Residue Rails, Dipoles, and Pythagorean Comma-Driven Ergodic Flow: a Deductive Geometric Construction

Deductive geometric construction formalizing a single affirmative chain on the mixed residue torus (ℤ/6ℤ) × S¹₁₂ with Haar probability measure. Rails arise as the complement of 2- and 3-torsion obstruction axes inside the regular hexagon. Dipoles arise as the step-2 chords whose endpoints remain inside determinant prime vertices of the regular dodecagon. The comma rotor κ = 12 log₂ 3 − 19 supplies the incommensurable translation component. The translation flow Φ(u,v) = (u+1, v+κ) is ergodic. Ergodicity yields infinite return visits to every positive-measure dipole region, with lifted geodesic advance producing an unbounded family of distinct dipole labels in the prime corridor.