One-Anchor Algebraic Reconstruction of the Wuxing-Meridian System from H4 / 600-Cell Geometry

We present a computational algebraic framework that reconstructs a substantial portion of the classical Wuxing-zangfu-meridian system from the H4 symmetry of the 600-cell. The model begins from a 60-axis decomposition and deterministic Z5 / Z4 actions that reproduce the generating and controlling cycles. A permutation search over 5! organ assignments is reduced to five cyclic candidates by the generating and controlling constraints; a single external anchor, Kidney = Water, selects a unique mapping. To sharpen that claim, the anchor is not introduced as an arbitrary tie-breaker: in the implementation it is the unique intersection of three pre-existing structural filters, namely an H4-height extremum, a distinguished source-sector label, and the yang polarity filter. On this basis, the paper formalizes six linked results: (i) one-anchor reconstruction of the five zang, (ii) a ring / fiber representation of the twelve principal meridians, with a Hopf-style topological interpretation at the topological level, (iii) a structural correspondence between acupoint inventories and 600-cell combinatorics, (iv) a pathology propagation model on the controlling cycle with phi-decay, (v) a five-dimensional vector-space formalization of Kampo formulas, and (vi) a spectral interpretation of qi in terms of the eigenvalue structure of the 600-cell adjacency matrix. Internal computation reports 39/39 verification checks passed. We distinguish exact results within the formal model from interpretive or biomedical hypotheses and propose the framework as a mathematically explicit platform for falsifiable study, not as a clinically validated diagnostic or therapeutic system. Scope note: This paper presents a formal mathematical and computational model. It reports internal consistency checks from a standalone implementation, but it does not claim clinical validation, medical efficacy, or diagnostic use.