TITLE:
Viscous Time Theory Frame for Birch-Swinnerton-Dyer Conjecture
AUTHORS:
Raoul Bianchetti, Payam Danesh
KEYWORDS:
Birch-Swinnerton-Dyer Conjecture, Viscous Time Theory, Elliptic Curves, Selmer Complexes
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.8,
August
27,
2026
ABSTRACT: We formulate an arithmetic Viscous Time Theory framework around Selmer complexes of elliptic curves. The construction replaces the Sobolev field space by a finite split model of a Selmer complex, treats local conditions as anchors, and eliminates a finite memory block by a Schur complement. Under the stated splitting and invertibility hypotheses, the active soft sector is isomorphic to the Bloch-Kato Selmer group. Standard determinant-line bookkeeping identifies the finite correction with the
p
-primary Tate-Shafarevich, Tamagawa, and torsion terms, while normalized Arakelov and nonarchimedean Green energies recover the Néron-Tate height pairing. These results establish an operator framework for organizing the arithmetic ingredients of the Birch-Swinnerton-Dyer formula. They do not prove the Birch-Swinnerton-Dyer conjecture. The rank and leading-term conclusions in Section 6 are obtained only under an explicit Comparison Hypothesis asserting that the active VTT determinant germ agrees with the central germ of the Hasse-Weil
L
-function with the prescribed normalization. That comparison is not established here and remains the principal open problem.