Addendum IX to the Berg Theory

Addendum IX develops the consistency, constraint, and falsification architecture of the Berg Theory. Extending the core article The Berg Theory: A scalar–tensor energy web as a common foundation of space–time, gravitation, quantum phenomena, and entropy (core collection DOI: 10.5281/zenodo.17937466; core record DOI: 10.5281/zenodo.17937467), this work tests whether the theory can remain one sign-anchored scalar–tensor framework when its gravitational, quantum-facing, thermodynamic, matter-formation, and cosmological sectors are read together. The addendum organizes the theory’s contact with established frameworks through a shared action convention, a fixed canonical field equation, a common prefactor/readout channel, and explicitly declared admissibility gates. Recovered weak-field, transport, cosmological, and coherence limits are distinguished from module hypotheses, bounded consistency results, protocol-ready tests, and open completion burdens. In this role, Addendum IX is not presented as a completed empirical proof, but as the series-level consistency map: a structured account of what must remain jointly true if one connected energy-web field Ψ is to describe geometry, support, transport, coherence, and observable gravitational response without separating into independent sector fits. A central output is the five-lock fingerprint linking growth, lensing, gravitational slip, standard-siren propagation, and local normalization to one shared branch history. The release fixes NGC6503 as the first rotation-backed Growth–Lensing target and includes the supporting public-release materials needed to preserve the frozen target logic: analogue target tables, projected-response worksheet templates, return-class definitions, validation scripts, source-rights notes, and release manifests. Until an independent projected-mass or weak-lensing shear return with covariance is available, the global five-lock state remains bounded rather than passed. This version also strengthens the companion structure of the addendum. Appendix A records derivational and conditional-theorem support for admissible-domain regularity, retained-core classicality, Born-baseline import, metric readout, and branch-vector uniqueness. Appendix B carries status discipline, evidence classes, downgrade rules, and data-facing interface conditions. Appendix C isolates coherence-management bridge targets and checkable kernels. The public supplement provides reproducibility and release artefacts rather than hidden adjustment material. The present record corresponds to Addendum IX Version 5, DOI: 10.5281/zenodo.20681525. It should be read as a falsifiable consistency and constraint framework for the Berg Theory: a publication-stage attempt to make the theory’s cross-domain commitments explicit, testable, and rejectable under one declared branch logic.