{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T04:21:51Z","timestamp":1787718111817,"version":"build-2784847793"},"reference-count":84,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T00:00:00Z","timestamp":1787529600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The pursuit of self-evolving AI raises a critical question: when is autonomous self-improvement sustainable rather than degenerative? Drawing an analogy to von Neumann\u2019s complexity threshold for self-reproducing automata, we argue that sustainable recursive self-improvement in large language models (LLMs) requires a functional analogue: introspection\u2014the system\u2019s capacity to simulate its own operations and target modifications. Grounded in Kleene\u2019s Second Recursion Theorem, we construct such introspective self-improvement programs and prove their key properties: completeness of self-modification, necessity of the reflective architecture, undecidability of improvement in general, and equivalence with Schmidhuber\u2019s G\u00f6del machine under a rewrite-equivalence notion, which transfers the global optimality guarantee. An empirical review, organized around these functional criteria, suggests that current LLMs exhibit only quasi-introspection.The available evidence does not establish complete introspection in the formal sense developed here, while pointing to several candidate structural bottlenecks, including incomplete self-access, feedforward processing, and limited computational depth. We outline architectural paths toward the threshold and discuss the safety implications of crossing it.<\/jats:p>","DOI":"10.3390\/e28090951","type":"journal-article","created":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T14:49:34Z","timestamp":1787582974000},"page":"951","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Self-Referential Introspection in Large Language Models: The Critical Threshold for Recursive Self-Improvement"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7402-7482","authenticated-orcid":false,"given":"Jiang","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Systems Science, Beijing Normal University, Beijing 100875, China"},{"name":"Swarma Research, Beijing 102300, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-9062-0383","authenticated-orcid":false,"given":"Bing","family":"Yuan","sequence":"additional","affiliation":[{"name":"Swarma Research, Beijing 102300, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-9084-8356","authenticated-orcid":false,"given":"Qian","family":"Zhang","sequence":"additional","affiliation":[{"name":"Swarma Research, Beijing 102300, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,24]]},"reference":[{"key":"ref_1","unstructured":"Fang, J., Peng, Y., Zhang, X., Wang, Y., Yi, X., Zhang, G., Xu, Y., Wu, B., Liu, S., and Li, Z. (2025). A Comprehensive Survey of Self-Evolving AI Agents: A New Paradigm Bridging Foundation Models and Lifelong Agentic Systems. arXiv."},{"key":"ref_2","unstructured":"Gao, H.A., Geng, J., Hua, W., Hu, M., Juan, X., Liu, H., Liu, S., Qiu, J., Qi, X., and Wu, Y. (2026). A Survey of Self-Evolving Agents: What, When, How, and Where to Evolve on the Path to Artificial Super Intelligence. arXiv."},{"key":"ref_3","unstructured":"Tao, Z., Lin, T.E., Chen, X., Li, H., Wu, Y., Li, Y., Jin, Z., Huang, F., Tao, D., and Zhou, J. (2024). A Survey on Self-Evolution of Large Language Models. arXiv."