# CEE Appendix F: Candidate Computational Models Survey v1 ## 1. Introduction This document summarizes the initial survey of candidate computational model classes considered at the outset of the Computational Emergence & EQR (CEE) project v1 (Sprint CEE-1). The goal is to identify promising foundational structures capable of generating emergent physical phenomena while also being compatible with the principles of the Emergent Quantization from Resolution (EQR) v1.0 framework (`EQR v1.0 Framework Report.md`), particularly its requirements S1-S5. This assessment is guided by [[CEE-B-OMF-v1]] and [[CEE-E-LessonsLearned-v1]]. ## 2. Candidate Model Classes & Assessment ### 2.1. Graph/Network Rewriting Systems (e.g., WPP) * **Description:** States = hypergraphs; Dynamics = discrete subgraph replacement rules. * **Emergence Potential:** Strong (spacetime, causality, particle-like patterns). Background independent. * **EQR Compatibility:** Weak (S1/S4 Hilbert/Linearity/Born rule major challenge; S3 Basis selection unclear). High risk of repeating IO failures without novel QM emergence mechanism. * **Assessment:** High priority for structure, but QM/EQR compatibility is critical hurdle. ### 2.2. Quantum Cellular Automata (QCA) / Quantum Walks (QW) * **Description:** Quantum states on discrete lattice/graph; Unitary local evolution. * **Emergence Potential:** Weak (assumes background lattice). Can support particle-like excitations. * **EQR Compatibility:** Strong for S1/S4 (built-in QM). Weak for S3/P5 (EQR process not emergent). Background dependence issue. * **Assessment:** Less aligned with full emergence goal. ### 2.3. Causal Set Theory (+ Dynamics) * **Description:** Spacetime = discrete partial order; Dynamics = stochastic growth. * **Emergence Potential:** Strong (spacetime manifold, Lorentz invariance). Background independent. * **EQR Compatibility:** Weak/Unclear (formulating QM/EQR on causal sets is challenging). * **Assessment:** Promising for spacetime, but QM/EQR integration needs major development. ### 2.4. Algorithmic / Information-Theoretic Models * **Description:** Universe as computation; laws from information/complexity constraints. * **Emergence Potential:** Abstract (complexity, statistical mechanics). * **EQR Compatibility:** Weak/Abstract (potential links via S5/P4, but S1/S3/S4 connection unclear). * **Assessment:** Too abstract currently; lacks clear path to concrete physics/EQR structure. ### 2.5. Generalized Iterative Systems (Beyond IO v4.2) * **Description:** Iterative rules $S_{t+1}=F(S_t)$ on potentially different state spaces (networks, functions) aiming to solve linearity/Born rule problem (e.g., via Koopman + envariance). * **Emergence Potential:** Dependent on specific model. * **EQR Compatibility:** Aims for compatibility by design. S3 (attractors) natural. S1/S4 (linearity/Born rule) remains key challenge requiring innovation (as identified in IO v4.2/EFD). * **Assessment:** Direct continuation of a promising but stalled thread. Success hinges on solving the identified formal QM emergence problem. ## 3. Prioritization and Conclusion (from Sprint CEE-1) * **Graph Rewriting Systems (GRS)** offer the strongest current potential for *emergent structure*. Priority: Investigate GRS focusing explicitly on integrating/deriving QM/EQR compatibility. * **Generalized Iterative Systems (GIS)** offer strongest potential for *EQR compatibility*. Priority: Keep as secondary path, contingent on novel ideas for solving linearity/Born rule problem. **Recommendation:** Initiate investigation into **Graph Rewriting Systems**, focusing on the QM/EQR interface.