distinction_first
distinction_first asserts that the distinction stage precedes every later stage in the pre-temporal forcing order. Researchers tracing the dependency chain from recognition to time would cite it as the base case. The argument reduces to exhaustive case analysis on the stage constructor followed by simplification of the rank comparison.
claimLet $s$ be any stage in the pre-temporal forcing chain. If $s$ is not the distinction stage, then the rank of distinction is strictly less than the rank of $s$.
background
The module records the dependency order that exists before time in Recognition Science. Physical time is itself a forced object, so the ordering here is a forcing order: stage A precedes B when B requires A as prior structure. The central distinction is between recognition-light (the primitive revealing act of distinction) and physical light (the null-cone downstream of J-cost and ticks).
proof idea
One-line wrapper that applies case analysis on the stage constructor s and then simplifies the inequality using the definitions of Before and rank.
why it matters in Recognition Science
This theorem initiates the sequence of order theorems in PreTemporalForcingOrder. It anchors the forcing chain by placing distinction (rank 0) as the earliest stage, prior to recognitionInterface, singleValuedPredicate, and later stages up to timeTick. It supports the broader claim that physical time and spacetime emerge only after these pre-temporal dependencies.
scope and limits
- Does not define the physical interpretation of distinction beyond its rank zero.
- Does not address stages after timeTick or their relation to spacetime.
- Does not connect the order to J-cost, RCL, or numerical constants.
- Does not prove transitivity or other order properties beyond this base fact.
formal statement (Lean)
69theorem distinction_first (s : Stage) (h : s ≠ Stage.distinction) :
70 Before Stage.distinction s := by
proof body
One-line wrapper that applies cases.
71 cases s <;> simp [Before, rank] at h ⊢
72