},{"key":"ref_4","first-page":"31","article-title":"Speculations Concerning the First Ultraintelligent Machine","volume":"Volume 6","author":"Alt","year":"1965","journal-title":"Advances in Computers"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Goertzel, B., and Pennachin, C. (2007). Levels of Organization in General Intelligence. Artificial General Intelligence, Springer.","DOI":"10.1007\/978-3-540-68677-4"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Shinn, N., Cassano, F., Gopinath, A., Narasimhan, K., and Yao, S. (2023, January 10\u201316). Reflexion: Language Agents with Verbal Reinforcement Learning. Proceedings of the NeurIPS 2023, New Orleans, LA, USA.","DOI":"10.52202\/075280-0377"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Madaan, A., Tandon, N., Gupta, P., Hallinan, S., Gao, L., Wiegreffe, S., Alon, U., Dziri, N., Prabhumoye, S., and Yang, Y. (2023, January 10\u201316). Self-Refine: Iterative Refinement with Self-Feedback. Proceedings of the NeurIPS 2023, New Orleans, LA, USA.","DOI":"10.52202\/075280-2019"},{"key":"ref_8","first-page":"13481","article-title":"Promptbreeder: Self-Referential Self-Improvement via Prompt Evolution","volume":"Volume 235","author":"Fernando","year":"2024","journal-title":"Proceedings of the 41st International Conference on Machine Learning (ICML 2024)"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Huang, J., Gu, S., Hou, L., Wu, Y., Wang, X., Yu, H., and Han, J. (2023, January 6\u201310). Large Language Models Can Self-Improve. Proceedings of the EMNLP 2023, Singapore.","DOI":"10.18653\/v1\/2023.emnlp-main.67"},{"key":"ref_10","first-page":"57905","article-title":"Self-Rewarding Language Models","volume":"Volume 235","author":"Yuan","year":"2024","journal-title":"Proceedings of the 41st International Conference on Machine Learning (ICML 2024)"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Yin, X., Wang, X., Pan, L., Lin, L., Wan, X., and Wang, W.Y. (2025). G\u00f6del Agent: A Self-Referential Agent Framework for Recursively Self-Improvement. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), Association for Computational Linguistics.","DOI":"10.18653\/v1\/2025.acl-long.1354"},{"key":"ref_12","unstructured":"Zhang, J., Hu, S., Lu, C., Lange, R.T., and Clune, J. (2026, January 23\u201327). Darwin G\u00f6del Machine: Open-Ended Evolution of Self-Improving Agents. Proceedings of the Fourteenth International Conference on Learning Representations (ICLR 2026), Rio de Janeiro, Brazil."},{"key":"ref_13","unstructured":"Huang, J., Chen, X., Mishra, S., Zheng, H.S., Yu, A.W., Song, X., and Zhou, D. (2024, January 7\u201311). Large Language Models Cannot Self-Correct Reasoning Yet. Proceedings of the Twelfth International Conference on Learning Representations, Vienna, Austria."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1038\/s41586-024-07566-y","article-title":"AI Models Collapse When Trained on Recursively Generated Data","volume":"631","author":"Shumailov","year":"2024","journal-title":"Nature"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Dohmatob, E., Feng, Y., and Kempe, J. (2024, January 10\u201315). Model Collapse Demystified: The Case of Regression. Proceedings of the Advances in Neural Information Processing Systems 37 (NeurIPS 2024), Vancouver, BC, Canada.","DOI":"10.52202\/079017-1490"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Acemoglu, D., Kong, D., and Ozdaglar, A. (2026, June 23). AI, Human Cognition and Knowledge Collapse. NBER Working Paper No. 34910. Available online: https:\/\/www.nber.org\/papers\/w34910.","DOI":"10.3386\/w34910"},{"key":"ref_17","unstructured":"Burks, A.W. (1966). Theory of Self-Reproducing Automata (John von Neumann), University of Illinois Press."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1080\/00207166808803030","article-title":"Three Approaches to the Quantitative Definition of Information","volume":"2","author":"Kolmogorov","year":"1968","journal-title":"Int. J. Comput. Math."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1145\/321356.321363","article-title":"On the Length of Programs for Computing Finite Binary Sequences","volume":"13","author":"Chaitin","year":"1966","journal-title":"J. ACM"},{"key":"ref_20","unstructured":"Hofstadter, D.R. (1979). G\u00f6del, Escher, Bach: An Eternal Golden Braid, Basic Books."