Mass as Information Friction: Topological Emergence of the Hadron Spectrum from Directed Information Channels in a Ramanujan Vacuum

The origin of hadron mass remains one of the fundamental open problems in physics; the Higgs mechanism accounts for less than 1% of the proton's mass, while Quantum Chromodynamics (QCD) confinement lacks a closed-form analytical derivation for the mass spectrum. Here, we propose that hadronic mass is not an intrinsic property of matter but the thermodynamic cost of maintaining information coherence (Information Friction) between confined constituents. Modeling the hadron as a directed complete graph interacting with a structured quantum vacuum (modeled as a Ramanujan graph), we derive a mass formula based on the Kullback-Leibler divergence of directed information channels. We demonstrate that the irreversibility of information updates between color charges generates a dissipative energy cost M = alpha * N(N-1), where alpha = 156.33 MeV is the vacuum impedance derived from our previous work. This framework predicts the proton mass with 0.03% precision (937.98 MeV) and explains the instability of tetraquarks via topological dissociation. Finally, we unify this result with our previous derivation of proton spin, showing that mass and spin are dual manifestations of the same spectral invariant.