Beyond Artificial Intelligence: The Mathematical Dynamics of General Intelligence — Recursive State-Space Dynamics, Self-Modeling, and Adaptive Goal Formation

Thanks to the hard work of the community the mathematics of AI and AGI have now been established. It is now time to focus on design, this paper will provide an angle to design AGI. While modular sector-gate dynamics and quantum state representations establish a candidate mathematical substrate for multi-domain routing [1, 2], treating quantum hard- ware directly as cognition remains a working hypothesis without an overarching, substrate- independent definition of general intelligence [1]. In this paper, we shift the core theoretical question from “how quantum hardware might implement AGI” to “what mathematical object constitutes an AGI.” We formulate General Intelligence Dynamics (GID), a formal mechanics of in- telligence defined by core dynamical mechanisms over an augmented recursive state tuple Xt = (Bt, Mt, Gt, St, Wt), spanning environmental belief states, internal memory struc- tures, structured goal topologies, self-referential models, and working computational scratch spaces. Under GID, cognition is formalized not as passive information routing or static re- ward optimization, but as an active, recursive dynamical loop governed by coupled equations of motion: Bt+1 = B(Bt, at, Ot+1, Wt), Mt+1 = M(Mt, Ot+1, Xt), St+1 = S(St, Xt, Mt, Ot+1), Gt+1 = Γ(Gt, St, Mt, Xt), Wt+1 = W(Wt, Xt, at), at = Π(Xt, θt), θt+1 = L(θt, Xt, Ot+1, Gt). We mathematically formalize: (1) closed-loop prediction-action-observation recursion separating external environmental states et ∈E from internal belief distributions Bt, (2) state-dependent internal transition operators Gij(Xt) that replace static circuits with belief- directed modular routing, building upon cross-sector interference models [1], (3) parametric learning dynamics yielding non-stationary transition kernels P(Xt+1|Xt, Ot+1; θt), (4) quan- titative self-modeling mappings St+1 = S(St, Xt, Mt, Ot+1) calibrated by self-performance divergence ES(t) = DKL(pt ∥ˆpt), (5) explicit structured goal-generation operators Γ : G × S × M × X →G over tuples (gi, ci, wi) and prove Pareto-optimal goal reconciliation on capacity-constrained domains, (6) formal cross-domain transfer operators T (τi →τj) and a counterfactual generality functional G = E(τi,τj)∼D2 ̸=[Pj(θ(i))−Pj(θ(0))] over ordered distinct task pairs, and (7) latent abstraction operators A : Dk →Z capturing shared structural invariances across task distributions. 1

@article{deceuster2026_68-beyond-artificial,
  title = {Beyond Artificial Intelligence: The Mathematical Dynamics of General Intelligence — Recursive State-Space Dynamics, Self-Modeling, and Adaptive Goal Formation},
  author = {De Ceuster, Peter},
  year = {2026},
  month = {02},
  institution = {SIG Labs},
  doi = {10.5281/zenodo.22126076},
  url = {https://peterdeceuster.uk/papers/68-beyond-artificial-intelligence-the-mathematical-dynamics-of-general},
  note = {Full text available at https://peterdeceuster.uk/articenter/work/agistates.pdf}
}