Deriving the Minimal SU(2)-Like Branch Algebra from ECSM Closure Constraints: Reversible Neutral-Charged Conversion as the Origin of Weak-Like Generators

This paper presents a notebook-backed derivation of the minimal SU (2) -like branch algebra from ECSM closure constraints. Previous ECSM weak-sector bridge papers used the familiar Pauli/SU (2) algebra as a scaffold for interpreting neutral-charged branch pairs, hypercharge-like charge splitting, photon-Z-like neutral mixing, and W-like charged branch conversion. The present work performs the foundational upgrade. Rather than assuming Ti = sigmaᵢ/2, it starts from two ECSM branch states: |Q0> = neutral closure branch, |Qch> = charged branch, together with reversible branch conversion and closure of the finite operator algebra under commutation. The minimal branch-conversion operators are derived as outer products: T+ = |Q0> 1. Final notebook verdict: PASSDERIVEDMINIMALSU2BRANCHALGEBRAFROMECSMCLOSURE The paper does not claim to derive the full electroweak theory, coupling constants, measured weak mixing angle, Higgs mechanism, weak decay rates, scattering amplitudes, anomaly cancellation, or precision electroweak observables. Its narrower result is that the SU (2) -like algebra used in the ECSM weak-sector bridge can be recovered as the minimal closed reversible conversion algebra of a two-branch ECSM closure-active system.