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Structural Coherence and the Birch and Swinnerton-Dyer Conjecture - Coerência Estrutural e a Conjectura de Birch e Swinnerton-Dyer
Abstract
This work presents a structural proof of the Birch and Swinnerton-Dyer Conjecture, based on the concept of structural coherence and self-similarity: an elliptic curve has infinitely many rational points if and only if its point distribution preserves a constant harmonic pattern across all scales. The vanishing order of the L-function at s = 1 equals the rank, counting independent directions of sustained coherence. When coherence breaks at any scale, the set of rational points becomes finite. The principle unifies number theory with observations from wave dynamics, resonance, and natural self-repeating structures.
Related
- Two proofs of the Cassels--Swinnerton-Dyer conjecture for cubic surfaces
- Birch and Swinnerton-Dyer Conjecture Proof via Causal Scattering and Analytic Torsion on Truncated Modular Coverings under Topological Vacuum Electrodynamics
- The Absolute Spectral Resolution of the Birch and Swinnerton–Dyer Conjecture: Colombeau–Takesaki L-Operators, Galois-Equivariant Dimensional Isomorphism, and Selmer–Sobolev Finiteness of Ш(E/ℚ) within the ZFC Axiomatic Bridge
- Spectral Geometry of Flytrons and the Birch–Swinnerton-Dyer Conjecture: A ZEBTS Framework
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BibTeX
@misc{saez2026structural,
title = {{Structural Coherence and the Birch and Swinnerton-Dyer Conjecture - Coerência Estrutural e a Conjectura de Birch e Swinnerton-Dyer}},
author = {Deni da Silva Saez},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23578766},
url = {https://zenodo.org/records/23578766},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Structural Coherence and the Birch and Swinnerton-Dyer Conjecture - Coerência Estrutural e a Conjectura de Birch e Swinnerton-Dyer
AU - Deni da Silva Saez
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23578766
UR - https://zenodo.org/records/23578766
AB - This work presents a structural proof of the Birch and Swinnerton-Dyer Conjecture, based on the concept of structural coherence and self-similarity: an elliptic curve has infinitely many rational points if and only if its point distribution preserves a constant harmonic pattern across all scales. The vanishing order of the L-function at s = 1 equals the rank, counting independent directions of sustained coherence. When coherence breaks at any scale, the set of rational points becomes finite. The principle unifies number theory with observations from wave dynamics, resonance, and natural self-repeating structures.
ER -