The Berg Theory: A scalar–tensor energy web as a common foundation of space–time, gravitation, quantum phenomena, and entropy

The manuscript presents the Berg Theory, a scalar–tensor field framework in which a single complex scalar field, Ψ, is interpreted as a universal energy web. Within this picture, space–time geometry, gravitation, matter formation, quantum wave phenomena, and entropy are treated as organizational regimes of one underlying field. Formally, the core model is defined by a non-minimally coupled complex scalar in curved space–time and a nonlinear, regularizing interaction functional that admits stable, knot-like bound configurations (“nodes”). A compact threshold operator is introduced as a regime-level representation of nucleation-like matter formation above a critical strength scale, with the controlled implementation delegated to the corresponding addendum. Version 3 introduces a sign-audit and convention lock: all sign-sensitive statements are tied to one anchored core equation and an explicit action check, together with an explicit Jordan-frame metric equation. It also resolves a common source of sign/normalization confusion in complex-scalar formulations by stating the link between field equation, Lagrangian density, stress tensor, and cosmological reduction in an explicit and audit-ready form. In addition, the manuscript deliberately uses V for the interaction term in the adopted Lagrangian convention. Readers who prefer the usual potential-energy notation can interpret V as the negative of the conventional potential term; the physics is unchanged—this choice is made only to keep the anchored field equation and the action conventions strictly consistent. Version 4 adds an explicit “field vs. observable” layer to prevent recurring interpretation errors in wave and measurement contexts. It clearly separates the fundamental web field (which may include a phase and thus supports coherent phenomena) from the actually measured laboratory quantity, namely the nonnegative strength or intensity proxy used in readouts such as count rates. With this separation, “extinction” in interference experiments is defined as a relative minimum of the measured strength, not as the complete disappearance of the web; nonzero minima are expected under finite coherence, unequal path contributions, and background signals. Version 4 also clarifies the difference between a truly vanishing field configuration and a physical vacuum baseline, which can be modeled as a nonzero ground level. Finally, it states the normalization convention for the complex-scalar kinetic term to avoid spurious factor-of-two ambiguities. The manuscript states explicit falsification paths, including (i) residual interference behavior in controlled which-way settings, (ii) systematic mass-dependent deformation of interference patterns for increasingly heavy objects, and (iii) observational constraints on a slowly drifting effective vacuum contribution. A no-singularity proposition is formulated as a concrete check and paired with a numerical demonstrator protocol (collapse scenario) specifying initial data, parameter scans, and pass/fail monitors. Topic-focused expansions are provided as a numbered addendum series (each with its own DOI), enabling precise citation of specific regimes and checks: Addendum I — The Physical Vacuum as a State of Maximal Prestress of the Energy Web (Restoring-Force Interpretation) — DOI: 10.5281/zenodo.18009771 Addendum II — Dark Matter as a Geometric Regime of the Energy Web: Amplitude-Supported, Dephased Halos and Effective Gravity Signatures — DOI: 10.5281/zenodo.18009285 Addendum III — Electromagnetism as Oriented Energy Transport in the Energy Web: Gauge-Invariant Phase Guidance and Lorentz-Force Structure — DOI: 10.5281/zenodo.18009127 Addendum IV — Quantum Fluctuations as Effective Stiffness Corrections of the Energy Web — DOI: 10.5281/zenodo.18008245 Addendum V — Spatial Shortening as an Operational Signature of Gravitation in the Energy Web — DOI: 10.5281/zenodo.18006854 Addendum VI — Matter formation as a threshold and nucleation process in the energy web — DOI: 10.5281/zenodo.18012051 Addendum VII — Cosmological Expansion and Cyclicity in a Closed Energy-Web Universe — DOI: 10.5281/zenodo.18025533 Addendum VIII — Double-slit interference, measurement, and decoherence as coherence management in the energy web Ψ — DOI: 10.5281/zenodo.18040521 Addendum IX — A Consistency Map across GR, QFT, Thermodynamics and Cosmology — DOI: 10.5281/zenodo.18064274 Addendum X — The Berg Theory (Diploma work): A universal explanation for energy, space–time, matter and gravitation. How a cocoa changed the world. (forthcoming) Core article DOI (Version 3): 10.5281/zenodo.18076026Core article DOI (first publication): 10.5281/zenodo.18011366