On a Branch-State Interpretation of the Spread in Measurements of the Newtonian Gravitational Constant

The Newtonian gravitational constant G remains the least precisely known of the major fundamental constants. Modern measurements report small internal uncertainties, yet their values remain spread beyond a simple common-error interpretation. This paper refines a branch-state proposal for organizing reliable G
measurements. The data are not treated as a single random cloud, nor primarily as a function of publication year, source-mass atomic number, mass number, or calendar month. Instead, the measurements are organized as LOW, MIDDLE, and HIGH branches, interpreted as signatures of apparatus family and campaign state. The 2026 NIST redetermination using the BIPM torsion balance is included as a central clue, because it connects the historical BIPM lineage to a lower central value. The proposed hidden variable X is the Gerber-Mach gravitational potential where the radial velocity (dr/dt) represents the relative velocity of the source mass + test mass towards the Sagittarius A*. The Mach angle ω describes the interaction of the mass of the Milky Way Galaxy with the measured system – the source mass + the test mass. The Mach angle can be adjusted by the observer and to obtain “the delayed choice” value of G – the observed spread of reliable values of G. The paper does not claim that the branch model is proven. It proposes a testable diagnostic map and a research program in order to scan suspected hidden variable – the Gerber-Mach gravitational potential.

Keywords: Earth ↔ Sagittarius A* Radial Velocity, Newtonian Gravitational Constant G, Gerber-Mach Gravitational Potential, Hidden Variable X, Delayed-Choice Experiment.