One of the hardest parts of trying to derive the Standard Model from first principles is avoiding hidden free parameters. In this part of the VERSF programme, there appeared to be a serious possibility that the theory might need twelve separate strength settings — one for each matter/commitment sector. This paper shows that, if the current and the primitive fact-commitment law really act on the same underlying events, those twelve independent settings are not allowed. The theory’s own probability structure forces them to collapse to a single common strength.
That matters because it removes a large amount of arbitrariness from the gauge sector. The paper also shows that the relative way the colour, weak and hypercharge directions act across matter is fixed by the structure already derived in VERSF. The same overlap matrix emerges from three structurally distinct routes, which makes it much harder to dismiss as a modelling choice or a lucky fit.
A second advance is that the remaining overall gauge strength is given a much clearer physical meaning. VERSF treats primitive facts as all-or-nothing events, so the continuous strength does not have to mean that a fact is “partly written.” Instead, it can show up in the rate at which complete facts occur. The paper demonstrates, on the current-cycle construction, that the relevant gauge information can be expressed as the curvature of that complete-fact occurrence rate.
In terms of the Standard Model derivation, the key step forward is that the gauge/current problem has been reduced from many possible representation-dependent strengths to one remaining common scale. The relative structure is fixed; what is still missing is the absolute physical value of that final scale and the remaining Abelian closure step. The paper therefore does not complete the Standard Model derivation, but it narrows one of the biggest remaining freedoms to a single source-derived number that the next calculation can now try to determine.