This monograph applies the Rank-3 Triad of the HC Rank Manifold to the strong interaction, interpreting quantum chromodynamics, nuclear physics, and the hadronic spectrum through three operational regimes: Apow — the Symmetric Core operation at RC = 2 — governs the long-range chiral and soft regime of QCD. Cpow — the HyperCore operation at R = 3 — governs confinement, string formation, and the intermediate QCD regime. e-ONS — ordinary exponentiation aᵇ as the asymmetric rank-3 operation — governs the short-distance, asymptotically free regime. The central structural claim is that these three regimes are not independent. They are the three faces of one Rank-3 operational Triad: Apow, Cpow, e-ONS. The Fluent Invariance of the Triad explains why QCD has a single fundamental scale: the three different regimes share the same underlying Hermit structure. With one physical input, LambdaQCD = 155 MeV, the monograph derives a broad family of quantitative predictions for strong-interaction physics. A representative result is the string tension formula sigma = 8 * LambdaQCD², which gives sqrt (sigma) = 438 MeV, close to the observed confinement scale. The vector meson scale is derived as Mᵣho = LambdaQCD * sqrt (8*pi), giving the rho-meson mass near 777 MeV. The baryon sector is treated through Regge trajectories and TrigCore zero-point corrections, yielding formulas for the nucleon, Delta (1232), and Roper resonance masses. The monograph also derives strong-interaction couplings and precision quantities from HC and SC invariants. The axial coupling is expressed as gA = |tauHC| - 1, while the fine structure constant is connected to the cascade discrepancy by alpha^ (-1) = 1 / (4sqrt (2) |kappadisc|). This places electromagnetic and strong-interaction constants inside a shared operational framework, where small physical discrepancies arise from mismatches between HC and SC cascade structures. Further topics include meson Regge trajectories, pion physics as a TrigCore zero mode, the pion-nucleon coupling, magnetic moment ratios, proton-neutron mass splitting, nuclear saturation, the running QCD coupling, and the Planck-QCD hierarchy. The latter is expressed through a double-exponential relation of the form mPl / LambdaQCD = exp (exp (|tauHC| * |w_+|) ), identifying the enormous separation between the QCD and Planck scales as an operational ascent through the HC/SC hierarchy. Overall, M27c presents the strong force as the physical realisation of the Rank-3 Triad. Chiral dynamics, confinement, and asymptotic freedom become three operational projections of one algebraic structure, with hadronic masses and couplings emerging from Hermit units, TrigCore corrections, cascade discrepancy, and the shared geometry of Apow, Cpow, and exponentiation.
Paweł Łukasz Garycki (Fri,) studied this question.