Papers · Preprint
A Conditional Proof of the Strong Birch-Swinnerton-Dyer Conjecture
A map of exactly what a proof of Strong BSD would need.
In plain words
The paper builds a shell around the BSD identity. A single residual is zero exactly when the identity holds. The deep arithmetic is isolated into three named inputs, which are supplied as hypotheses, not derived.
Given those inputs and a few headline theorems from the literature, the framework forces the residual to zero, and Strong BSD follows. So the result is a conditional theorem: if these things hold, Strong BSD holds.
The value is in making the dependencies exact. Two of the inputs are still open problems, and the paper says so. The structure is formalized in Lean as a checked schema.
What it shows
- A residual that vanishes exactly when Strong BSD holds.
- Three named recognition sources that would close the problem.
- A Lean checked conditional schema.
What it does not claim
It is not an unconditional proof. The higher rank Gross Zagier identity and a small prime Iwasawa main conjecture remain open.
Cite
Tsiokos, I. (2026). A Conditional Proof of the Strong Birch-Swinnerton-Dyer Conjecture. Zenodo. https://doi.org/10.5281/zenodo.20713968