A Falsifiable Framework for Coupling Constant Generation with Explicit Open Problems

This work proposes a coupling constant generation framework based on a pair of conjugate real scalar fields (F, τ) on a trefoil-knotted closed string as the fundamental degrees of freedom. Its core contribution is not claiming the completion of a unified field theory, but providing a falsifiable derivation chain from the geometric-topological data of the string to the coupling constants of the four fundamental forces: the trefoil knot topology yields D₃ three-branch degeneracy (N_c=3), the sewing conditions yield a discrete wave number spectrum kₙ, and the mode stiffness kₙ² defines the coupling constant αₙ=kₙ²/(2N_c) after branch equipartition. This chain is internally consistent within the framework, yielding quantitative results such as a deviation of 0.72% for α_EM, zero deviation for quark charges, a deviation of 5.43% for m_W, and a deviation of 0.12% for the bare value of α_s after one-loop running; the only input for the coupling predictions of the electromagnetic, weak, and strong forces is v=246 GeV. The author strictly stratifies the strength of the conclusions: α_EM, quark charges, and m_W are classified as "internally consistent" (containing one definitional bridge); β₀=7 and the gluon number 8 are classified as "strict"; the gravitational constant G and the Planck mass are not treated as predictions, but are introduced as experimental anchors, because the three-dimensional projection operator is explicitly calculated as diag(3/2, 3/2, 0), which lacks the z-direction, and the projection mechanism remains unclosed. The framework also provides a decoupling statement for the three "6"s (N_f, n_vib, 2N_c), a retraction list of nine early erroneous conclusions, and eleven open problems classified into levels A and B. The positioning of this paper is: the coupling constant generation mechanism is presented as a testable internally consistent system, and the gravitational projection is presented as an unclosed secondary response. The two are stated in separate tiers so that when the framework is tested or refuted, the broken link can be clearly identified.