},{"key":"ref_21","unstructured":"Kleene, S.C. (1952). Introduction to Metamathematics, North-Holland. Number 1 in Bibliotheca Mathematica."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Cutland, N.J. (1980). Computability: An Introduction to Recursive Function Theory, Cambridge University Press.","DOI":"10.1017\/CBO9781139171496"},{"key":"ref_23","unstructured":"Rogers, H. (1967). Theory of Recursive Functions and Effective Computability, MIT Press."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Goertzel, B., and Pennachin, C. (2007). G\u00f6del Machines: Fully Self-Referential Optimal Universal Self-Improvers. Artificial General Intelligence, Springer. Cognitive Technologies.","DOI":"10.1007\/978-3-540-68677-4"},{"key":"ref_25","first-page":"7","article-title":"The singularity: A philosophical analysis","volume":"17","author":"Chalmers","year":"2010","journal-title":"J. Conscious. Stud."},{"key":"ref_26","unstructured":"Yampolskiy, R.V. (2015). From Seed AI to Technological Singularity via Recursively Self-Improving Software. arXiv."},{"key":"ref_27","unstructured":"Yudkowsky, E. (2001). General Intelligence and Seed AI 2.3, Singularity Institute for Artificial Intelligence. Technical report."},{"key":"ref_28","unstructured":"Xia, P., Chen, J., Wang, H., Liu, J., Zeng, K., Wang, Y., Han, S., Zhou, Y., Zhao, X., and Chen, H. (2026). SkillRL: Evolving Agents via Recursive Skill-Augmented Reinforcement Learning. arXiv."},{"key":"ref_29","unstructured":"Zhou, Z., Cao, C., Feng, X., Li, X., Li, Z., Lu, X., Yao, J., Huang, W., Cheng, T.L., and Zhang, J. (2025). AlphaApollo: A System for Deep Agentic Reasoning. arXiv."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Ye, P., Yang, X., Feng, S., Zhang, S., Bai, L., Ouyang, W., and Hu, S. (2026, January 2\u20137). Nature-Inspired Population-Based Evolution of Large Language Models. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), San Diego, CA, USA.","DOI":"10.18653\/v1\/2026.acl-long.2044"},{"key":"ref_31","unstructured":"Zelikman, E., Lorch, E., Mackey, L., and Kalai, A.T. (2024, January 7\u20139). Self-Taught Optimizer (STOP): Recursively Self-Improving Code Generation. Proceedings of the COLM 2024, Philadelphia, PA, USA."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Qu, Y., Zhang, T., Garg, N., and Kumar, A. (2024, January 10\u201315). Recursive Introspection: Teaching Language Model Agents How to Self-Improve. Proceedings of the Advances in Neural Information Processing Systems 37 (NeurIPS 2024), Vancouver, BC, Canada.","DOI":"10.52202\/079017-1754"},{"key":"ref_33","unstructured":"Iacob, A., Jovanovi\u0107, A., Shen, W.F., Burkhardt, D., Kurmanji, M., Tastan, N., Sani, L., Venanzi, N.A.E., Odonnat, A., and Cao, Z. (2026). The Red Queen G\u00f6del Machine: Co-Evolving Agents and Their Evaluators. arXiv."},{"key":"ref_34","unstructured":"Lu, H., Liu, Y., Xu, J., Nan, G., Yu, Y., Chen, Z., and Wang, K. (2025, January 2\u20137). Auditing Meta-Cognitive Hallucinations in Reasoning Large Language Models. Proceedings of the NeurIPS 2025, San Diego, CA, USA. Mexico City, Mexico, 30 November\u20135 December 2025."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0167-2789(84)90264-1","article-title":"Space-time dynamics in video feedback","volume":"10","author":"Crutchfield","year":"1984","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_36","unstructured":"Wikipedia Contributors (2026, July 10). Quine (Computing)\u2014Wikipedia, The Free Encyclopedia. Available online: https:\/\/en.wikipedia.org\/wiki\/Quine_(computing)."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"150","DOI":"10.2307\/2267778","article-title":"On Notation for Ordinal Numbers","volume":"3","author":"Kleene","year":"1938","journal-title":"J. Symb. Log."},{"key":"ref_38","unstructured":"Bolander, T. (2003). Logical Theories for Agent Introspection. [Ph.D. Thesis, Technical University of Denmark]."