The Andros Connex: A Universal Geometric Structure of Matter from Nuclei to Cosmos

10.5281/zenodo.18806069 A universal geometric structure governing matter across 45 orders of magnitudefrom atomic nuclei to cosmic voids is presented. The theory is based on a singleaxiom: the projection operator P : O → R3,1 from 8-dimensional octonion space to 4-dimensional spacetime. Its spectrum yields three fundamental constants: κ1 = 8/9(synchronization), κ2 = 1/3 (structural hierarchy), κ3 = 1/7 (cyclic periodicity).From these, the universal series an = 3 + n(n + 9)/2 emerges, which generatesmasses in seven independent sectors: 14 stable isotopes (p < 10−14), tetraneutron(triple coincidence, p < 10−6), vector mesons (accuracy 0.0030.43%), tensor mesons(0.011.0%), glueballs, hydrogen isotopes, and baryons. The four numbers 4, 14, 21, 98from the series sum to 137, explaining the fine-structure constant with 0.026%accuracy. Helium-4 is identified as the first geometron a purely geometric objectwith exponent n = 3/14, existing outside time. The Law of Andros V 2 = 2/3 GeffM/Rgoverns galactic dynamics without dark matter. The androsecond T0 = 5.33 × 10−13s connects Planck time to the age of the Universe. Combined statistical significanceexceeds p < 10−82 (> 18σ). New neutron clusters and the superheavy element 304120Ubn are predicted. Twenty-five parameters of the Standard Model and cosmologyreduce to one geometric axiom. Keywords: Andros Connex, 8/9, universal constant, isotopes, tetraneutron, mesons, glueballs,cosmic voids, fullerenes, octonions, number 137, geometron, androsecond.