ledger_is_minimal_recognition_tracker
plain-language theorem explainer
Any recognition tracker whose events satisfy the balanced list condition yields a ledger whose recorded events match the tracker exactly. Researchers tracing the cost-to-recognition forcing chain would cite this to establish minimality of the ledger representation. The proof is a direct term construction that assembles the ledger record from the tracker's events and the symmetry hypothesis then closes equality by reflexivity.
Claim. Let $T$ be a recognition tracker and suppose its list of recognition events is balanced. Then there exists a ledger $L$ such that the events of $L$ equal the events of $T$.
background
The RecognitionForcing module develops the forcing of recognition structures from the cost foundation. A recognition tracker is the structure whose sole field is a list of recognition events taken from the LedgerForcing layer. The J-symmetry preservation hypothesis is defined to be exactly the balanced_list predicate on that event list.
proof idea
The proof is a one-line term wrapper. It constructs a ledger record whose events field copies the tracker's events and whose double_entry field is supplied by the symmetry hypothesis, then discharges the required equality by reflexivity.
why it matters
The result supplies the final local bridge inside the recognition forcing development, showing that trackers obeying the symmetry condition are minimal ledgers. It contributes directly to the master theorem on recognition forcing complete that is documented on the RecognitionTracker structure. In the larger framework it closes the passage from cost structures to observable recognition without extra hypotheses.
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