photonEM_before_embodiedObserver
The pre-temporal forcing order places the electromagnetic photon stage strictly before the embodied observer stage. Researchers tracing the emergence of physical light from recognition primitives would cite this link when sequencing stages from distinction through J-cost to spacetime. The proof is a one-line decision procedure that compares the ranks assigned to these two stages via the decidable Before relation.
claimIn the pre-temporal forcing order, the electromagnetic photon stage precedes the embodied observer stage: $rank(photonEM) < rank(embodiedObserver)$, where $Before(a,b)$ holds iff $rank(a) < rank(b)$ for stages in the dependency chain.
background
The module records a forcing order among stages that must precede the emergence of physical time. Stage is the inductive type enumerating these dependencies, starting from distinction and recognitionInterface and continuing through single-valued predicates, symmetric comparison, composition consistency, the recognition composition law, J-cost, arithmetic objects, and time ticks. Before a b is defined as rank a < rank b and carries a decidable instance via natural-number comparison.
proof idea
The proof is a one-line wrapper that applies the decidable instance for Before. The decide tactic resolves the rank inequality between photonEM and embodiedObserver directly from the Nat.decLt instance attached to the definition.
why it matters in Recognition Science
This theorem supplies one concrete link in the pre-temporal chain, confirming that physical light (the null-cone photon) appears after J-cost and ticks but before any embodied observer. It reinforces the module's distinction between pre-temporal recognition-light and downstream physical light. The declaration sits among sibling order theorems that culminate in time_before_spacetime and supports the overall claim that time itself is a forced object rather than primitive.
scope and limits
- Does not assign explicit numerical ranks to photonEM or embodiedObserver.
- Does not derive the stages from more primitive axioms.
- Does not claim a chronological order in physical time.
- Does not address the transition from recognition-light to physical light.
formal statement (Lean)
113theorem photonEM_before_embodiedObserver :
114 Before Stage.photonEM Stage.embodiedObserver := by
proof body
Decided by rfl or decide.
115 decide
116
117/-! ## Light: two senses -/
118
119/-- Recognition-light: the revealing act of an interface making distinction
120available. This is pre-temporal. -/