Addendum IV to the Berg Theory

Addendum IV extends the Berg Theory by introducing a minimal and conservative effective-field-theory module for quantum fluctuations within the single-field “energy-web” framework. Quantum fluctuations are not modeled as classical noise in the equations of motion; they enter as leading symmetry-allowed corrections to the effective action, implemented as an amplitude-dependent dressing of the kinetic (“stiffness”) sector. The corrected field equation is obtained strictly from a variational principle, which uniquely fixes the accompanying gradient structure required for consistency and typically missed by heuristic short forms. The module vanishes in a strictly constant vacuum background, thereby preserving the strict vacuum null tests established in Addendum I. Version 3 strengthens internal consistency and reproducibility by making all conventions explicit (signature, d’Alembert operator, curvature conventions, symbol policy) and by tying every “derived from action” statement to a single clearly identified action kernel. It also refines the operational calibration strategy: instead of assuming direct access to the web strength, the addendum introduces an effective contrast parameter that translates measurements into bounds on the new EFT parameter combination. Finally, the module yields directly falsifiable signatures of spatial stiffness inhomogeneities, including scattering and reflection at stiffness transitions and an induced effective potential for canonically normalized perturbations. The document is explicitly linked to the core article Version 3 (DOI: 10.5281/zenodo.18076026).