Superstring-Fabric Spacetime (SFS): A Geometric Derivation of the Standard Model Gauge Structure, Fermion Chirality, and Mass Spectrum from Spacetime Torsion V2

The Superstring-Fabric Spacetime (SFS) framework models spacetime as a continuous elastic medium — a three-dimensional Nambu-Gotō brane — whose irreducible SO (1, 3) torsion sectors are identified with the gauge sectors of the Standard Model. This paper presents the complete canonical reference for the SFS framework (Version 2026), deriving the Standard Model gauge group G = U (1) Y × SU (2) L × SU (3) c, fermion chirality, and the mass spectrum entirely from spacetime torsion geometry, without external input. Key results include: the derivation of the Navier-Lamé elastic action from the Nambu-Gotō worldvolume; the unique decomposition of the torsion tensor into three orthogonal sectors (PV, PA, PT) forcing the SM gauge group; a Higgsless electroweak symmetry-breaking mechanism via axial torsion condensate; derivation of the Weinberg angle (cos²θW = 7/9) ; the W/Z mass ratio from the torsion sector geometry; chiral matter content from parity-odd torsion winding; and partial results on the fermion mass spectrum. All results are classified explicitly as PROVEN, CONDITIONALLY TRUE, or OPEN PROBLEM. V2 – Citation corrections, structural revisions, and Appendix A expansionThis version includes the following updates: Citations: All cross-references and theorem citations have been corrected and consistently renumbered throughout the document. Structural and typographical corrections: Several structural inconsistencies and typographical errors identified in the previous version have been resolved. Appendix A (fully expanded): The original Appendix A has been replaced with a comprehensive treatment of the elastic fabric and torsion geometry foundations, significantly extending the theoretical groundwork of the SFS framework. Overall, this version represents a more organized and self-consistent presentation of the theory.