This paper shows that the kinematic skeleton of gauge theory appears inside the reciprocal dual model (Papers 1–9) without ever assuming the gauge principle. The direction of approach is the reverse of the usual one: each time we pressed on different questions — the inventory of conserved quantities, stability, and observability — components of gauge theory appeared as by-products. The main results are as follows. (1) Kinematic uniqueness of the connection: the radial direction of each fragment is the indicator of its local timelike axis (Paper 6), and the connection must transport it. The two conditions of time-axis transport and twist-free minimality uniquely select the minimal-rotation connection of the position-adapted frame — no dynamical input was required. (2) The first holonomy: the sibling-triangle holonomy of a mutually orthogonal three-fragment configuration (tripod) is a 90° rotation, and its rotation angle coincides exactly with the area of the geodesic triangle on the direction sphere (an octant, π/2) — discrete transport reproduces continuous curvature exactly. The curvature quantum π/2 is universal, independent of shell and hierarchy. The second exact holonomy arccos(4/5) has infinite order by Niven's theorem, so the holonomy group is infinite. (3) Continuization theorem for the structure group: the closure of the group generated by adjoining to B4 the 45° rotation required by transport between fragments of different shapes is all of SO(4) (proved via the 3-dimensional crystallographic restriction). The continuous gauge group is a consequence, not an assumption. (4) The locus of curvature: curvature on genealogical links and static transverse twist are unrecordable and hence gauge (a derivation from the record theorem). Curvature concentrates on sibling triangles, and the place where internal gauge structure can be physical is localized at transition events (vertices). (5) Spin lift: the half-angle lift is consistent; the tripod holonomy has order 8 in the spin representation, and the all-axes planar ring configuration carries the first loop that is trivial in the vector representation and −1 in the spin representation. The screw lift (coupling rotation with translation) is unique with pitch 1/2 and identifies a new gauge-invariant Z2, the excitation parity (−1)Σ|k|. (6) Kinematic default of the coupling constant: for the parameter β of Wilson-type weights, we show that pure counting (β = 0) is forced under the current axiom system — a finite β would signify genuinely new dynamical input. Finally, we identify the gauge structure that has emerged as being not of Yang–Mills type but of the type of first-order gravity (vierbein plus spin connection). The claim of this paper extends only to "gauge structure plus computed holonomies"; we do not claim a "gauge theory." Bilingual edition (Japanese and English): Markdown, LaTeX, and PDF for each language, plus three figures (PNG).
Noriaki Kihara (Sun,) studied this question.
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