One of the hardest problems in trying to derive the Standard Model from a deeper theory is making sure the mathematics produces the particles we actually see — and not unwanted extra copies. When particle physics is represented on a discrete underlying structure, those unwanted copies can naturally appear. Earlier VERSF work had already derived its own mechanism for suppressing them: rapidly changing particle states carry an additional energetic cost, effectively pushing the unwanted copies out of the low-energy world.
This new paper takes an important next step. It shows that this VERSF-derived mechanism fits naturally into a well-established mathematical framework for describing particles such as electrons and quarks while preserving their crucial “handedness”, or chirality. The calculation finds a whole region in which exactly one physical particle remains light while the unwanted copies become heavy, and it identifies a preferred point inside that region purely from the mathematics rather than by fitting it to experimental data.
The result also connects much more directly back to the foundations of VERSF. The same underlying connection that VERSF uses to describe the gauge forces can be used to transport matter, and the resulting structure naturally produces the term needed to remove the unwanted particle copies. In other words, the regulator is no longer something that simply has to be borrowed from conventional particle physics and attached afterwards: a source-matched version can be built from structures that are already present inside VERSF itself. The paper then shows that this construction remains mathematically well behaved for a finite neighbourhood of non-trivial force-field backgrounds, preserving particle handedness, topology and locality.
There is another important advance because VERSF does not assume that time is simply a fourth microscopic direction equivalent to the three directions of space. Instead, change happens sequentially. The paper shows that this genuinely VERSF-style description still produces the correct low-energy left- and right-handed particle equations with exactly the right normalisation. It also proves that the sequential description does not accidentally introduce another hidden copy of the particle: within the fundamental range there is only one zero-energy, zero-momentum particle state.
For the wider VERSF programme, this removes another substantial obstacle on the road toward a derivation of the Standard Model. The theory now has a much stronger bridge from its proposed microscopic structure to the chiral fermions used by the Standard Model, while retaining the familiar one-loop pattern by which the three gauge forces change with energy. That running result is presently graded as conditional for the VERSF sequential formulation because the fully force-coupled version of the sequential operator still has to be written out and tested explicitly. The local chiral-regulator problem itself, however, is now marked as passed at the source-matched grade; the remaining work is increasingly concentrated on that fully gauged sequential calculation, strict source-level identification of the complete fermion operator, and the stronger global/topological proof across all allowed backgrounds.