Reading Relations, Loops, Flux, and Condensates from the Closure of Complex Numbers: A Minimal-Assumption Thought Experiment That Shaves Off Axiom Candidates

This paper proposes no new algebraic law and no new equation of motion. Starting only from ordinary complex numbers and their closure under addition, multiplication, and squaring, the trivial identity Σ z_n² = C² is reread as an ordinary complex sum Σ Z_n = K of squared quantities Z_n := z_n². From this single rereading the paper reads off sums of multiple relations, loops, loop residuals, face fluxes, cancellation of shared parts, closed polyhedra as condensates, and hierarchical condensates, all within the same complex-number type. Hidden assumptions - complete networks, external standards, ratios, primitive equality tests, presupposed zero closure, presupposed triangles and vertices - are examined and removed one by one; for a closed oriented 2-manifold-like face complex, the vanishing of the global flux is derived as a discrete del-squared-equals-zero type identity rather than assumed. Structural similarities with lattice gauge theory, spin-network coarse-graining, closure defects, the Bianchi identity, bubble networks, and genuine multi-partite entanglement are compared only after the construction, and the completeness of pair relations and loop residuals for many-body relational information is explicitly left as an open problem. Japanese and English versions are included.