K41 and CTP--2PI Regimes in an E8 Yang--Mills Framework: Theoretical Reconciliation and an Indirect Experimental Protocol

This manuscript separates two readings that must remain distinct. At the theoretical level, the K41 spectrum E(k) proportional to k^(-5/3) and the CTP--2PI/Yang--Mills occupation scaling n(p) proportional to p^(-4/3) are not a contradiction: they describe different observables and different regimes. At the experimental level, the exponent 4/3 should not be compared with raw final-state ALICE/ATLAS spectra. The correct observable requires a class-dependent response matrix and a deconvolved latent spectrum n_dec^c(q), or equivalently a reconstructed local exponent alpha_dec^c(q)=4/3. The public data reviewed so far do not provide a sufficient response matrix for that reconstruction. The manuscript is therefore presented as a theoretical block and conditional protocol, not as a completed experimental test.