Commitment Causal Sets and the Thermodynamic Recovery of Einstein Dynamics

This paper develops a Planck-regulated commitment causal-set framework for the thermodynamic recovery of Einstein dynamics. A commitment event is any physical interaction that produces durable downstream constraint; semantic observers form a special reconfigurable subclass, while ordinary nonsemantic interactions still contribute to causal, thermodynamic, and geometric structure. The construction separates the Planck substrate (E_Pl, ≺Pl, μ_Pl), which reconstructs metric geometry by causal order plus counting measure, from the commitment layer, which carries records, boundary anchors, comparison structure, heat flux, entropy, and stress-energy. Interaction influence is propagated by a raw kernel K_raw and saturated kernel K̂ = 1 − exp(−K_raw), with finite-budget decay over interaction distance. In a manifoldlike phase, the Planck causal substrate recovers the continuum metric g_μν, while commitment boundary anchors supply an entropy-area bridge δS∂com = α_com δA. The main result is a conditional Einstein-recovery theorem. Under local horizon equilibrium, universal commitment entropy density, Clausius thermodynamics δQ_com = T_U δS_∂com, flux-action stress compatibility, and on-shell conservation, the commitment stress tensor sources the Einstein equation G_μν + Λg_μν = 8πG_com T^com_μν, with effective coupling G_com = k_Bc³/(4ℏα_com). Deviations from exact recovery are organized by an obstruction tensor/vector separating order, density, kernel, anchor, entropy, heat, stress, Clausius, conservation, Planck-scale, nonequilibrium, and finite-size defects. The paper also gives a finite-size numerical protocol using causal-set dimension diagnostics, boundary-link area estimators, Benincasa–Dowker scalar curvature, trace-corrected null-flux reconstruction, and positive-slice obstruction norms. The result is a structured route from operational commitments and Planck-scale causal order to continuum Einstein dynamics, with all failures localized in named obstruction sectors.