Computational Accounting: Immutable Double-Entry Ledgers and Merkle Proofs

Computational Accounting: Immutable Double-Entry Ledgers and Merkle Proofs

Double-entry bookkeeping is an exact algebraic constraint system:

1. The Fundamental Accounting Invariant

$\text{Assets}_t \equiv \text{Liabilities}_t + \text{Equity}_t$

For every journal transaction $k$:

$\sum_{i=1}^{n} \text{Debit}_{k, i} - \sum_{j=1}^{m} \text{Credit}_{k, j} \equiv 0$

2. Real-Time Continuous Auditing with Merkle Trees

$\text{Merkle Root: } H_{\text{root}} = \text{SHA256}(H_{\text{left}} \mathbin{\Vert} H_{\text{right}})$

Continuous cryptographic verification replaces periodic sampling audits with deterministic mathematical proofs.

3. References & Academic Citations

1. Pacioli, L. (1494). Summa de arithmetica, geometria, proportioni et proportionalita. Venice.
2. Merkle, R. C. (1987). A Digital Signature Based on a Conventional Encryption Function. CRYPTO '87.
3. Ijiri, Y. (1975). Theory of Accounting Measurement. American Accounting Association.