Emergence of Gravity from QCD Mass Generation: A Unified Framework Based on Fermion–Boson Duality, Auxiliary Metrics, and ETC Phase Symmetry

Changes in Version 2 Version 2 substantially revises and extends the theoretical framework of the original manuscript. The main conceptual focus has been shifted from a QED/electromagnetic-field statistical phase transition to a QCD-based mechanism for the emergence of gravity. In particular, the revised version emphasizes the empirical fact that the dominant part of the mass of ordinary matter originates from QCD dynamics, and reformulates the gravitational source as arising from mass terms generated by a fermion–boson duality statistical phase transition in QCD. The previous electron–photon formulation has been replaced by a quark–gluon FBD-QCD formulation. The revised manuscript introduces two independent transition functions for the quark and gluon sectors, (T_q(E)) and (T_g(E)), and describes the effective channels (q_F), (q_B), (g_F), and (g_B). This provides a more natural framework for connecting dynamical mass generation, hadron masses, and spacetime curvature. A major addition in Version 2 is the generally covariant FBD-QCD Lagrangian. This Lagrangian is explicitly separated into two sectors: a standard (SU(3)_c) gauge-invariant gauge sector and a gravitational-source sector consisting of B-type quark and gluon mass terms. The gravitational-source sector is interpreted as generating an effective energy–momentum tensor, which is inserted into the right-hand side of the standard Einstein equation while leaving the geometric left-hand side unchanged. The revised version also introduces and clarifies the two-metric structure based on the auxiliary metrics (g_Γ) and (g_Ω). In this formulation, (g_Ω) selects the transverse gauge-sector degrees of freedom, while (g_Γ-g_Ω) selects the complementary time/longitudinal degrees of freedom that contribute to massification. This structure is used to explain how the four polarization degrees of freedom of a B-type gluon field are divided between the gauge sector and the gravitational-source sector. Figure 3 has been completely revised. In the original version, Figure 3 illustrated a QED-like statistical phase transition inside atoms. In Version 2, Figure 3 now illustrates the distribution of the four polarization degrees of freedom of the B-type gluon field into transverse and time/longitudinal components by means of the auxiliary metrics (g_Ω) and (g_Γ-g_Ω). The figure has also been adjusted so that it fits properly within the page layout. Version 2 further strengthens the connection with the author’s hadron-mass framework. The revised manuscript explains that the same FBD-QCD action functional can be read in two complementary ways: as a hadron-mass formula in the QCD application, and as a source of the energy–momentum tensor in the gravitational interpretation. The empirical reconstruction of meson and baryon masses is therefore positioned as supporting evidence for the same underlying action functional. An additional interpretive layer has been added through the unified field function (U(E,t)), which connects FBD statistical weights with ETC phase symmetry. This function provides a field-level interpretation in which matter, mass, and spacetime appear as different limiting regimes of a single two-phase structure. Overall, Version 2 changes the manuscript from a primarily QED-based proposal into a QCD-centered theory of gravity emergence. It clarifies the role of dynamical mass generation, introduces a covariant FBD-QCD Lagrangian, connects the framework to hadron-mass phenomenology, revises the figures accordingly, and improves the logical connection between QCD, mass generation, and spacetime curvature.