References & citations

The work the stack rests on. Each group is a body of theory or practice that contributes a value, a constraint, or an axis to the coordinate space.

The OpenIE periodic stacks

The sibling projections. The same axes recur — T inherits from the compute stack; V is shared with synthesis and data.

  1. Charlot, D. (2026). The Periodic Stack of Computation v2. OpenIE.
  2. Charlot, D. (2026). The Periodic Stack of Digital Information Synthesis. OpenIE.
  3. Charlot, D. (2026). The Periodic Stack of Data Systems. OpenIE.
  4. Charlot, D. (2026). The Periodic Stack of Information. OpenIE.
  5. Charlot, D. (2026). The Periodic Tensor of Structured Reality. OpenIE.

Foundations of state machines

The lineage that gave hierarchy, orthogonality, and broadcast to discrete-event control.

  1. Turing, A. M. (1936). On Computable Numbers, with an Application to the Entscheidungsproblem. Proceedings of the London Mathematical Society.
  2. Mealy, G. H. (1955). A Method for Synthesizing Sequential Circuits. Bell System Technical Journal.
  3. Moore, E. F. (1956). Gedanken-experiments on Sequential Machines. Automata Studies, Princeton University Press.
  4. Harel, D. (1987). Statecharts: A Visual Formalism for Complex Systems. Science of Computer Programming 8(3), 231–274.
  5. Drusinsky, D. (2006). Modeling and Verification Using UML Statecharts. Elsevier.

Concurrent state — process calculi and Petri nets

The formal vocabularies for state that runs in parallel.

  1. Petri, C. A. (1962). Kommunikation mit Automaten. PhD thesis, University of Bonn.
  2. Hoare, C. A. R. (1978). Communicating Sequential Processes. Communications of the ACM 21(8), 666–677.
  3. Milner, R. (1980). A Calculus of Communicating Systems. LNCS 92, Springer.
  4. Milner, R., Parrow, J., & Walker, D. (1992). A Calculus of Mobile Processes, I & II. Information and Computation 100(1).
  5. Bergstra, J. A., & Klop, J. W. (1984). Process Algebra for Synchronous Communication. Information and Control 60(1–3).

Actor model and isolated state

State as an architectural boundary — shared-nothing, message-passing, supervised.

  1. Hewitt, C., Bishop, P., & Steiger, R. (1973). A Universal Modular ACTOR Formalism for Artificial Intelligence. IJCAI.
  2. Agha, G. (1986). Actors: A Model of Concurrent Computation in Distributed Systems. MIT Press.
  3. Armstrong, J. (2003). Making Reliable Distributed Systems in the Presence of Software Errors. PhD thesis, Royal Institute of Technology, Stockholm.

Discrete-event simulation

The formalism for systems whose state advances on events, not on a clock.

  1. Zeigler, B. P. (1976). Theory of Modeling and Simulation. Wiley. (DEVS formalism)
  2. Zeigler, B. P., Praehofer, H., & Kim, T. G. (2000). Theory of Modeling and Simulation, 2nd ed. Academic Press.
  3. Barros, F. J. (1995). Dynamic Structure Discrete Event System Specification. Proceedings of the Winter Simulation Conference.

Specification and verification

Treating state as a mathematical object — provable, checkable, reproducible.

  1. Lamport, L. (1994). The Temporal Logic of Actions. ACM Transactions on Programming Languages and Systems 16(3).
  2. Lamport, L. (2002). Specifying Systems: The TLA⁺ Language and Tools for Hardware and Software Engineers. Addison-Wesley.
  3. Klein, G., et al. (2009). seL4: Formal Verification of an Operating-System Kernel. SOSP '09.

Distributed state and complexity

What changes when state crosses a machine boundary, and what it costs the program when it does not have to.

  1. Helland, P. (2007). Life Beyond Distributed Transactions: An Apostate's Opinion. CIDR 2007 (reprinted ACM Queue, 2016).
  2. Helland, P. (2005). Data on the Outside vs. Data on the Inside. CIDR 2005.
  3. Moseley, B., & Marks, P. (2006). Out of the Tar Pit. (Functional Relational Programming as a complexity-minimizing architecture.)

Data-oriented and game-AI state

State organized for the substrate it runs on, and state organized to make decisions visible.

  1. Bilas, S. (2002). A Data-Driven Game Object System. Game Developers Conference. (Early ECS articulation.)
  2. Marzinotto, A., Colledanchise, M., Smith, C., & Ögren, P. (2014). Towards a Unified Behavior Trees Framework for Robot Control. ICRA 2014.
  3. Colledanchise, M., & Ögren, P. (2018). Behavior Trees in Robotics and AI: An Introduction. CRC Press.

