This paper introduces triple entry accounting (TEA), a new method of bookkeeping that combines financial cryptography innovations like the signed receipt with standard double entry bookkeeping. TEA creates a system where each transaction is recorded three times, once for each party involved, ensuring reliability and stronger governance. This approach challenges traditional double entry bookkeeping by expanding accounting beyond internal firms to interactions between firms. When applied to digital cash and assets, TEA reduces costs by providing reliable data and enables stronger governance, positively impacting corporate and public accounting. By turning the opinions of firm owners into facts agreed between firms, TEA creates a bulletproof accounting layer, supporting both aggressive and adversarial users, as seen in the Bitcoin system. TEA is based on the concept of a digitally signed receipt, which provides a reliable record of transactions. This method addresses the limitations of single entry bookkeeping, which is prone to errors and fraud. TEA introduces a system where each transaction is recorded three times, ensuring accuracy and transparency. The paper discusses the history of accounting, the evolution of double entry bookkeeping, and the role of digital signatures in creating reliable records. It also explores the implementation of TEA, the requirements for a system to support TEA, and the implications of TEA for corporate and public accounting. The paper highlights the importance of TEA in addressing the limitations of traditional accounting methods, particularly in the context of digital cash and digital assets. It argues that TEA provides a more robust and transparent system for accounting, which can be applied to both corporate and public sectors. The paper also discusses the challenges of implementing TEA, including the need for strong pseudonymity, entry signing, message passing, and integrated payment systems. It concludes that TEA represents an advance in accounting, offering a more reliable and transparent system for recording transactions.This paper introduces triple entry accounting (TEA), a new method of bookkeeping that combines financial cryptography innovations like the signed receipt with standard double entry bookkeeping. TEA creates a system where each transaction is recorded three times, once for each party involved, ensuring reliability and stronger governance. This approach challenges traditional double entry bookkeeping by expanding accounting beyond internal firms to interactions between firms. When applied to digital cash and assets, TEA reduces costs by providing reliable data and enables stronger governance, positively impacting corporate and public accounting. By turning the opinions of firm owners into facts agreed between firms, TEA creates a bulletproof accounting layer, supporting both aggressive and adversarial users, as seen in the Bitcoin system. TEA is based on the concept of a digitally signed receipt, which provides a reliable record of transactions. This method addresses the limitations of single entry bookkeeping, which is prone to errors and fraud. TEA introduces a system where each transaction is recorded three times, ensuring accuracy and transparency. The paper discusses the history of accounting, the evolution of double entry bookkeeping, and the role of digital signatures in creating reliable records. It also explores the implementation of TEA, the requirements for a system to support TEA, and the implications of TEA for corporate and public accounting. The paper highlights the importance of TEA in addressing the limitations of traditional accounting methods, particularly in the context of digital cash and digital assets. It argues that TEA provides a more robust and transparent system for accounting, which can be applied to both corporate and public sectors. The paper also discusses the challenges of implementing TEA, including the need for strong pseudonymity, entry signing, message passing, and integrated payment systems. It concludes that TEA represents an advance in accounting, offering a more reliable and transparent system for recording transactions.