Möbius Field Theory: Klein-bottle spacetime, Z6 holonomy, and a structured program relating topology to Standard Model gauge structure, couplings, mixing, and mass templates

V9 — Major revision of Möbius Field Theory (MFT), a geometric framework proposing 4D spacetime as a compact Klein bottle with Z6 holonomy in which particles are topological solitons. Key advances in this version: first theoretical derivation of the Koide lepton mass relation Q=2/3 from Z3 symmetry (44-year open problem), complete photon sector derivation from Klein bottle phase field, systematic Phase A mass mapping investigation (16 candidate approaches documented and eliminated), corrected soliton picture (Z3-Z3 kink interpolating between vacua), false vacuum stability S_E=3.545×10⁷ (lifetime >> age of universe by 10⁷ orders), C2 field equation closed (massless Dirac with anti-periodic BC), Klein bottle Casimir coefficients c₁≈+0.771 and c₂≈+0.578 computed numerically (both positive — repulsive Casimir pressure from non-orientable topology, consequence of Z6 holonomy). Expanded epistemic classification throughout with Pmath/CMFT/Hphys labels on all major claims. Four-step Koide proof verified independently by three nodes (Cursor, Grok, Gemini). Claude also used for coordination.