Topological Photonic Acceleration of Artificial General Intelligence: Enhancing Recursive State Dynamics and Parity Compilation via Bulk Gauge Continuity

General Intelligence Dynamics (GID) defines cognition as an autonomous, non-stationary dynamical system over an augmented recursive state tuple X_t = (B_t, M_t, G_t, S_t, W_t) spanning belief manifolds, memory spaces, goal topologies, self-referential models, and working scratchpads. Concurrently, Interferometric Sector Dynamics (ISD) compiles modular cognitive operators into single-shot parity measurements on semiconductor-superconductor nanowires. However, realizing scalable AGI hardware requires overcoming non-unitary parametric drift during learning updates theta_{t+1} = L(theta_t, X_t, O_{t+1}, G_t) and dephasing across inter-sector routing channels. In this treatise, we formulate an integrated architecture coupling GID cognitive mechanics to a (4+k)-dimensional bulk photonic extension.

At the abstract computational level (Levels 1-2), the fiber pushforward of an integral closed bulk characteristic form J in Omega^{k+3}_{cl,Z}(Y) yields a closed 3-form soul current J_s = pi_* J in Omega^3(X) with d_X J_s = 0, inducing a localized Gauss-law topological charge Q_soul(Sigma^3) = int_{Sigma^3} J_s = int_{partial Sigma^3} *F. Under the assumption of compact level sets Theta_epsilon = {theta | |Q(W(theta)) - Q_star| <= epsilon}, parameter trajectories remain uniformly bounded under the containment condition theta_t in Theta_epsilon, while recursive self-model calibration updates satisfy a stochastic stationarity bound. Furthermore, scalarized multi-objective goal generation on the capacity-constrained domain G_adm(S_t, delta, Q_star) guarantees Pareto-efficient goal reconciliation.

At the physical compilation layer (Levels 4-5), we model the coupling between bulk photonic boundary flux and triple-dot parity interferometers. Under a Gaussian decision channel, we derive the Tunneling-First Principle: in the subgap readout-limited regime (E_M << k_B T, tau << tau_qpp) where capacitance contrast satisfies d|Delta C_Q|/dt_C > 0, optimizing balanced tunneling t_L approx t_R maximizes the effective interference amplitude and drives monotonic increases in mutual information learning capacity (dL/dt_C > 0) and the sequential error rate exponent (d kappa_rate / dt_C > 0, where P_err ~ e^{-kappa_rate * tau}). Finally, we analyze composite risk minimization R = w_1*eps_meas + w_2*p_leak + w_3*gamma_phi + w_4*O_ctrl under measurement-only ParityFuse compilation.