add_event_balanced
plain-language theorem explainer
Adding a recognition event together with its reciprocal to a ledger preserves the double-entry balance property. Workers on the ledger forcing principle cite this result when constructing ledgers from J-symmetric paired events. The proof is a one-line term extraction that selects the double_entry field of the ledger returned by the add_event construction.
Claim. Let $L$ be a ledger and let $e$ be a recognition event. Then the ledger obtained by prepending $e$ and its reciprocal to the event list of $L$ satisfies the balanced predicate.
background
The module proves that J-symmetry forces double-entry ledger structure. A Ledger is a structure consisting of a list of RecognitionEvents equipped with a proof that the list satisfies the balanced_list predicate. A RecognitionEvent is a structure carrying source and target agents together with a positive real ratio. The upstream add_event definition constructs a new ledger by prepending both an event and its reciprocal to the existing list, while the balanced predicate simply checks that the event list meets the double-entry constraint.
proof idea
The proof is a one-line term that extracts the double_entry field from the ledger value produced by add_event.
why it matters
This result closes the construction step inside the ledger forcing principle, confirming that paired events maintain balance as required once J-symmetry is in place. It directly supports the module outline step from symmetry to double-entry bookkeeping. The theorem sits inside the forcing chain that begins with J-uniqueness and leads to conservation via log-sum cancellation.
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papers checked against this theorem (showing 1 of 1)
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