balanced
plain-language theorem explainer
The definition states that a ledger L is balanced precisely when its list of recognition events satisfies the balanced_list predicate, meaning every event has equal multiplicity to its reciprocal. Researchers modeling double-entry accounting or ledger-based computation in recognition science cite this when invoking conservation properties. It is implemented as a direct one-line wrapper around the balanced_list predicate on the events field.
Claim. A ledger $L$ is balanced if and only if for every recognition event $e$ the multiplicity of $e$ in the events list of $L$ equals the multiplicity of its reciprocal.
background
The module proves that J-symmetry forces double-entry ledger structure. A Ledger is a structure consisting of a list of RecognitionEvent together with the double_entry constraint. The balanced_list predicate on a list $l$ requires that for every event $e$, the count of $e$ in $l$ equals the count of reciprocal($e$). This definition directly references the balanced_list definition from the same module.
proof idea
This is a one-line definition that applies the balanced_list predicate to the events field of the Ledger structure.
why it matters
This definition supplies the double-entry constraint used by downstream results including IsBalanced and computeBalance in LedgerAlgebra as well as ledger_forces_separation in ComputationBridge. It realizes the J-symmetry to double-entry forcing step in the Ledger Forcing module and connects to the Recognition framework's balanced structures.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.