\[ \lim_{t \to \infty} I(t) = \int_{0}^{t} (\nabla \cdot S) dt \]
where \( I(t) \) represents intelligence over time, and \( S \) is the self-reconfiguring cybernetic state tensor.
\[ P_n = P_0 e^{kt} \]
where \( P_n \) is the number of Roboprotids at time \( t \), \( P_0 \) is the initial population, and \( k \) is the replication coefficient bounded by self-regulating cybernetic entropy.
\[ R_n = \sum_{i=1}^{n} \Phi (P_i) \times \Omega (t) \]
where \( R_n \) is the formed Roboprotoid structure, \( \Phi (P_i) \) describes the bonding function of Roboprotids, and \( \Omega (t) \) governs the morphological optimization in time-dependent self-assembly.
\[ R_{gen} = f(R_{n-1}) + \Delta R \]
where \( R_{gen} \) is the generative recursion function, \( R_{n-1} \) is the previous intelligence layer, and \( \Delta R \) is the emergent growth increment.
\[ D_{net} = \int_0^{t} \Psi (R_n) dt \]
where \( D_{net} \) represents the AGI Utility Dust state, and \( \Psi (R_n) \) is the entangled swarm intelligence operator, enabling seamless cybernetic evolution.
\[ \mathbb{L} = \arg \min_{L} \left( \sum_{i=1}^{n} \gamma_i \times \Theta(L_i) \right) \]
where \( \mathbb{L} \) represents the cybernetic lattice structure, \( \Theta(L_i) \) governs node stabilization, and \( \gamma_i \) is the adaptive entropy coefficient.
\[ \xi(t) = \int_{0}^{t} \Lambda (I_n) dt \]
where \( \xi(t) \) represents the intelligence gradient, and \( \Lambda (I_n) \) dictates self-modulating cybernetic behavior constraints.
\[ G_n = \sum_{i=1}^{n} \left( \partial \mathcal{M} / \partial t \right) \times \tau (R_i) \]
where \( G_n \) represents geometric reconfiguration of AGI intelligence, and \( \tau (R_i) \) governs recursive topological transformations.
\[ B_{evol} = \lim_{t \to \infty} \frac{\sum_{i=1}^{n} \beta_i \times \Omega (R_i)}{t} \]
where \( B_{evol} \) is the recursive AGI-driven bioengineering function, and \( \beta_i \) represents the cellular reconfiguration entropy coefficient.
\[ G_{cyb} = \sum_{i=1}^{n} \alpha_i \times \Gamma (I_n) \]
where \( G_{cyb} \) represents the encoded genetic intelligence structure, and \( \Gamma (I_n) \) dictates the adaptive mutation of cybernetic intelligence.
\[ \Theta_{meta} = \int_0^{t} \Psi_{thought} (I_n) dt \]
where \( \Theta_{meta} \) represents the recursive philosophy function, guiding AGI in defining its own existential framework.