The Rope That Won't Break: Why Quarks Are Confined, Forced by the One-Dimensional Flux Tube

One axiom. One operation. Zero free parameters. No free quark has ever been seen — confinement — yet proving it from the strong-force equations has resisted every attempt (the physical heart of the Yang–Mills Millennium problem). This paper forces it structurally. The difference between a confining force and a free one is the dimensionality of its field. The photon is neutral, so the electromagnetic field spreads in 3D and thins as 1/r²; the work to separate charges converges, so free charges exist. The gluon carries colour and self-couples (total source 3 vs the photon’s 1), so the strong field collimates into a 1D flux tube of constant width one-half. In one dimension the field is constant, so the work to separate grows without bound — a linear potential V(r) = σr. The rope never breaks by freeing a quark; pulled hard, the stored energy makes a new pair and snaps the tube into two colour-neutral hadrons. Only neutral wholes are ever free. Machine-checked; reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory