A Finite Elastic Scattering-Amplitude Doorway for an Electron-Like Packet in the ECSM Framework

This paper presents the V29 continuation of the electron-like packet programme in the Emergent Condensate Superfluid Medium (ECSM) framework. Previous stages established an inherited finite-radius, occupancy-locked electron-like response packet with effective charge close to −1, a near-electron rest-energy scale, coherent-limit Dirac-like propagation, minimal gauge coupling, Pauli-limit magnetic coupling, Schwinger-scale magnetic-moment structure, finite radiative self-energy behaviour, Lamb-shift-like scale closure, and a finite vacuum-polarisation/running-response doorway. V29 tests whether the inherited packet can support a finite elastic scattering-amplitude doorway. The construction imports the V28 running-response structure and adds a finite-transfer amplitude form factor. In the low-transfer regime, the ECSM amplitude and cross-section shape track an ordinary Rutherford/Mott-like reference within controlled tolerance. In the high-transfer regime, the finite response of the packet strongly suppresses the amplitude and cross-section rather than allowing an unregulated pointlike continuation. The numerical audit gives a maximum low-transfer amplitude relative difference of approximately 2. 92%, a maximum low-transfer cross-section relative difference of approximately 5. 75%, a high-transfer amplitude ratio at the largest tested momentum transfer of approximately 4. 99×10⁻⁵, and a high-transfer cross-section ratio of approximately 2. 49×10⁻⁹. The alpha/beta/sigma algebra remains exact to numerical precision, with maximum algebra error zero. All sixteen final criteria pass, giving the verdict PASSSTRONGSCATTERINGAMPLITUDEDOORWAY. This result is deliberately framed as a doorway test. It does not claim a full QED scattering calculation, a renormalised S-matrix, a precision Mott/Rutherford prediction, external-leg renormalisation, loop-complete vertex correction, or a fit to measured scattering data. It establishes that the inherited ECSM electron-like packet can reproduce low-transfer elastic-amplitude structure while naturally imposing finite-response suppression at high momentum transfer.