Dual Projection of Geometry and Probability in Informational Physics:Dimensions, Stability, Exceptions and Limits

We develop a unified informational framework in which geometric and probabilistic structures emerge as dual projections of a single analytic spinor field defined on a higher-dimensional Kähler manifold. The fundamental object—the Kähler spinor—carries coupled amplitude and phase degrees of freedom whose internal dynamics generate effective four-dimensional geometry and quantum amplitude structure.

Coherence of the dual projections imposes informational stability constraints. Linearizing the spinor flow yields a spectral balance condition: only modes lying on a distinguished critical line in a complex stability plane admit non-divergent evolution. While no proof of the Riemann Hypothesis is claimed, 
a smooth emergent geometry is shown to require an analogous balance between amplitude decay and phase oscillation.

Departures from this balance produce phase decoherence and geometric instability.  The resulting fermion mass spectrum admits a compact organization in terms of integer spectral indices and a universal quartic structure. Near minimal deviation, the neutrino sector selects normal mass ordering with a total mass close to $0.059\,\mathrm{eV}$. At the opposite extreme, black-hole formation corresponds to an informational saturation regime in which the internal spinor flow approaches a vacuum-like fixed point. Within this mechanism, horizon formation, Page-curve behavior, information recovery, and singularity avoidance arise while global unitary is preserved on the full manifold.

These results suggest that geometry, probability, mass generation, and gravitational extremality may share a common informational origin, 
providing a minimal mathematical basis for connecting analytic spinor dynamics with large-scale physical phenomena.