{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T05:12:53Z","timestamp":1779340373183,"version":"3.51.4"},"reference-count":45,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T00:00:00Z","timestamp":1778457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science, Technological Development and Innovation of the Republic of Serbia","award":["200151"],"award-info":[{"award-number":["200151"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Adaptive and evolutive software systems are characterized by ontologically defined non-determinism\u2014not a defect but the primary force of their evolution. Non-determinism arises from recursion, interaction, and selection between abstract components and can only be resolved as the execution sequence grows sufficiently for one outcome to become determinate. In adaptive systems, managing this non-determinism through structural adaptation of abstract components during execution is the defining operational characteristic\u2014one that no existing execution substrate formally supports. The problems of evolutive AI systems\u2014inconsistency, non-reproducibility, absence of causal traceability, and an inability to enforce purpose-constrained autonomy\u2014cannot be resolved within AI architectures alone. Resolving them requires a formal execution substrate in which causal context growth, resolution-moment detection, and structural adaptation of abstract components are first-class properties. This paper introduces the Zero Tier Execution Substrate (ZTES), grounded in a foundational model that defines execution as a sequence generated by recursive invocations of abstract components with ontologically specified purpose, in which non-determinism is resolved within the causal context of the sequence before commitment. ZTES is a homomorphic specification of this model, achieved through disciplined composition of the Mesarovi\u0107\u2013Takahara system ontology, Lamport-consistent causal ordering, P-DEVS transition semantics, and the Three-Phase execution kernel\u2014mechanisms individually proven at a global scale. System execution is formally identified with the causal evolution of knowledge: Execution(\u03a3) \u2261 Evolution(K). The historical knowledge base K has a two-dimensional orthogonal structure\u2014the eschatological dimension encoding purpose lineage through recursive specialization, and the sequential dimension encoding event order through iterative mapping\u2014which establishes purpose integrity as a substrate-level property of evolutive execution. The semantic closure of ZTES establishes deterministic reproducibility, governance\u2013execution equivalence, and purpose-constrained autonomy as structural consequences of substrate closure rather than as additional architectural layers.<\/jats:p>","DOI":"10.3390\/systems14050547","type":"journal-article","created":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T16:07:26Z","timestamp":1779206846000},"page":"547","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Zero Tier Execution Substrate for Evolutionary Software Systems"],"prefix":"10.3390","volume":"14","author":[{"given":"Aleksandar","family":"Ivanovi\u0107","sequence":"first","affiliation":[{"name":"School of Computing, Union University, 11000 Belgrade, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Milo\u0161","family":"Radenkovi\u0107","sequence":"additional","affiliation":[{"name":"School of Computing, Union University, 11000 Belgrade, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergei","family":"Prokhorov","sequence":"additional","affiliation":[{"name":"S.I. Vavilov Institute for the History of Science and Technology, Russian Academy of Sciences, Moscow 199034, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7716-5845","authenticated-orcid":false,"given":"Aleksandra","family":"Labus","sequence":"additional","affiliation":[{"name":"Department of e-Business, Faculty of Organizational Sciences, University of Belgrade, 11000 Belgrade, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo\u017eidar","family":"Radenkovi\u0107","sequence":"additional","affiliation":[{"name":"Department of e-Business, Faculty of Organizational Sciences, University of Belgrade, 11000 Belgrade, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/S0925-7535(03)00047-X","article-title":"A new accident model for engineering safer systems","volume":"42","author":"Leveson","year":"2004","journal-title":"Saf. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"de Lemos, R., Giese, H., M\u00fcller, H.A., and Shaw, M. (2013). Software Engineering for Self-Adaptive Systems II: Case Studies and Applications, Springer.","DOI":"10.1007\/978-3-642-35813-5"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1007\/s00165-006-0001-8","article-title":"Angelic nondeterminism and unifying theories of programming","volume":"18","author":"Cavalcanti","year":"2006","journal-title":"Form. Asp. Comput."},{"key":"ref_4","unstructured":"Ariew, R., and Garber, D. (1989). Monadology (1714). G.W. Leibniz: Philosophical Essays, Hackett Publishing."