A Preregistered Protocol for the Completion-Density Ordering, the Single-Quantum Test, and the Bound Verdicts of the Strike Clause
The Eigenmode Decision marks an important transition in the VERSF programme. Many earlier papers focused on building the theoretical structure: explaining why distinguishability matters, why closure classes exist, why there are three generations, and why those generations appear to be ordered by mass. This paper takes the next step. Rather than proposing a new physical theorem, it establishes a formal protocol for testing whether the mass hierarchy can genuinely emerge from the underlying closure dynamics.
The central idea is straightforward. If the Mass Hierarchy Theorem is correct, then deeper refinement levels should correspond to greater completion activity within the substrate. In practical terms, that means a future eigenmode computation should produce a sequence of completion densities that rise with generation depth. The paper does not perform that computation. Instead, it specifies in advance exactly what would count as success, failure, ambiguity, or protocol breach. In effect, it creates the rulebook before the game is played.
One of the most interesting parts of the paper is that it does not simply assume success. A series of public-data checks, toy models, and referee exercises are run against the protocol itself. The charged-lepton and quark hierarchies are confirmed as genuine empirical facts, but simple toy constructions are shown to be insufficient. They can easily reproduce the direction of the hierarchy, yet fail to reproduce the actual spacing of the masses. This turns out to be a valuable result. It demonstrates that obtaining the correct ordering is relatively easy, while reproducing the observed spectrum is genuinely difficult. The protocol is therefore shown to be capable of distinguishing superficial success from a meaningful physical explanation.
The paper also reveals something important about the next stage of the programme. Attempts to derive the observed mass spacings directly from simple closure labels fail, while more complicated parameterisations can always be made to fit the data. This leads to a crucial conclusion: fitting the known spectrum is not enough. The real challenge is constructing an explicit operator whose cycle structure naturally generates the required completion counts and anchoring lengths. In other words, the problem is no longer a hierarchy problem; it has become an operator-construction problem.
In the context of the wider VERSF route, this paper sits directly after the Generation Theorem, the Mass Hierarchy Theorem, and the Structural Origin of Yukawa Operators. Those papers proposed that mass hierarchy should emerge from deeper structural principles. The Eigenmode Decision does not add another layer of theory. Instead, it establishes the machinery that will decide whether those earlier claims survive contact with calculation. It is the programme’s first serious attempt to move from structural arguments toward a genuinely predictive computational test.
Perhaps the most important message of the paper is one of scientific discipline. The protocol fixes the victory conditions before the computation is performed. It states openly what would count as confirmation and what would count as refutation. In doing so, it makes the eventual result meaningful regardless of which way it points. The paper does not answer the question “Is the strike on the bill?” Instead, it ensures that when the answer finally arrives, everyone will know exactly what it means.
The Generation Theorem explained why there are three generations. The Mass Hierarchy Theorem explained why they should be ordered. The Eigenmode Decision establishes the test that will determine whether that ordering truly emerges from the underlying substrate dynamics.