physical_light_not_first
plain-language theorem explainer
Physical light cannot precede every other stage in the pre-temporal forcing order. Foundation researchers cite this result to separate recognition-light (primitive distinction) from electromagnetic propagation, which requires prior spacetime structure. The proof assumes the universal claim, instantiates it at the distinction stage via decidable inequality, and normalizes the rank comparison to reach an immediate numerical contradiction.
Claim. It is not the case that for every stage $s$, if $s$ differs from the physical light stage then the physical light stage precedes $s$ in the forcing order defined by rank comparison.
background
The module defines a pre-temporal forcing order among dependency stages that must be in place before time or spacetime can appear. Stage is the inductive type listing these stages in dependency sequence: distinction, recognitionInterface, singleValuedPredicate, symmetricComparison, compositionConsistency, rcl, jCost, arithmeticObject, timeTick. Physical light is defined as the lightCone stage, the null boundary that carries electromagnetic signals once spacetime exists. Before(a, b) holds precisely when rank(a) < rank(b), with the instance of Decidable supplied by Nat.decLt.
proof idea
The term proof begins by introducing the assumed universal quantifier. It then instantiates the hypothesis at the distinction stage, using a decidable proof that distinction differs from physical light. Normalization of the Before, PhysicalLight, and rank definitions at that point produces an immediate numerical falsehood.
why it matters
The result anchors the distinction drawn in the module documentation between primitive recognition-light and physical light as the first boundary of spacetime. It sits inside the forcing chain that ultimately forces D = 3 spatial dimensions after J-cost and the eight-tick octave. No downstream theorems are recorded yet, so the declaration closes one segment of the order without feeding further lemmas.
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