Papers · Preprint
Decomposing the Bloch-Kato Fundamental Line: Adequacy and No-Go Results for the BSD Invariants
What one number about an elliptic curve keeps, and what it throws away.
In plain words
The Birch and Swinnerton-Dyer conjecture ties a curve to a product of numbers. This paper takes that product apart into five typed columns: heights, periods, Tamagawa factors, p adic data and the determinant.
For each column a residual measures what the final scalar loses. When the residual is zero, the public number is a faithful projection of a richer typed object. A comparison theorem shows the usual scalar package is exactly such a projection.
An audit suite records where public numbers underdetermine their targets. Those are the no go results. All finite claims are checked in Lean without mathlib.
What it shows
- A five column typed decomposition of the BSD invariants.
- Zero residual for the contraction to the standard scalar package.
- A catalog of places where scalar data is not enough.
What it does not claim
It does not prove BSD. Deep arithmetic inputs are carried as hypotheses.
Cite
Tsiokos, I. (2026). Decomposing the Bloch-Kato Fundamental Line: Adequacy and No-Go Results for the BSD Invariants. Zenodo. https://doi.org/10.5281/zenodo.20713981