This paper tackles one of the hardest parts of the VERSF programme: whether the theory can recover the relative strengths of the forces in the Standard Model without quietly choosing a convenient energy scale or multiplying everything by an adjustable overall factor. Earlier calculations contained both of those freedoms, which made it harder to see exactly what VERSF was predicting. SGRI-1 shows that there is a particular relationship between the strong, weak and electromagnetic sectors that survives regardless of those two unknown settings. In effect, once two of the force strengths are known, the frozen VERSF branch fixes the third.
That turns the calculation into a much sharper experimental test. Using the measured electromagnetic and strong couplings, the simplest VERSF branch predicts a weak mixing angle of about 0.2244. Including the standard two-loop running of the gauge forces improves that prediction to about 0.2273. The measured value is about 0.2312. So the more refined calculation moves substantially in the right direction, removing roughly 43% of the original discrepancy, but it does not make the disagreement disappear. The remaining difference is about 1.7%, and it is much larger than the uncertainty caused by the present experimental error in the strong coupling.
That is important scientifically because the paper is not using the measured weak angle to choose the answer. The VERSF branch was frozen first and then compared with experiment. Nor can the remaining discrepancy be repaired simply by changing the overall scale at which the comparison is made or by rescaling all three couplings together. Those possibilities have been mathematically removed from the test. What remains is therefore a genuine piece of physics that the deeper VERSF source calculation has to explain.
This advances the VERSF derivation of the Standard Model because it converts what had been a fairly complicated multi-parameter gauge comparison into one precise target. Instead of asking whether some combination of scale, normalisation and source effects can reproduce the observed force strengths, we can now ask a much cleaner question: does the microscopic VERSF gauge-response calculation generate the specific relative correction needed to close the remaining gap?
That makes SGRI-1 less a claim that the gauge sector is finished and more a major tightening of the derivation. The theory has effectively lost two places in which an incorrect result could have been hidden. The next source calculation either produces the required relative shift, moves the prediction closer in a principled way, or it does not. In that sense the paper makes VERSF more falsifiable and more predictive, while also telling us exactly what the next calculation must accomplish.