recognition_light_before_time
Recognition-light precedes the time tick in the pre-temporal forcing order. Researchers deriving time from prior structure in Recognition Science cite this to fix the dependency hierarchy before spacetime. The proof is a one-line decision that evaluates the rank comparison via the decidable instance on natural numbers.
claimThe forcing priority satisfies $rank(RecognitionLight) < rank(timeTick)$, where RecognitionLight is the recognition interface stage and timeTick is the arithmetic time stage.
background
The module records the forcing order among dependency stages before physical time. Stage is the inductive type with constructors distinction, recognitionInterface, singleValuedPredicate, symmetricComparison, compositionConsistency, rcl, jCost, arithmeticObject, timeTick. Before (a b) is the proposition rank a < rank b, equipped with a Decidable instance via Nat.decLt.
proof idea
One-line wrapper that applies the decidable instance for Before. The decide tactic evaluates the strict inequality on the natural-number ranks of RecognitionLight and timeTick.
why it matters in Recognition Science
The result supplies one field of the PreTemporalOrderCert record. It anchors the pre-temporal segment of the chain that later forces timeTick, J-cost, and spacetime, separating the primitive recognition act from downstream physical light.
scope and limits
- Does not claim chronological precedence, only forcing dependency.
- Does not identify recognition-light with electromagnetic radiation.
- Does not compute explicit numerical ranks, only their order.
- Does not extend to post-time physical laws.
formal statement (Lean)
126theorem recognition_light_before_time :
127 Before RecognitionLight Stage.timeTick := by
proof body
Decided by rfl or decide.
128 decide
129