DRSN XXVI: Birch and Swinnerton–Dyer Conjecture under Spectral Drift (De Rerum Spectrale Natura, Report XXVI, Version 1.0)

We apply the drifted spectral framework developed in the previous Clay–Perspectives to
the Birch and Swinnerton–Dyer conjecture.
Rather than attempting a proof of the conjecture, we identify the precise analytic and
spectral sector in which the BSD obstruction must reside. Starting from the Hasse–Weil
L-function of an elliptic curve over Q, we introduce a bounded real spectral drift acting on a
naturally associated Hilbert space.
The associated Baker–Campbell–Hausdorff expansion isolates a zero-order operator encoding the order of vanishing of the L-function at s = 1. We show that the BSD conjecture
may be reformulated as a spectral coercivity and projection problem relating this sector to
arithmetic invariants such as the Mordell–Weil rank and the regulator.
This work localises the BSD obstruction as a concrete spectral problem and completes the
drifted spectral analysis of all unresolved Clay Millennium Problems.