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/0167-2789(84)90256-2","article-title":"Self-reproduction in cellular automata","volume":"10","author":"Langton","year":"1984","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/0167-2789(89)90242-X","article-title":"Self-reproduction in small cellular automata","volume":"34","author":"Byl","year":"1989","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1162\/106454698568576","article-title":"Fifty years of research on self-replication: An overview","volume":"4","author":"Sipper","year":"1998","journal-title":"Artif. Life"},{"key":"ref_42","unstructured":"Anthropic (2026, July 10). Exploring Model Welfare. Anthropic Research Announcement, 2025. Welfare Findings for Claude Opus 4 Are Reported in the Claude Opus 4 Model Welfare Assessment (2025). Available online: https:\/\/www-cdn.anthropic.com\/6d8a8055020700718b0c49369f60816ba2a7c285\/Claude%204%20System%20Card.pdf."},{"key":"ref_43","unstructured":"Berg, C., de Lucena, D., and Rosenblatt, J. (2025). Large Language Models Report Subjective Experience Under Self-Referential Processing. arXiv."},{"key":"ref_44","unstructured":"Bae, J.H. (2026). When Self-Reference Fails to Close: Matrix-Level Dynamics in Large Language Models. arXiv."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1162\/tacl_a_00562","article-title":"The Parallelism Tradeoff: Limitations of Log-Precision Transformers","volume":"11","author":"Merrill","year":"2023","journal-title":"Trans. Assoc. Comput. Linguist."},{"key":"ref_46","unstructured":"Kadavath, S., Conerly, T., Askell, A., Henighan, T., Drain, D., Perez, E., Schiefer, N., Hatfield-Dodds, Z., DasSarma, N., and Tran-Johnson, E. (2022). Language Models (Mostly) Know What They Know. arXiv."},{"key":"ref_47","unstructured":"Ferrando, J., Obeso, O., Rajamanoharan, S., and Nanda, N. (2025, January 24\u201328). Do I Know This Entity? Knowledge Awareness and Hallucinations in Language Models. Proceedings of the ICLR 2025, Singapore."},{"key":"ref_48","unstructured":"Li, Y., Huang, Y., Lin, Y., Wu, S., Wan, Y., and Sun, L. (2024). I Think, Therefore I Am: Benchmarking Awareness of Large Language Models Using AwareBench. arXiv."},{"key":"ref_49","unstructured":"Song, S., Lederman, H., Hu, J., and Mahowald, K. (2025). Privileged Self-Access Matters for Introspection in AI. arXiv."},{"key":"ref_50","unstructured":"Comsa, I.M., and Shanahan, M. (2025). Does It Make Sense to Speak of Introspection in Large Language Models?. arXiv."},{"key":"ref_51","unstructured":"Binder, F.J., Chua, J., Korbak, T., Sleight, H., Hughes, J., Long, R., Perez, E., Turpin, M., and Evans, O. (2025, January 24\u201328). Looking Inward: Language Models Can Learn About Themselves by Introspection. Proceedings of the Thirteenth International Conference on Learning Representations (ICLR 2025), Singapore."},{"key":"ref_52","unstructured":"Song, S., Hu, J., and Mahowald, K. (2025, January 7\u201310). Language Models Fail to Introspect About Their Knowledge of Language. Proceedings of the Conference on Language Modeling (COLM), Montreal, QC, Canada."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Li, J.A., Xiong, H., Wilson, R.C., Mattar, M.G., and Benna, M.K. (2025, January 2\u20137). Language Models Are Capable of Metacognitive Monitoring and Control of Their Internal Activations. Proceedings of the Advances in Neural Information Processing Systems 38 (NeurIPS 2025), San Diego, CA, USA.","DOI":"10.52202\/085713-2009"},{"key":"ref_54","unstructured":"Fonseca Rivera, J., and Africa, D.D. (2025). Steering Awareness: Detecting Activation Steering from Within. arXiv."},{"key":"ref_55","unstructured":"Lindsey, J. (2026). Emergent Introspective Awareness in Large Language Models. arXiv."