We consolidate five independent mathematical constraints into a single funnel theorem: n = 3 is the unique positive integer satisfying all five simultaneously. The constraints are: (C1) gauge-covariant Derrick virial balance admitting stable solitons only for n ≤ 3; (C2) the Lie algebra isomorphism so(n) ≅ su(2), required for electroweak structure, holding only for n = 3; (C3) existence of non-trivial knots, required for topological confinement, holding only for n = 3; (C4) the pre-metric Hodge constraint requiring n = 3, corroborated by the Eckmann cross-product theorem; (C5) the Cartan decomposition sl(n,ℝ) = so(n) ⊕ Sym₀(n) matching dim su(3) = 8 only for n = 3. The constraints are evidentially independent: their proofs invoke disjoint mathematical machinery. The convergence of five proof-independent results on a single dimension is the content of the funnel theorem.
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Ilja Schots
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Ilja Schots (Thu,) studied this question.
www.synapsesocial.com/papers/69f594ca71405d493afffa1a — DOI: https://doi.org/10.5281/zenodo.19901717