Decoding the Physics of Intelligence in Complex Adaptive Systems.

Algoplexity is a long-term research initiative dedicated to establishing a new field of study: Algorithmic Cognitive Systems.

We posit that complex adaptive systems—whether financial markets, biological swarms, or social institutions—are not merely stochastic processes. They are Distributed Computational Entities possessing system-level cognition. Our mission is to develop the Theory, Instrumentation, and Agency required to understand and navigate the "Dancing Landscape" of these systems.

Our work unifies seven foundational theories into a coherent engineering framework (The "Tower" Hypothesis):

1. Algorithmic Information Dynamics (AID): The physics of causal structure and complexity (Zenil).
2. Universal Artificial Intelligence (UAI): The mathematics of optimal general intelligence (Hutter).
3. Nested Learning Theory (NL): The mechanics of hierarchical optimization and continuum memory (Behrouz).
4. Quantum-Complex-Entropic-Adaptive (QCEA) Theory: The thermodynamics of strategic viability (Williams).
5. Entropic Valuation: The reconstruction of value based on Epistemic Fragility ($dH/d\tau$) rather than temporal decay.
6. Coherence Theory ($\Lambda / \eta_K$): The rigorous condition for eco-evolutionary stability (Williams). We define regime collapse as a deterministic threshold where Environmental Drift ($\Lambda$) exceeds the Hereditary Update Rate ($\eta_K$).
7. Graph Neural Cellular Automata (GNCA): The topology of distributed computation (Grattarola).

We are executing a "Reduction-Synthesis" cycle: zooming in from the macro-swarm to the atomic unit of cognition (The Agent) to solve the problem of Perception, before zooming out to model the distributed network (The Society).

• Discovery: Financial markets contain discoverable algorithmic structures (Rule 131, Pair 35/115) that are invisible to standard econometrics.
• Method: Genetic Algorithms (Search) + MILS Encoding.
• Legacy: Established the Ontology (Markets are Computers) but lacked Real-Time Diagnosis.
• Artifact: Discovering Hidden Structures in Stock Market Data.

• Discovery: "Less is More." High-resolution statistical multivariate models (VAR) fail to detect breaks due to parameter explosion. A simple univariate proxy (Predictive Error) works better.
• The Physics: Identified the "Pain" signal ($dP/dt$) necessary for the inner-loop optimizer, marking the point where the environment outpaces the model ($\Lambda > \eta_K$).
• Artifact: SSRN Working Paper

• Discovery: Taxonomy of Cognitive Failure.
  • Cognitive Saturation (Rule 54 / Colliding Solitons): The market "thinks itself into a corner."
  • Cognitive Overload (Rule 60 / Fractal Shattering): The shock outruns the mixing time.
• The NL Perspective: Engineered the Slow Context Flow. The AIT Physicist compresses the long-term computational regime into a tractable state vector, acting as a "Lyapunov Meter" for the system.
• Validation: Achieved -29.95% early-warning lead time on unseen out-of-sample data (The Generalization Inversion).

• Discovery: Entropic Valuation & Plasticity. An agent that adjusts its "Wingspan" (Uncertainty) based on the Physicist's diagnosis outperforms statistical baselines by +19.0%.
• The Physics: Solves the Frequency Gap via Nested Optimization. We define viability as the ratio between market bandwidth ($\Lambda$) and agent plasticity ($\eta_K$).
  • System 0 (The Coherence Veto): Hard-coded survival prior (Lyapunov Prior $\lambda > 0$) when $\Lambda \gg \eta_K$ (Cold Start/Crash). This prevents "Ruin Events."
  • System 1 (The Iron Dome): Fast homeostatic reflex enforcing variance floors.
  • System 2 (The Physicist): Slow context compression adapting policy when $\Lambda \approx \eta_K$.
• Method: QCEA-AIXI Agent. A cybernetic loop utilizing Entropic Valuation to trigger zero-shot policy shifts.

• Hypothesis: Systemic Risk is a Graph Neural Cellular Automata (GNCA). A market crash is the propagation of a specific computational state (Rule 54/Default) across the asset topology.
• The Scientific Goal: To engineer Deep GNCA Titans [Behrouz et al., 2025]—graph nodes that are self-referential learners. We will simulate how "Flash Crashes" emerge when these self-modifying agents synchronize their internal optimization logic, causing Global Coherence Loss.
• The Architectural Trinity:
  1. r-GCA (Relation-Based Neighborhoods): Moving beyond physical adjacency to model influence across abstract financial topologies [Grattarola et al.].
  2. E(n)-Equivariance: Ensuring the model learns isotropic rules that hold regardless of the specific asset permutation [Gala et al.].
  3. DiffLogic (Differentiable Logic): Utilizing differentiable logic gates (AND/OR/XOR) to extract human-readable boolean rules for governance [Miotti et al.].

