photonEM_before_embodiedObserver
plain-language theorem explainer
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.
Claim. In 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
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.
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