Pacioli

The constraint behind double-entry bookkeeping is a group completion of a monoid.

In ordinary language: commerce is made of actions that only move forward — goods ship, cash settles, obligations arise. Double-entry gives those forward actions an opposite orientation. What one party records as a pull, the other records as a push.

That symmetry creates a conservation law. In a valid transaction, both participants move forward, but across the shared boundary nothing is created or destroyed. Every local change has a counterparty orientation, and the event balances.

To see more: https://aac.sh/specs/rfc/

The core is generating a valid transaction by both parties committing to an exact inverse of the other's transaction to facilitate the transfer: https://aac.sh/specs/applications/bcc-1/

Specifically, we take advantage of the pederson commitment's homomorphic scheme to add together the entry from both ledgers and check if it nets to zero (balanced).