment server, packages it into a receipt and signs that too. The receipt carries the whole authorisation, and all three parties keep an identical copy. Grigg's principle is that "the Receipt is the Transaction": the signed receipt, not the two entries each party makes in its own books, is the authoritative record. Each party still derives double-entry books from its receipts for the convenience of cross-checking them locally, which gives three entries in each of three roles.

Grigg's case was about fraud and governance. A digital signature gives a receipt the force of evidence, and because payer, payee and issuer each hold a copy, none of them can alter or drop a transaction without the others' records showing it. He argued that the mutual-fund trading scandal would have been impossible with such records, that Barings would have survived, and that Enron's swaps would have been easier to follow. In a 2016 interview on the Epicenter podcast he put the economic claim in Ronald Coase's terms. Double entry made accounts reliable inside a firm and let firms grow beyond the size at which an owner could keep track of the money; triple entry would do the same between firms, by removing the reconciliation of disagreeing records that makes trade across a firm's boundary costly, and he expected firms to shrink as a result (see transaction costs and property rights).

Grigg did not coin the term in this sense. His paper records that a draft listed Boyle as co-author until Boyle withdrew "due to wider differences between the views", and in the Epicenter interview Grigg said Boyle had invented the term and understood the concept five years before him. Ijiri played no part in either. Ibañez, Chris Bayer, Paolo Tasca and Jiahua Xu, in REA, Triple-Entry Accounting and Blockchain (Journal of Risk and Financial Management, 2023), correct the popular account in which Grigg revived Ijiri's 1982 idea: Ijiri's momentum accounting "bore almost no relationship" with Grigg's. Boyle's line of descent runs instead through the Resource-Event-Agent (REA) model, which the accounting professor William McCarthy proposed in 1982 for accounting in a shared database.

The Ricardian contract

Grigg's receipts identify what is being paid by the hash of a Ricardian contract, a document form he and Howland built into their Ricardo payment system, in use since 1996, and described in The Ricardian Contract (First IEEE International Workshop on Electronic Contracting, 2004). The problem it solves is describing an issued instrument: a ticker symbol or a currency code says too little about what a holder is owed. Grigg's answer is that "whereas other issues have contracts, our issues are contracts". A Ricardian contract is one document, signed by the issuer, that offers holders a right the issuer manages. It reads to a person like a paper contract and parses for a program like a database record, and its cryptographic hash is the instrument's identifier.

Every signed record in the system carries that hash, so an issuer cannot change the terms its holders accepted without producing a new hash, and with it a new instrument. Grigg's name for what this blocks is frog-boiling, the gradual revision of a form contract by the stronger party; the terms of service discussed under virtual economies reserve that power to the issuer. In the Epicenter interview Grigg described the Ricardian contract as the shipping container of financial cryptography: lawyers write the prose, it reduces to a hash, and engineers build the accounting around the hash. He also argued there that a smart contract needs the prose as well as the code, because some events cannot be foreseen in code. His example was The DAO, whose response to the 2016 attack on it could not have been written in advance (see history of DAOs).

Is a blockchain triple-entry?

In June 2011 Grigg asked on his blog whether Bitcoin is a triple-entry system, and wrote that Bitcoin "may have shown the first successful widescale test of triple entry". A Bitcoin payment is signed by the payer, as in his design, but no issuer countersigns it. Instead, in Grigg's words, Bitcoin "achieves the issuer part by creating a distributed and published database over clients that conspire to record the transactions reliably". He noted that publishing the repository to keep it honest had first been explored in Boyle's design.

The account later repeated in accounting papers, that Bitcoin made triple entry workable by replacing the trusted issuer, is disputed on two counts. On history, Ibañez and his co-authors argue that Bitcoin was not an outside invention that happened to enable the idea. It probably drew on the shared repository Boyle had discussed on the same 1990s cryptography mailing lists as the people the Bitcoin whitepaper cites, although with Satoshi Nakamoto unidentified that evidence is limited. On terminology, their Triple-entry Accounting, Blockchain and Next of Kin separates bookkeeping, the sequential record of transactions in a journal, from accounting, which classifies those records into ledgers. By that test Bitcoin is a triple-entry bookkeeping system: its signed entries form a shared journal, but it has no accounting layer, so it is neither triple-entry accounting nor, strictly, a distributed ledger.

DAO treasuries show both halves of that distinction. A transfer from a treasury is a transaction on a public chain, so the DAO and the recipient read one record of it rather than two to be reconciled (see DAO treasury management). The books around the transfer are not on the chain: invoices, expense categories and statutory accounts are kept off it, in tools such as Request Finance that export to conventional accounting software.

How Caper approaches this

A caper's treasury is a vault its members control only by proposal. Trade and proposal fees flow into it as those transactions happen, and it pays out only through a proposal the members have passed, with no signer set standing between the vote and the payment. Members read the treasury's position from the same ledger that moved its funds.

References

1. Yuji Ijiri (1982). Triple-Entry Bookkeeping and Income Momentum. Studies in Accounting Research No. 18. American Accounting Association.
2. Yuji Ijiri (1986). A Framework for Triple-Entry Bookkeeping. The Accounting Review 61(4): 745–759.
3. Yuji Ijiri (1989). Momentum Accounting and Triple-Entry Bookkeeping: Exploring the Dynamic Structure of Accounting Measurements. Studies in Accounting Research No. 31. American Accounting Association.
4. Eric Melse (2004). Accounting in three dimensions: a case for momentum. Balance Sheet 12(1): 31–36.
5. Ian Grigg (2004). The Ricardian Contract. Proceedings of the First IEEE International Workshop on Electronic Contracting, 25–31.
6. Ian Grigg (2005). Triple Entry Accounting. Systemics, Inc. Republished in Journal of Risk and Financial Management 17(2): 76 (2024).
7. Ian Grigg (2011). Is BitCoin a triple entry system? Financial Cryptography (blog).
8. Epicenter (2016). Ricardian Contracts and Digital Assets Prehistory. Episode 151, interview with Ian Grigg by Brian Crain and Meher Roy.
9. Juan Ignacio Ibañez, Chris N. Bayer, Paolo Tasca and Jiahua Xu (2023). REA, Triple-Entry Accounting and Blockchain: Converging Paths to Shared Ledger Systems. Journal of Risk and Financial Management 16(9): 382.
10. Juan Ignacio Ibañez, Chris N. Bayer, Paolo Tasca and Jiahua Xu (2025). Triple-entry Accounting, Blockchain and Next of Kin: Towards a Standardisation of Ledger Terminology. In Digital Assets: Pricing, Allocation and Regulation, 198–226. First circulated as arXiv:2101.02632 (2021).