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Laine, R., Chughtai, B., Betley, J., Hariharan, K., Scheurer, J., Balesni, M., Hobbhahn, M., Meinke, A., and Evans, O. (2024, January 10\u201315). Me, Myself, and AI: The Situational Awareness Dataset (SAD) for LLMs. Proceedings of the Advances in Neural Information Processing Systems 37 (NeurIPS 2024), Vancouver, BC, Canada.","DOI":"10.52202\/079017-2044"},{"key":"ref_57","unstructured":"Betley, J., Bao, X., Soto, M., Sztyber-Betley, A., Chua, J., and Evans, O. (2025, January 24\u201328). Tell Me About Yourself: LLMs Are Aware of Their Learned Behaviors. Proceedings of the Thirteenth International Conference on Learning Representations (ICLR), Singapore."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1177\/09637214251391158","article-title":"Metacognition and Uncertainty Communication in Humans and Large Language Models","volume":"35","author":"Steyvers","year":"2025","journal-title":"Curr. Dir. Psychol. Sci."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Panickssery, A., Bowman, S.R., and Feng, S. (2024, January 10\u201315). LLM Evaluators Recognize and Favor Their Own Generations. Proceedings of the Advances in Neural Information Processing Systems 37 (NeurIPS 2024), Vancouver, BC, Canada.","DOI":"10.52202\/079017-2197"},{"key":"ref_60","unstructured":"Vaugrante, L., Weckauff, A., and Hagendorff, T. (2026). Emergently Misaligned Language Models Show Behavioral Self-Awareness That Shifts With Subsequent Realignment. arXiv."},{"key":"ref_61","unstructured":"Gurnee, W., Sofroniew, N., Pearce, A., Piotrowski, M., Kauvar, I., Chen, R., Soligo, A., Bogdan, P., Ong, E., and Wang, R. (2026). Verbalizable Representations Form a Global Workspace in Language Models. arXiv."},{"key":"ref_62","unstructured":"Merrill, W., and Sabharwal, A. (2024, January 7\u201311). The Expressive Power of Transformers with Chain of Thought. Proceedings of the Twelfth International Conference on Learning Representations (ICLR 2024), Vienna, Austria."},{"key":"ref_63","unstructured":"Dehghani, M., Gouws, S., Vinyals, O., Uszkoreit, J., and Kaiser, \u0141. (2019, January 6\u20139). Universal Transformers. Proceedings of the ICLR 2019, New Orleans, LA, USA."},{"key":"ref_64","unstructured":"Hao, S., Sukhbaatar, S., Su, A., Li, X., Hu, Z., Weston, J., and Tian, Y. (2025, January 24\u201328). Training Large Language Models to Reason in a Continuous Latent Space. Proceedings of the Thirteenth International Conference on Learning Representations (ICLR 2025), Singapore."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Geiping, J., McLeish, S., Jain, N., Kirchenbauer, J., Singh, S., Bartoldson, B.R., Kailkhura, B., Bhatele, A., and Goldstein, T. (2025, January 2\u20137). Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach. Proceedings of the Advances in Neural Information Processing Systems 38 (NeurIPS 2025), San Diego, CA, USA.","DOI":"10.52202\/085713-1380"},{"key":"ref_66","unstructured":"Chen, X., Zhao, A., Xia, H., Lu, X., Wang, H., Chen, Y., Zhang, W., Wang, J., Li, W., and Shen, X. (2025). Reasoning Beyond Language: A Comprehensive Survey on Latent Chain-of-Thought Reasoning. arXiv."},{"key":"ref_67","unstructured":"S\u0119dzikowska, J. (2026, July 10). The Proto-Self Field in AI Systems, 2026. Unpublished Manuscript, PhilArchive; Formerly Cited Under the Title \u201cHypothesis of The Proto-Self Field in LLMs\u201d. Available online: https:\/\/philarchive.org\/archive\/SDZTPF."},{"key":"ref_68","unstructured":"Jaegle, A., Gimeno, F., Brock, A., Zisserman, A., Vinyals, O., and Carreira, J. (2021, January 18\u201324). Perceiver: General Perception with Iterative Attention. Proceedings of the ICML 2021, Virtual."},{"key":"ref_69","unstructured":"Baars, B.J. (1988). A Cognitive Theory of Consciousness, Cambridge University Press."},{"key":"ref_70","unstructured":"Butlin, P., Long, R.P., Elmoznino, E., Bengio, Y., Birch, J., Constant, A., Deane, G., Fleming, S.M., Frith, C., and Xu, J. (2023). Consciousness in Artificial Intelligence: Insights from the Science of Consciousness. arXiv."