recognition_before_predicate
Recognition Science places the recognition interface before the single-valued predicate in its pre-temporal forcing chain. Researchers tracing dependency order from distinction onward cite this result to fix the sequence prior to time ticks. The proof is a one-line decision that evaluates the rank comparison directly via the decidable instance on natural numbers.
claimIn the pre-temporal forcing order, the recognition interface precedes the single-valued predicate: $rank(recognitionInterface) < rank(singleValuedPredicate)$.
background
The module records a forcing order among dependency stages that exists before physical time is introduced. Stage is the inductive type whose constructors are distinction, recognitionInterface, singleValuedPredicate, symmetricComparison, compositionConsistency, rcl, jCost, arithmeticObject, and timeTick. Before is the relation defined by rank a < rank b, equipped with a decidable instance that reduces to Nat.lt. The local setting distinguishes recognition-light (the primitive act of distinction) from physical light (the null-cone carrier that appears only after J-cost and spacetime).
proof idea
One-line wrapper that applies the decidable instance for Before, which compares the ranks of the two Stage constructors using the natural-number ordering.
why it matters in Recognition Science
The declaration fixes an early link in the pre-temporal forcing chain that runs from distinction through recognitionInterface to singleValuedPredicate and onward to rcl and jCost. It supports the overall ordering that must be in place before timeTick and spacetime can be forced. No downstream theorems are recorded yet, but the result belongs to the sequence that precedes the Recognition Composition Law and the eight-tick octave.
scope and limits
- Does not assign explicit numerical ranks to any Stage constructor.
- Does not prove transitivity or totality of the order.
- Does not connect the order to physical constants or the J-cost function.
- Does not address post-temporal structures such as spacetime.
formal statement (Lean)
73theorem recognition_before_predicate :
74 Before Stage.recognitionInterface Stage.singleValuedPredicate := by
proof body
Decided by rfl or decide.
75 decide
76