Three-Tag Two-Way Event Construction: Discrete Skeleton of the Standard Model Gauge Group

Abstract -------- This paper starts from the most parsimonious ontology: there exist two entities A and B, each carrying three countable but physically uninterpreted distinction points, labeled by {1, 2, 3}. Physical interactions between A and B are described by directed connections across the entities; each complete interaction consists of a pair of oppositely directed minimal events occurring simultaneously. The essence of a minimal event is an indivisible comparison of differences. The comparison operation has three progressive levels: (1) Same-label connections (parallel pairings) perform the fundamental confirmation of category identity: they confirm that A and B belong to the same category (both are tigers or both are stools), thereby granting legitimacy to cross-label comparisons; this gives u(1). (2) Partially crossed connections, within the already confirmed same category, establish local difference networks between two distinction points, accomplishing partial counting; after "two-subset permutation degeneracy" they merge into su(2). (3) Fully crossed connections exhaust all off-diagonal comparisons among the three distinction points, accomplishing complete counting; their fully antisymmetric closure rigidly generates su(3). The three factors mutually commute because their event patterns do not overlap and they share the endpoints A and B, forming the direct product SU(3) × SU(2) × U(1), which exactly reproduces the Standard Model gauge group structure.