Geometric Origin of CMB Large-Angle Anomalies from Discrete Vacuum Nucleation

In this paper, we trace the geometric origin of several large-angle Cosmic Microwave Background (CMB) anomalies directly to the discrete vacuum nucleation kinematics of the Selection-Stitch Model (SSM) [12, 13]. During the inflationary epoch, the three-dimensional tetrahedral foam is generated by a kinematic “Lift” operator acting on a two-dimensional hexagonal ground state. Be- cause the lift height h= 2/3 L is fixed relative to the lateral bond length L, the perturbation generation process carries an inherent, fixed geometric eccentricity of e2 = 1/3. We demonstrate that this eccentricity imprints a scale-dependent quadrupolar modulation on the primordial power ˆ spectrum, P(k) = P0[1 + g(l) cos2 θk ], where g(l) =−2/(3l). This specific 1/ldecay arises naturally from the progressive isotropization of the expanding foam. Remarkably, this framework yields four parameter-free geometric predictions: (i) the leading-order quadrupole power is suppressed by a fac- tor CSSM 2 /Ciso 2 ≈7/9, consistent with the anomalously low observed quadrupole; (ii) the quadrupole and octupole share a common symmetry axis (the lift direction ˆ z), explaining their observed mu- tual alignment; (iii) this preferred axis coincides exactly with the hemispherical asymmetry dipole direction derived in our companion work [14]; and (iv) an outward-expanding parity asymmetry favors odd-l modes at low multipoles. The built-in 1/l decay naturally explains why these CMB anomalies are concentrated at l≲ 5 and fade away at l≳ 30, offering a structural scale dependence that standard ΛCDM cosmology currently lacks.