String Vibrations and Particle Families: <em>A Resonance Classification Framework in String Phenomenology</em>

We introduce a Resonance--Particle Classification Framework (RPCF) that attempts to bring some order to the correspondence between the vibrational modes of strings and the particle content of the Standard Model. Building upon earlier work connecting hypercomplex manifold geometry with particle genesis via chiral permutation cycles and upon a detailed study of Calabi--Yau compactifications with Euler number $\chi = \pm 6$ that reproduces three net chiral generations, the present manuscript develops a unified classification in which closed-string, open-string, and Ramond--sector modes are mapped, respectively, to the gravitational sector, gauge bosons, and fermionic matter of the Standard Model. We introduce a…