## 3 Monte Carlo Track Chemistry Simulations  
The radiolysis of both subcritical (300 and 350 \({}^{\circ}\)C) and supercritical (400-600 \({}^{\circ}\)C) water at a pressure of 25 MPa was simulated using the latest version of our Monte Carlo track chemistry code, IONLYS-IRT [31], detailed elsewhere [19; 32; 33]. Briefly, the IONLYS step-by-step program models the initial physical and physicochemical stages of radiation up to \(\sim\)1 ps in a 3D environment. It provides a complex, highly non-homogeneous spatial distribution of reactants at the end of the physicochemical stage, including \(\mathrm{e^{-}}_{\mathrm{aq}}\), \(\mathrm{H^{\bullet}}\), \(\mathrm{H_{2}}\), \(\mathrm{{}^{\bullet}}\)OH, \(\mathrm{H_{2}O_{2}}\), \(\mathrm{H_{3}O^{+}}\), \(\mathrm{OH^{-}}\), \(\mathrm{HO_{2}}\)\(\mathrm{{}^{\bullet}}\)/\(\mathrm{O_{2}}\)\(\mathrm{{}^{\bullet-}}\), \(\mathrm{{}^{\bullet}}\)O\(\mathrm{{}^{\bullet}}\)(\(\mathrm{{}^{3}P}\)), \(\mathrm{O^{\bullet-}}\), and others. The results serve as the initial conditions for the subsequent chemical stage, where the various radiolytic species randomly diffuse and react until all track processes are complete. This stage is handled by our IRT program, utilizing the 'independent reaction times' (IRT) method [34; 35; 36]. This computationally efficient stochastic simulation technique applies the independent pairs approximation to simulate reaction times without following the trajectories of diffusing species. The implementation of this method has been described previously [37], and its accuracy in providing time-dependent chemical yields across a wide range of irradiation conditions has been validated through comparisons with full random flights (or step-by-step) Monte Carlo simulations that precisely follow reactant trajectories (for a review, see [31]). The reaction scheme, rate constants, and diffusion coefficients for reactive species in our IRT program for pure liquid water at 300 and 350 \({}^{\circ}\)C follow those used in previous studies [19; 25; 33; 38][PERSON] Beyond the critical point, we applied the SCW radiolysis database from [PERSON] et al. [39; 40], specifically using their reported reaction rate constants for the three temperatures selected for this study: 400, 500, and 600 \({}^{\circ}\)C at 25 MPa. Consistent with prior assumptions, we assumed that the diffusion coefficients for all species scaled proportionally with the self-diffusion of compressed SCW at these temperatures, as documented by [PERSON] et al. [41] and [PERSON] et al. [42]. Furthermore, the [PERSON] dielectric constants and the ionic products of SCW (\(K_{\mathrm{w}}\)) were obtained from [PERSON] et al. [23] and [PERSON] and [PERSON] [43], respectively. As discussed previously (see, e.g., [32]), in our calculations we also assumed that the thermalization distance of subexcitation-energy electrons (e\({}^{-}\)sub)--those with kinetic energies below \(\sim\)7.3 eV, the first-electronic excitation threshold of condensed water--and the prompt geminate electron-cation (H\({}_{2}\)O\({}^{\bullet+}\)) recombination occurring prior to thermalization of the e\({}^{-}\)sub are influenced solely by changes in water density at all selected temperatures above 400 \({}^{\circ}\)C.  
From a microscopic perspective, we opted to overlook the heterogeneous structural nature of SCW [44], which arises from the existence of large local density fluctuations (or water 'clustering') associated with criticality. In our simulations, we treated the overall instantaneous representation of SCW as a uniform medium, characterized by a mean density equal to the bulk water density (\(\rho\)). Finally, we accounted for the fact that the three considered recoil protons completely stopped in the water due to their limited ranges. Using the SRIM software (version SRIM-2013, see [PERSON] et al. [45]), we calculated their trajectories and energies as functions of penetration depth in SCW.