add_event_balanced
Adding a recognition event together with its reciprocal to a ledger preserves the double-entry balance property. Researchers deriving conservation from J-symmetry in Recognition Science cite this step to maintain ledger integrity under event insertion. The proof is a one-line term that projects the double_entry field of the ledger returned by the add_event construction.
claimLet $L$ be a collection of recognition events equipped with a double-entry constraint and let $e$ be a recognition event with positive ratio. The collection formed by adjoining $e$ and its reciprocal also satisfies the double-entry constraint.
background
The module shows that J-symmetry forces double-entry ledger structure. A ledger is a list of recognition events together with a proof that the list obeys the balanced_list predicate. A recognition event records a source agent, target agent, and positive real ratio. The upstream add_event definition prepends both $e$ and its reciprocal to the event list and invokes a preservation lemma for balanced_list. The balanced predicate on a ledger is defined exactly as balanced_list applied to its events list.
proof idea
The proof is a term-mode one-liner that selects the double_entry field of the ledger value constructed by add_event. No tactics are used; the field access directly supplies the required balanced_list witness.
why it matters in Recognition Science
This result completes the third step of the Ledger Forcing Principle: paired events imply double-entry bookkeeping and therefore log-sum conservation. It sits inside the chain from T5 J-uniqueness through symmetry to the eight-tick octave and D=3. The declaration supplies the concrete bookkeeping invariant needed for later cost and observer forcing arguments.
scope and limits
- Does not establish balance for event lists modified without reciprocal pairing.
- Does not derive J-symmetry or the existence of recognition events.
- Does not compute numerical costs or ratios for the added events.
- Does not address ledgers whose events fail the ratio_pos hypothesis.
formal statement (Lean)
330theorem add_event_balanced (L : Ledger) (e : RecognitionEvent) :
331 balanced (add_event L e) := (add_event L e).double_entry
proof body
Term-mode proof.
332
333/-! ## Ledger Forcing Principle -/
334
335/-- **LEDGER FORCING PRINCIPLE**
336
337The cost landscape forces ledger structure:
338
3391. d'Alembert → J unique → J(x) = J(1/x) (symmetry)
3402. Symmetry → recognition events come in pairs
3413. Paired events → double-entry bookkeeping required
3424. Double-entry → conservation (log-sums cancel) -/