Memory, context, understanding

The cognitive-science vocabulary the temporal reading rests on — the canonical decompositions of what state holds across the past, the present, and the future.

  1. Atkinson, R. C., & Shiffrin, R. M. (1968). Human Memory: A Proposed System and Its Control Processes. In K. W. Spence & J. T. Spence (Eds.), The Psychology of Learning and Motivation, vol. 2.
  2. Tulving, E. (1972). Episodic and Semantic Memory. In E. Tulving & W. Donaldson (Eds.), Organization of Memory. Academic Press.
  3. Baddeley, A. D., & Hitch, G. (1974). Working Memory. In G. H. Bower (Ed.), The Psychology of Learning and Motivation, vol. 8.
  4. Squire, L. R. (1992). Declarative and Nondeclarative Memory: Multiple Brain Systems Supporting Learning and Memory. Journal of Cognitive Neuroscience 4(3).
  5. Baddeley, A. (2000). The Episodic Buffer: A New Component of Working Memory? Trends in Cognitive Sciences 4(11).
  6. Minsky, M. (1974). A Framework for Representing Knowledge. MIT AI Memo 306.
  7. Schank, R. C., & Abelson, R. P. (1977). Scripts, Plans, Goals and Understanding: An Inquiry into Human Knowledge Structures. Lawrence Erlbaum.
  8. McCarthy, J., & Hayes, P. J. (1969). Some Philosophical Problems from the Standpoint of Artificial Intelligence. Machine Intelligence 4. (The frame problem.)
  9. Tolman, E. C. (1948). Cognitive Maps in Rats and Men. Psychological Review 55(4).
  10. Clark, A., & Chalmers, D. (1998). The Extended Mind. Analysis 58(1).
  11. Hutchins, E. (1995). Cognition in the Wild. MIT Press. (Distributed cognition.)
  12. Rowlands, M. (2010). The New Science of the Mind: From Extended Mind to Embodied Phenomenology. MIT Press. (4E cognition.)

Predictive processing and active inference

The framework that treats understanding the future as the central operation of cognition — generative models, prediction error, action as inference.

  1. Friston, K. (2010). The Free-Energy Principle: A Unified Brain Theory? Nature Reviews Neuroscience 11(2).
  2. Clark, A. (2013). Whatever Next? Predictive Brains, Situated Agents, and the Future of Cognitive Science. Behavioral and Brain Sciences 36(3).
  3. Clark, A. (2015). Surfing Uncertainty: Prediction, Action, and the Embodied Mind. Oxford University Press.
  4. Parr, T., Pezzulo, G., & Friston, K. J. (2022). Active Inference: The Free Energy Principle in Mind, Brain, and Behavior. MIT Press.

Cognitive architectures and the Common Model

Integrated systems that hold memory, context, and decision under one roof — and the convergent abstract model the field has settled on as their shared structure.

  1. Newell, A. (1990). Unified Theories of Cognition. Harvard University Press.
  2. Anderson, J. R. (2007). How Can the Human Mind Occur in the Physical Universe? Oxford University Press. (ACT-R.)
  3. Laird, J. E. (2012). The Soar Cognitive Architecture. MIT Press.
  4. Sun, R. (2016). Anatomy of the Mind: Exploring Psychological Mechanisms and Processes with the CLARION Cognitive Architecture. Oxford University Press.
  5. Rosenbloom, P. S., Demski, A., & Ustun, V. (2016). The Sigma Cognitive Architecture and System: Toward Functionally Elegant Grand Unification. Journal of Artificial General Intelligence 7(1).
  6. Franklin, S., Madl, T., D'Mello, S., & Snaider, J. (2014). LIDA: A Systems-level Architecture for Cognition, Emotion, and Learning. IEEE Transactions on Autonomous Mental Development 6(1).
  7. Laird, J. E., Lebiere, C., & Rosenbloom, P. S. (2017). A Standard Model of the Mind: Toward a Common Computational Framework across Artificial Intelligence, Cognitive Science, Neuroscience, and Robotics. AI Magazine 38(4).

Computational memory architectures

Engineered systems that have given a substrate explicit memory — read, write, retain, recall. The line of work the temporal cell already partially occupies.

  1. Hawkins, J., with Blakeslee, S. (2004). On Intelligence. Times Books. (Hierarchical Temporal Memory.)
  2. Weston, J., Chopra, S., & Bordes, A. (2014). Memory Networks. arXiv:1410.3916.
  3. Graves, A., Wayne, G., & Danihelka, I. (2014). Neural Turing Machines. arXiv:1410.5401.
  4. Graves, A., et al. (2016). Hybrid Computing Using a Neural Network with Dynamic External Memory. Nature 538(7626). (Differentiable Neural Computer.)
  5. Hawkins, J. (2021). A Thousand Brains: A New Theory of Intelligence. Basic Books.