DRSN IV: Drifted M-Theory Spectral Geometry (De Rerum Spectrale Natura, Report IV, Version 1.0)

We develop the eleven–dimensional drifted spectral geometry underlying the M–theoretic
sector of the De Rerum Spectrale Natura programme. Extending the drift deformation of
Dirac operators introduced in Reports I–III, we construct the drifted eleven–dimensional
Dirac operator, prove domain stability, self–adjointness, isospectrality and preservation of
the principal symbol, and derive the full drifted Lichnerowicz formula. The associated
BCH hierarchy generates torsion, geometric and non–geometric flux layers, including the
complete M–theory C3 and G4 field content. Using heat–kernel factorisation across worldsheet,
target–space and eleven–dimensional blocks, we obtain the drifted Spectral Action in eleven
dimensions and show that it contains a universal quartic drift potential. Variation of the
Spectral Action yields the drifted Einstein and Maxwell–type equations, reproducing the
bosonic equations of eleven–dimensional supergravity, while the drifted Killing spinor equation
ensures compatibility with supersymmetry. We further prove that dimensional reduction of
the drifted operator recovers the ten–dimensional drifted geometry of Report III, including
the Type IIA flux tower. Examples of drifted eleven–dimensional backgrounds confirm the
operational consistency of the theory. This establishes drifted spectral geometry as a complete
operator–theoretic foundation for M–theory.