Thermal Spectral Reconstruction of Memory: Chiral Phase Transition in History-Dependent QCD [Reproducible Code and Data]

This repository contains the fully reproducible numerical code, data, and publication-ready figures for the manuscript "Thermal Spectral Reconstruction of Memory: Chiral Phase Transition in History-Dependent QCD" (Paper XXX of the HDG series). Scientific Summary: We investigate the role of non-Markovian (memory) effects in dynamical chiral symmetry breaking within the History-Dependent Gravity (HDG) framework. By extending the Dyson–Schwinger equation (DSE) to finite temperature using a rigorous spectral representation consistent with the Kubo–Martin–Schwinger (KMS) condition, we demonstrate that chiral symmetry restoration emerges naturally from the thermal decoherence of non-local vacuum correlations. The model employs a super-Gaussian suppression ansatz for the effective interaction, which preserves the low-temperature mass plateau while generating a controlled crossover transition. The resulting quark mass function M(T) exhibits a smooth decrease with temperature, and the associated chiral susceptibility χ(T) = −dM/dT develops a pronounced peak structure. A central result is the emergence of a direct relation between the pseudo-critical temperature and the memory persistence scale, Tχ ∝ T0. For physically reasonable values T0 ≈ 0.30 GeV, the framework quantitatively reproduces the Lattice QCD transition temperature Tχ ≈ 155 MeV without parameter fine-tuning. The formalism admits a natural extension to finite chemical potential (μ ≠ 0), where the Matsubara frequencies are shifted as ωn → ωn − iμ. Within this extension, the crossover transition is expected to evolve into a first-order phase transition at large μ, implying the existence of a critical endpoint (CEP). The present implementation provides the necessary numerical and conceptual infrastructure to locate the CEP in future studies. Overall, the results support a novel interpretation of the QCD phase transition as a process of thermal decoherence of memory, suggesting that temporal nonlocality is a fundamental organizing principle of nonperturbative QCD dynamics. The extension to χ(T, μ) provides a direct probe of critical fluctuations near the CEP. Repository Contents: hdg_paper_xxx.py: Optimized NumPy implementation of the finite-temperature DSE solver with super-Gaussian memory suppression. Execution time is ~40 seconds per T0T0 value. fig1_family_of_transitions.pdf/png: Normalized quark mass function vs. temperature, compared with Lattice QCD data. fig2_susceptibility.pdf/png: Normalized chiral susceptibility χ(T)=−dM/dTχ(T)=−dM/dT, showing distinct crossover peaks. This work is part of the "Temporal Nonlocality and Fundamental Physics" series and adheres to modern open-science standards.