gauge_sum_value
plain-language theorem explainer
The gauge sum prediction from the three-dimensional hypercube geometry equals twelve times pi. Researchers deriving the strong coupling constant within the Recognition Science framework would reference this equality when establishing bounds on the gauge structure. The proof is a direct unfolding of the gauge sum prediction definition followed by simplification using the spatial dimension.
Claim. The predicted sum of the three gauge couplings at the unification scale, obtained from the number of edges in the three-dimensional hypercube multiplied by $pi$, equals $12pi$.
background
In the Recognition Science treatment of strong coupling, the gauge sum prediction is defined as the product of the number of edges in a three-dimensional hypercube and $pi$. The function cube_edges counts the edges of a D-dimensional hypercube via the formula $d cdot 2^{d-1}$. For D = 3 this yields exactly twelve edges, so the sum is twelve $pi$ (see upstream result cube_edges).
proof idea
The proof is a one-line term-mode wrapper. It unfolds the definitions of gauge_sum_prediction and cube_edges, then applies simplification using the value of D.
why it matters
This equality supplies the exact value needed to certify the gauge structure in the strong coupling module. It is invoked directly by the bounds theorem that places the sum between thirty-six and forty-eight, and by the existence theorem for the StrongCouplingCert. Within the framework it realizes the prediction that the strong coupling emerges from the eight-tick gauge structure and the three-dimensional cube geometry at the unification scale (see module doc on Q9).
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