},{"key":"ref_71","unstructured":"Jiang, X., Li, F., Zhao, H., Qiu, J., Wang, J., Shao, J., Xu, S., Zhang, S., Chen, W., and Tang, X. (2024). Long Term Memory: The Foundation of AI Self-Evolution. arXiv."},{"key":"ref_72","doi-asserted-by":"crossref","unstructured":"Chang, O., and Lipson, H. (2018, January 23\u201327). Neural Network Quine. Proceedings of the 2018 Conference on Artificial Life (ALIFE 2018), Tokyo, Japan.","DOI":"10.1162\/isal_a_00049"},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Pedersen, J.W., Plantec, E., Nisioti, E., Barylli, M., Montero, M., Korte, K., and Risi, S. (2025). Hypernetworks That Evolve Themselves. Proceedings of the ALIFE 2025: Ciphers of Life: Proceedings of the Artificial Life Conference 2025, MIT Press.","DOI":"10.1162\/ISAL.a.845"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1038\/s41593-022-01070-0","article-title":"A Synergistic Core for Human Brain Evolution and Cognition","volume":"25","author":"Luppi","year":"2022","journal-title":"Nat. Neurosci."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/BF00355521","article-title":"Two Concepts of Consciousness","volume":"49","author":"Rosenthal","year":"1986","journal-title":"Philos. Stud."},{"key":"ref_76","unstructured":"Cerullo, M. (2026). The Case for Consciousness in Current Frontier Large Language Models. PhilArchive, Available online: https:\/\/philarchive.org\/archive\/CERTCF."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1007\/s12559-012-9124-9","article-title":"A Computability Argument Against Superintelligence","volume":"4","author":"Wiedermann","year":"2012","journal-title":"Cogn. Comput."},{"key":"ref_78","unstructured":"Yudkowsky, E., and Herreshoff, M. (2013). Tiling Agents for Self-Modifying AI, and the L\u00f6bian Obstacle, Machine Intelligence Research Institute (MIRI). Available online: https:\/\/paperzz.com\/doc\/7167313\/tiling-agents-for-self-modifying-ai\u2013and-the-l%C3%B6bian-obstacle."},{"key":"ref_79","unstructured":"Christiano, P., Yudkowsky, E., Herreshoff, M., and B\u00e1r\u00e1sz, M. (2013). Definability of Truth in Probabilistic Logic (Early Draft), Machine Intelligence Research Institute. Technical Report."},{"key":"#cr-split#-ref_80.1","unstructured":"Mahoney, M. (2026, July 10). A Model for Recursively Self Improving Programs, 2010. Self-Published Preprint (Final Version v.3, December 2010)"},{"key":"#cr-split#-ref_80.2","unstructured":"An Earlier Version Was Submitted to the Journal of Artificial General Intelligence in 2008. Available online: https:\/\/www.academia.edu\/66745654\/A_Model_for_Recursively_Self_Improving_Programs."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1080\/0952813X.2014.895114","article-title":"Utility Function Security in Artificially Intelligent Agents","volume":"26","author":"Yampolskiy","year":"2014","journal-title":"J. Exp. Theor. Artif. Intell."},{"key":"ref_82","unstructured":"Nivel, E., Th\u00f3risson, K.R., Steunebrink, B.R., Dindo, H., Pezzulo, G., Rodr\u00edguez, M., Hern\u00e1ndez, C., Ognibene, D., Schmidhuber, J., and Sanz, R. (August, January 31). Bounded Recursive Self-Improvement. Proceedings of the AGI 2013, Beijing, China."},{"key":"ref_83","doi-asserted-by":"crossref","unstructured":"Smith, B.C. (1984, January 15\u201318). Reflection and Semantics in LISP. Proceedings of the 11th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages (POPL \u201984), Salt Lake City, UT, USA.","DOI":"10.1145\/800017.800513"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/9\/951\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T04:11:40Z","timestamp":1787717500000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/9\/951"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,24]]},"references-count":84,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["e28090951"],"URL":"https:\/\/doi.org\/10.3390\/e28090951","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,24]]}}}