Environment-Dependent Hadronic Interactions as a Multi-Scale Probe of Relational Physics

This work presents a quantitative reinterpretation of the first ATLAS measurement of proton–oxygen collisions at √sNN = 9.62 TeV, designed to emulate cosmic-ray interactions with Earth's atmosphere. Although the ATLAS experimental uncertainties remain at the few-percent level, significant discrepancies persist among state-of-the-art hadronic interaction models. Rather than interpreting these discrepancies as purely stochastic or model-dependent uncertainties, we introduce a derived observable: the environmental modulation parameter, λ_env = Data / Model. Using the official MC/Data ratio panels released by the ATLAS Collaboration (STDM-2025-08), we perform a direct bin-by-bin extraction of λ_env across multiple observables, including pseudorapidity (η), transverse momentum (pT), charged-particle multiplicity (n_ch), and fiducial proton–oxygen cross-sections. The extracted λ_env distributions reveal smooth and strongly model-dependent structure across phase space. In particular: - λ_env(η) exhibits systematic deviations reaching ~28%, - λ_env(pT) reaches λ_env ≃ 3.33 at high transverse momentum, corresponding to discrepancies exceeding 200%, - λ_env(n_ch) increases systematically in high-density regimes, - integrated fiducial cross-sections show persistent normalization-level mismatch across all models. These deviations are continuous, structured, and observable-dependent, strongly suggesting that the discrepancies are not random fluctuations, but coherent phase-space-dependent mismatches between models and experimental data. We demonstrate that λ_env cannot be interpreted as a simple normalization factor, but instead behaves as a structured function of phase space, λ_env(η, pT, n_ch, A), providing a direct quantitative probe of system–environment coupling in hadronic interactions. More broadly, this work proposes that environment-dependent modulation may represent a generic feature of physical systems across scales, drawing connections between hadronic collisions, atmospheric air showers, and cosmological models in which effective dynamics depend on environmental density and structure. The results suggest that what is traditionally interpreted as “model uncertainty” may instead contain physically meaningful environmental information encoded in the mismatch structure itself.