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We propose the Extended Integrated Symmetry Algebra (EISA) as an exploratory effective field theory (EFT) model for investigating aspects of quantum mechanics and general relativity unification, augmented by the Recursive Info-Algebra (RIA) extension that incorporates dynamic recursion through variational quantum circuits (VQCs) minimizing losses involving Von Neumann entropy and fidelity. EISA’s triple superalgebra AEISA = ASM × AGrav × AV ac encodes Standard Model symmetries, gravitational norms, and vacuum fluctuations, while RIA optimizes information loops for emergent quantum field dynamics without invoking extra dimensions. Transient processes like virtual pair rise-fall are coupled to a scalar phi in a modified Dirac equation, potentially sourcing curvature and initial phase transitions. To explore these ideas, we implement four numerical simulations in PyTorch. Recursive entropy stabilization (c1b.py) evolves noisy matrices, achieving entropy reduction from ∼ 0.1633 to ∼ 0.1133 (30.6% average reduction , with standard deviation <1% across multiple runs with varying seeds ) and fidelity up to 0.9478. Transient fluctuations (c2a.py) model ϕ(t) via RNN, yielding GW frequencies around 1017 Hz for original parameters and tuned to 10-16 Hz in adjusted runs (std deviation ∼ 4.98% for curvature), with CMB soliton deviations ∼ 6 × 10-8, addressing concerns on frequency matching by tuning (based on EFT parameter scanning, e.g., varying τP ) to nHz-mHz range for PTA/LISA sensitivity motivated by multi-messenger observations [30]. Particle spectra (c3a1.py) compute hierarchies (∼ 105) and constants like α ≈ 0.0073529 (0.76% CODATA error) via gradient descent. Cosmic evolution (c4a.py) integrates Friedmann with RIA densities using ODE solvers, simulating late H (CMB norm) ∼ 0.84, with GW peak ∼ 10-8 Hz and soliton deviations 2 × 10-08. EISA-RIA suggests observables like fractal masses (∼ 1.618, linked to conformal symmetry [34]) and collider anomalies, proposing a pathway for testing in the multi-messenger era, though further validation is required.