PreservesJSymmetry
A recognition tracker preserves J symmetry exactly when its event list is balanced under reciprocal pairing. This definition is cited in ledger construction steps of the recognition forcing argument. It is implemented as the balanced_list predicate applied to the tracker's events.
claimFor a recognition tracker $T$ with event list $L$, $T$ preserves $J$-symmetry when $L$ is balanced: $forall e, count_L(e) = count_L(reciprocal(e))$.
background
The Recognition Forcing module derives recognition structures from cost foundations. A RecognitionTracker is a structure whose sole field is a list of recognition events. The balanced_list predicate from LedgerForcing states that a list is balanced when every event appears exactly as often as its reciprocal, enforcing the double-entry constraint on the ledger.
proof idea
One-line definition that applies the balanced_list predicate directly to the events field of the supplied tracker.
why it matters in Recognition Science
This supplies the symmetry hypothesis for ledger_is_minimal_recognition_tracker, which constructs a LedgerForcing.Ledger from the tracker. It advances the recognition_forcing_complete master theorem by guaranteeing balanced events. In the framework it supports J-uniqueness (T5) by maintaining the symmetry needed to reach recognition structures from cost minima.
scope and limits
- Does not assert that every recognition tracker preserves symmetry.
- Does not define the reciprocal operation or link it explicitly to the J function.
- Does not extend the balance condition to continuous or infinite collections.
- Does not compute J-cost values or rung assignments for the events.
formal statement (Lean)
185def PreservesJSymmetry (T : RecognitionTracker) : Prop :=
proof body
Definition body.
186 LedgerForcing.balanced_list T.events
187