Two-Energy Theory TDE Octant Mass Ladder and Geometric Mass Lattice — Pilot Study

This preprint reports a pilot "first-principles" mass model developed within the Two-Energy Theory (TDE) program. The central result is an octant (geometric) mass ladder: a discrete barrier scale E0 emerging from a dimensionless geometric constant k = 4pi + 1 and the electromagnetic fine-structure scale E1 = alpha^ (-1) /4. This yields E0 = kE1 (approx. 465 MeV) and a fine unit E2 = E1/k (approx. 2. 53 MeV). Masses are represented on a geometric lattice: M = AE0 + BE1 + C*E2 (where A, B are half-integers, and C is an integer). Two complementary evaluations are provided. First, a reverse-lookup lattice audit maps each PDG hadron mass to the nearest lattice node (A, B, C), confirming internal lattice consistency (closure at the E2 scale). Second, a predictive, rule-based sector is tested where (A, B, C) are assigned from quantum numbers and quark content without using the target mass as an input. In the currently covered domain—stable light hadrons (u, d, s ground states) and S-wave quarkonia (charmonium and bottomonium) —the model achieves sub-percent relative errors for most anchors and demonstrates an integer-step ladder A = Aₛtart + n for radial excitations. Coverage of the full PDG spectrum is intentionally limited at this stage due to the missing explicit excitation index n (radial/orbital) for many states. The release therefore focuses on validated ground-state rules and reproducible tooling, and outlines the next modules required to extend coverage to open-flavor heavy hadrons and general excited spectra.