symmetry_before_composition
plain-language theorem explainer
Symmetric comparison precedes composition consistency in the pre-temporal forcing order of Recognition Science. Researchers mapping dependency stages from distinction to time would cite this ordering to confirm the sequence before J-cost or spacetime appears. The proof is a one-line wrapper that invokes the decidable instance of the Before relation on stage ranks.
Claim. In the forcing order on dependency stages, the rank of the symmetric comparison stage is strictly less than the rank of the composition consistency stage: $rank(symmetricComparison) < rank(compositionConsistency)$.
background
This module records the forcing order among pre-temporal stages in Recognition Science. The Before relation holds precisely when the rank of one stage is smaller than the rank of another, and Stage is the inductive enumeration of those stages beginning with distinction and continuing through symmetricComparison and compositionConsistency to rcl, jCost, and timeTick. The order is a dependency priority rather than a chronological sequence, since physical time itself is a later forced object.
proof idea
The proof is a one-line wrapper that applies the decidable instance of Before, which reduces the claim to a natural-number less-than comparison on the ranks of symmetricComparison and compositionConsistency.
why it matters
The result places symmetric comparison before composition consistency inside the pre-temporal chain that runs from distinction to timeTick. It supports the overall forcing sequence that precedes the Recognition Composition Law and J-cost, consistent with the module's distinction between recognition-light and downstream physical light. No direct downstream theorems are recorded yet.
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