A tower of Kochen-Specker circles: even-dimensional unimodular families and the maximal-Galois holonomy law

What this paper does. It builds a tower of Kochen–Specker circles: continuous one-parameter families of KS sets in even dimensions 4, 6, 8, 10 and 12, all carried by the unimodular cancellation mechanism |x|² = 1 over two-symbol coordinate alphabets. For each rung it computes the Wilczek–Zee holonomy of the KS loop and determines the Galois group of the holonomy's characteristic polynomial, which is the full symmetric group S_d at all five even rungs for cores with irreducible coupling. It also proves a trace law — |Tr S| = d/2 identically on the working stratum, hence det W(2π) = 1 — and assembles a p-cycle certificate route whose required prime exists at every even dimension.

Attribution. The three-dimensional Peres/Penrose family originates with Gould and Aravind; this program's contribution there is the gauge reduction showing the moduli space is a circle rather than a 3-torus, which corrects their pairwise-inequivalence claim. The Kochen–Specker uncolorability of the integer {0,±1} ray pools is due to Pavičić and collaborators, not to this program; the paper records only an independent re-derivation and a mechanism-independence observation downstream of their result. The dimension-three two-symbol classification is Kernaghan's (arXiv:2603.16988). The Galois machinery is classical and is not claimed as new: Jordan's 1873 theorem, the block argument of Wielandt (Finite Permutation Groups, Thm. 13.9), the standard practice recorded by Isaacs and Zieschang, and Nagura's 1952 prime-interval theorem. Only the application of that machinery to these holonomy polynomials is this program's.

Status and scope. This is a preprint, not a peer-reviewed article. Every claim in the paper carries an explicit evidence label (proved, exact, numerical, conjecture, literature, open), and the scope limits are stated rather than implied. In particular: the S_d law is established only at the rungs actually built, and the general even-dimensional statement is a conjecture; the hypothesis of irreducible coupling is necessary, and the paper exhibits the counterexamples that show it; existence of cores beyond d = 12 is not claimed constructively; and flex certificates have been run at d = 10 only, not at d = 8 or d = 12. All arithmetic is exact; no claim rests on floating-point evidence.

Relation to arXiv:2603.16988. An earlier version of that survey reported the Peres/Penrose flex as infinitesimal only. In v8 its author retracts that statement in a labelled correction note and publishes the cause, a constraint-ordering error. The present paper describes the matter as settled, and does not treat v8 as independent confirmation of finiteness: v8's own continuation is double precision and its modular rank computation bounds flex only from above, as its author states. The finite-flexibility verdict rests on the exact certificates of the companion paper.

Use of AI assistance. This work was produced with substantial assistance from AI language models, used for exact symbolic and combinatorial computation, for drafting, for literature search, and for adversarial review of the arguments. Every mathematical claim was independently recomputed, and an adversarial pre-publication audit was run against the manuscript. The author is responsible for the content. This disclosure is made unconditionally.

Verification code. https://github.com/manuflog/contextuality-obstructions