Paper 7: the anyon Standard Model, and why it was withdrawn
This post covers an archived paper, and I want to be clear about the genre before starting: Paper 7 is wrong, it is kept because wrong papers with visible reasoning are more instructive than clean summaries, and nothing in the current framework depends on it. What follows is the anatomy of how it failed.
What the paper tried
The idea was attractive enough to be worth trying. The framework’s boundary category, SU(2) at level 4, SU(3) at level 3, U(1) at level 6, has anyons with fusion rules, and the Standard Model has particles with charges. The paper attempted to construct a functor: a structure-preserving map from the category’s anyon content onto the Standard Model’s particle content, such that fusion of anyons reproduced composition of particles, and braiding reproduced the physics of gauge interactions. If it worked, the Standard Model’s charge quantisation would be derived from the substrate’s topology, and the framework would have its first direct bridge from the multiverse machinery to particle physics.
How it failed
It failed at the load-bearing step, and the failure is instructive because it is arithmetic rather than philosophy. The functor needs the anyon content to match the particle content in the right multiplicities: enough anyon types of each grading class to cover the multiplets, with fusion multiplicities that agree. The early draft asserted the matching with a table of quantum dimensions, and the audit recomputed the table. The SU(3) entries summed to the wrong value: the claimed 36, which the 2592 calculation needs, was not what the fusion rules give when evaluated carefully. After correction the sum landed exactly, but in the process a second issue surfaced: the anomaly-cancellation route the paper used to police the functor was making assumptions about simple versus composite anyons that the audit listed as unproved, and the uniqueness of the embedding, which the paper needed for its derivation claim, was never established.
The paper was archived, and its salvageable pieces were redistributed. The corrected quantum dimension table went into the 2592 calculation, where it belongs. The anomaly-cancellation content, which is genuine, became Paper 8. The admissibility question, which fields the category can consistently couple to, survived as the Z6 congruence theorem from the walkthrough series. What died was the functor itself: the claim that the substrate’s anyons are the Standard Model’s particles, as opposed to a structure the Standard Model happens to be compatible with.
Why archive rather than delete
Deleting a failed paper saves embarrassment and loses information. The archive keeps three things that a deletion would not. The audit trail, so nobody re-derives the functor without hitting the same wall and knowing where it is. The correct fragments, which are now load-bearing elsewhere with their own status labels. And the pattern, which recurs: a construction whose pieces are each defensible, assembled into a claim stronger than any piece supports. The gauge coupling paper and the baryogenesis paper, archived alongside, failed the same way, and their posts follow.
The current framework’s claim about the Standard Model is correspondingly smaller: the category is consistent with the Standard Model’s grading and anomaly structure, and nothing more. That is a much weaker statement than the functor would have been, and it is the statement that has survived every audit so far.
The next paper is the series’ most solid bridge to the Standard Model, and the one result here that a particle physicist would recognise: Paper 8, anomaly cancellation.