A Minimal Photon-Z Mixing Bridge in ECSM: Coherent Rotation of Branch-Phase and Neutral Closure Modes

This paper presents a notebook-backed minimal photon-Z-like mixing bridge in the ECSM weak-sector programme. A branch-phase / hypercharge-like field B and a neutral closure-imbalance field W3 are combined through a coherent rotation to produce one massless photon-like survivor A and one mass-locked neutral Z-like response mode. The notebook verifies that the neutral mass-locking matrix has m_A^2 ≈ 0 and m_Z^2 = m_0^2(g^2+g'^2), that the coherent rotation diagonalizes the matrix, and that the electric-like coupling identity e = g sin(theta) = g' cos(theta) is recovered. A coupling-ratio scan confirms that the photon-like zero mode is structural, and a finite-response deformation test shows recovery of photon-like masslessness as chi -> 1. Final notebook verdict: PASS_MINIMAL_PHOTON_Z_MIXING_BRIDGE The paper is deliberately scoped as a bridge result and does not claim to derive the full electroweak theory, measured Weinberg angle, physical W/Z masses, Higgs phenomenology, weak scattering amplitudes, or precision electroweak observables.