DiscreteConservativeSystem
DiscreteConservativeSystem encodes a countable state space equipped with a conservation constraint. Researchers auditing the Recognition Science ledger uniqueness argument cite this structure as the minimal starting point before deriving the forced parameters of the RS ledger. The declaration is a bare structure definition with three fields and no proof obligations.
claimA discrete conservative system consists of a countable type $S$ together with a conservation law.
background
In the Meta.LedgerUniqueness module the structure captures the minimal assumptions needed to address the objection that discreteness alone permits many ledgers. The fields are a state space of arbitrary type, an instance of Countable asserting that the space is enumerable, and a placeholder proposition hasConservation standing for any conservation law. This sits downstream of the forcing chain steps that already fix the J-cost function, the self-similar fixed point phi, the eight-tick octave, and three-dimensional linking.
proof idea
The declaration is a structure definition that introduces the type with the three listed fields; no tactics or lemmas are applied.
why it matters in Recognition Science
The structure supplies the hypothesis for the downstream theorem ledger_structure_unique, which concludes that any such system recovers dimension 3, ratio phi, and cycle length 8. It therefore closes Gap 9 by showing that the specific choices T5 through T8 remain forced once a generic discrete conservative system is assumed. The placeholder conservation law leaves open the question of whether a stronger, non-trivial conservation axiom would alter the uniqueness conclusion.
scope and limits
- Does not encode explicit transition rules or dynamics on the state space.
- Does not specify the concrete form of the conservation law beyond the placeholder True.
- Does not prove equivalence to the RS ledger; that step occurs in the downstream theorem.
- Does not reference the J-function, phi-ladder, or Gray-code traversal directly.
formal statement (Lean)
189structure DiscreteConservativeSystem where
190 stateSpace : Type*
191 countable : Countable stateSpace
192 hasConservation : True -- Placeholder for conservation law
193
194/-- Any discrete conservative system is equivalent to the RS Ledger. -/