This preprint develops a framework for controlling p-adic defect accumulation in Birch–Swinnerton–Dyer comparisons, indicating implications for arithmetic finiteness.
Key Points
The aim is to establish a framework to control defect accumulation in Birch–Swinnerton–Dyer comparisons using operator-theoretic methods.
Developed a spectral determinant line from finite-level strict perfect complexes over p-adic integers.
Introduced a determinant-line transport mechanism to align an arithmetic reference element.
Applied a budget dominance principle to enforce uniform ceiling transitions along finite-level towers.
Examined the capacity-barrier interface to analyze p-corank in the context of obstructions.
Established canonical local unit control at all primes except for a finite exceptional set.
Produced zero p-corank for the p-primary obstruction, indicating structural finiteness for the Shafarevich–Tate group.
Decoupled internal proofs from interface assumptions to enhance audit-friendliness.