• The Theory: Market stability relies on Cognitive Diversity. When AI agents converge on identical strategies (or identical Update Rules per NL theory), the system becomes rigid ($\eta_{Hive} \to 0$).
• The Simulation: We will use GNCA to model this Strategy Convergence. By simulating the network over long time horizons, we aim to prove that "Flash Crashes" are the inevitable mathematical result of homogenized decision rules in a connected graph.

• The Theory: Leadership is the stewardship of system topology.
• The Tool: A Systemic Dashboard. Using the GNCA to visualize how "Cognitive Saturation" (information overload) spreads through an organization's communication network, allowing leaders to intervene before the graph loses coherence.

• The Theory: The economy is a non-equilibrium system of interacting automata.
• The Model: Modeling supply chains not as input-output matrices, but as Evolving Computation. We track how shocks (Rule 60) propagate through the global trade network, testing which topologies are robust to "Fractal Shattering."

To ensure unassailable reproducibility, all Horizons operate on immutable scientific benchmarks.

• Algoplexity Structural Break Benchmark: The 1D Time Series corpus (Horizon 0/1).
• QCEA Adaptive Agent Benchmark: The 2D "Dancing Landscape" corpus (Horizon 2).

1. Behrouz, A., et al. (2025). Nested Learning: The Illusion of Deep Learning Architectures. NeurIPS 2025. (Theoretical basis for Continuum Memory and Titans).
2. Williams, C. F. (2025b). Eco-evolutionary regime transitions as coherence loss in hereditary updating. arXiv/Preprint. (Theoretical basis for Coherence Threshold $\Lambda / \eta_K$).
3. Zenil, H., & Adams, A. (2022). Algorithmic Information Dynamics of Cellular Automata. arXiv:2112.13177. (Foundation for AID).
4. Hutter, M., Quarel, D., & Catt, E. (2024). An Introduction to Universal Artificial Intelligence. CRC Press. (Foundation for UAI).
5. Williams, C. F. (2025a). Strategy as Ontology: QCEA-P and QCEA-T Formalised Mathematically. SSRN Electronic Journal. (Strategic Framework).
6. Grattarola, D., Livi, L., & Alippi, C. (2021). Learning Graph Cellular Automata. NeurIPS 2021. (Topology foundation for Horizon 3).

7. Mak, Y. W. (2023). Discovering Hidden Structures in Stock Market Data using Algorithmic Generative Modeling. Master's Thesis. DOI: [10.13140/RG.2.2.22740.46722].
8. Algoplexity. (2025a). The Somatic Marker of Markets: Falsifying Statistical Complexity in Structural Break Detection. ResearchGate. DOI: [10.13140/RG.2.2.19275.25122].
9. Algoplexity. (2025b). The Computational Phase Transition: Decoding the Cognitive State of Financial Markets via Algorithmic Information Dynamics. arXiv/In Submission.

10. Farmer, J. D., & Skouras, S. (2013). An ecological perspective on the future of computer trading. Quantitative Finance, 13(3). (Basis for UCL pillar: Algorithmic Monoculture).
11. ANU School of Cybernetics. (2021). Redefining 21st Century Leadership: A Cybernetic Approach. Menzies Foundation White Paper. (Basis for ANU pillar: Cybernetic Governance).
12. Arthur, W. B. (2021). Foundations of Complexity Economics. Nature Reviews Physics, 3. (Basis for Oxford INET pillar: Evolutionary Economics).

13. Burtsev, M. S. (2024). Learning Elementary Cellular Automata with Transformers. arXiv:2412.01417. (Identified the Receptive Field Limit).
14. Tesfaldet, M., et al. (2022). Attention-based Neural Cellular Automata (ViTCA). NeurIPS 2022. (Solving long-range dependency via Attention).
15. Gala, G., et al. (2023). E(n)-equivariant Graph Neural Cellular Automata. arXiv:2301.10497. (Ensuring topological robustness via symmetry).
16. Miotti, P., et al. (2024). Differentiable Logic Cellular Automata. arXiv. (Extracting interpretable boolean rules for governance).

If you utilize the Algoplexity framework or dataset in your research, please cite the meta-program:

@misc{algoplexity_program,
  author = {Mak, Yeu Wen},
  title = {The Algoplexity Research Program: Foundations of Algorithmic Cognitive Systems},
  year = {2025},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/algoplexity/algoplexity}}
}