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 Xt = (Bt, Mt, Gt, St, Wt) span- ning belief manifolds, memory spaces, goal topologies, self-referential models, and working scratchpads [1]. Concurrently, Interferometric Sector Dynamics (ISD) compiles modular cognitive operators into single-shot parity measurements on semiconductor-superconductor nanowires [2,6]. However, realizing scalable AGI hardware requires overcoming non-unitary parametric drift during learning updates θt+1 = L(θt, Xt, Ot+1, Gt) and dephasing across inter-sector routing channels [1,2]. In this treatise, we formulate an integrated architecture coupling GID cognitive mechanics to a (4 + k)-dimensional bulk photonic extension [1–3]. At the abstract computational level (Levels 1–2), the fiber pushforward of an integral closed bulk characteristic form J ∈Ωk+3 cl,Z (Y ) yields a closed 3-form soul current Js = π∗J ∈Ω3(X) with dXJs = 0, inducing a localized Gauss-law topological charge Qsoul(Σ3) = ∫︁ Σ3 Js = ∫︁ ∂Σ3 ∗F [3]. Under the assumption of compact level sets Θϵ = {θ | |Q(W(θ)) − Q⋆| ≤ϵ}, parameter trajectories remain uniformly bounded under the containment condition θt ∈Θϵ, while recursive self-model calibration updates satisfy a stochastic stationarity bound [1]. Furthermore, scalarized multi-objective goal generation on the capacity-constrained domain Gadm(St, δ, Q⋆) guarantees Pareto-efficient goal reconciliation [1]. At the physical compilation layer (Levels 4–5), we model the coupling between bulk pho- tonic boundary flux and triple-dot parity interferometers [2,3,6]. Under a Gaussian decision channel, we derive the Tunneling-First Principle: in the subgap readout-limited regime (EM ≪kBT, τ ≪τqpp) where capacitance contrast satisfies ∂|∆CQ|/∂tC > 0, optimizing balanced tunneling tL ≈tR maximizes the effective interference amplitude and drives mono- tonic increases in mutual information learning capacity (∂L/∂tC > 0) and the sequential error rate exponent (∂κrate/∂tC > 0, where Perr ∼e−κrateτ) [2]. Finally, we analyze com- posite risk minimization R = w1ϵmeas + w2pleak + w3γϕ + w4Octrl under measurement-only ParityFuse compilation [2]. 1

@article{deceuster2026_64-topological-photo,
  title = {Topological Photonic Acceleration of Artificial General Intelligence: Enhancing Recursive State Dynamics and Parity Compilation via Bulk Gauge Continuity},
  author = {De Ceuster, Peter},
  year = {2026},
  month = {02},
  institution = {SIG Labs},
  doi = {10.5281/zenodo.22165659},
  url = {https://peterdeceuster.uk/papers/64-topological-photonic-acceleration-of-artificial-general-intelligence-enhancing},
  note = {Full text available at https://peterdeceuster.uk/articenter/work/AInew.pdf}
}