DRSN XXIII: P vs. NP under Spectral Drift (De Rerum Spectrale Natura, Report XXIII, Version 1.0)

We apply the drifted spectral framework developed in the previous Clay–Perspectives to
the P vs. NP problem. Rather than attempting a resolution of this foundational question
in complexity theory, we identify the precise spectral sector in which the obstruction to
polynomial-time computation must reside.
By representing candidate solutions on a discrete Hilbert space and encoding the verification
predicate as a nonnegative cost operator, we reformulate algorithmic hardness as a problem of
discrete spectral geometry. Bounded spectral drift generates a BCH hierarchy that captures
increasingly global features of the cost landscape.
We show that polynomial-time solvability would follow from discrete spectral coercivity of
the drifted cost operator, while the failure of such coercivity provides a structural explanation
for NP-hardness. This work localises the P vs. NP problem as a concrete question of spectral
coercivity and completes the trilogy of Clay–Perspectives under spectral drift.