BSD Grid v1.4_r3: A Grid-Theory Module Toward BSD via Symmetric-Power Contraction

# Overview This record uploads **BSD Grid v1.4_r3 (PDF-only)**, a companion / module paper in the **Grid Theory** program. It organizes a BSD-oriented upgrade pipeline by treating analytic and arithmetic components as explicitly separated modules: - **Main hub:** *Grid Theory v2.4* (DOI: 10.5281/zenodo.18709740)- **Symmetric-power contraction module:** *Sym-Power v2.3* (DOI: 10.5281/zenodo.18710856)- **This record:** BSD-oriented module that links the contraction interface to BSD-style rank statements through standard arithmetic bridges. This is intentionally **not** a claim of a complete unconditional proof of BSD. Instead, it is a **program-level closure interface** with explicit “proved vs imported vs assumed” status labeling. # Status legend (read this first) - **(P)** proved in this paper (within a fixed parameter box PB and stated inputs)- **(I)** imported input (standard external theorems; cited and used as black boxes)- **(H)** standing hypothesis / engine-level assumption (recorded as an acceptance-test interface)- **(V)** protocol / acceptance-test item (checkable template rather than a proved theorem) # Theory summary ## 1) Analytic module (symmetric-power contraction)For holomorphic \(\mathrm{GL}(2)\) newforms \(\pi\) over \(\mathbb{Q}\) in a balanced admissible regime, and for low degrees \(2 \le m \le 4\), the paper uses a calibrated contraction interface of the form\[E_{\mathrm{glob}}(\mathrm{Sym}^m\pi) \le \lambda_m^2\,E_{\mathrm{glob}}(\pi),\qquad 0