},{"key":"ref_5","unstructured":"Loemker, L.E. (1969). Specimen Dynamicum (1695). Philosophical Papers and Letters, Reidel. [2nd ed.]."},{"key":"ref_6","unstructured":"Loemker, L.E. (1969). Primae Veritates (c. 1686). Philosophical Papers and Letters, Reidel. [2nd ed.]."},{"key":"ref_7","unstructured":"Mesarovi\u0107, M.D., and Takahara, Y. (1975). General Systems Theory: Mathematical Foundations, Academic Press."},{"key":"ref_8","unstructured":"Zeigler, B.P., Praehofer, H., and Kim, T.G. (2000). Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems, Academic Press. [2nd ed.]."},{"key":"ref_9","unstructured":"Tocher, K.D. (1963). The Art of Simulation, English Universities Press."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1145\/1323293.1294281","article-title":"Dynamo: Amazon\u2019s highly available key-value store","volume":"41","author":"DeCandia","year":"2007","journal-title":"ACM SIGOPS Oper. Syst. Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1145\/1773912.1773922","article-title":"Cassandra: A decentralized structured storage system","volume":"44","author":"Lakshman","year":"2010","journal-title":"ACM SIGOPS Oper. Syst. Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1145\/359545.359563","article-title":"Time, clocks, and the ordering of events in a distributed system","volume":"21","author":"Lamport","year":"1978","journal-title":"Commun. ACM"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/S0928-4869(01)00030-1","article-title":"Distributed discrete event simulation using the three-phase approach and Java","volume":"8","author":"Cassel","year":"2001","journal-title":"Simul. Pract. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1145\/362384.362685","article-title":"A relational model of data for large shared data banks","volume":"13","author":"Codd","year":"1970","journal-title":"Commun. ACM"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1145\/319587.319592","article-title":"A normal form for relational databases that is based on domains and keys","volume":"6","author":"Fagin","year":"1981","journal-title":"ACM Trans. Database Syst."},{"key":"ref_16","unstructured":"Date, C.J., Darwen, H., and Lorentzos, N.A. (2002). Temporal Data and the Relational Model, Morgan Kaufmann."},{"key":"ref_17","unstructured":"Klimbie, J.W., and Koffeman, K.L. (1974). Data semantics. Data Base Management, North-Holland."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Halpin, T.A. (2001). Information Modeling and Relational Databases, Morgan Kaufmann.","DOI":"10.1016\/B978-155860672-2\/50014-2"},{"key":"ref_19","unstructured":"van Benthem, J. (2019). Logical Dynamics of Information and Interaction, Cambridge University Press."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Fagin, R., Halpern, J.Y., Moses, Y., and Vardi, M.Y. (1995). Reasoning About Knowledge, MIT Press.","DOI":"10.7551\/mitpress\/5803.001.0001"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Liu, L., and \u00d6zsu, M.T. (2009). Temporal databases. Encyclopedia of Database Systems, Springer.","DOI":"10.1007\/978-0-387-39940-9"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1017\/S0269888900008122","article-title":"Intelligent agents: Theory and practice","volume":"10","author":"Wooldridge","year":"1995","journal-title":"Knowl. Eng. Rev."},{"key":"ref_23","unstructured":"Papazoglou, M.P. (2004, January 5\u20138). Service-oriented computing: Concepts, characteristics and directions. Proceedings of the 4th Annual Hawaii International Conference on System Sciences, Big Island, HI, USA."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Bergenti, F., Gleizes, M.P., and Zambonelli, F. (2004). Methodologies and Software Engineering for Agent Systems, Springer.","DOI":"10.1007\/b116049"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/S0019-9958(63)90290-0","article-title":"Probabilistic automata","volume":"6","author":"Rabin","year":"1963","journal-title":"Inf. Control"},{"key":"ref_26","first-page":"5998","article-title":"Attention is all you need","volume":"30","author":"Vaswani","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_27","unstructured":"Vernon, V. (2013). Implementing Domain-Driven Design, Addison-Wesley Professional."},{"key":"ref_28","unstructured":"Evans, E. (2003). Domain-Driven Design: Tackling Complexity in the Heart of Software, Addison-Wesley Professional."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/BF02650179","article-title":"Simulating physics with computers","volume":"21","author":"Feynman","year":"1982","journal-title":"Int. J. Theor. Phys."},{"key":"ref_30","unstructured":"Wiener, N. (1948). Cybernetics: Or Control and Communication in the Animal and the Machine, MIT Press."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1080\/00207727008920220","article-title":"Every good regulator of a system must be a model of that system","volume":"1","author":"Conant","year":"1970","journal-title":"Int. J. Syst. Sci."},{"key":"ref_32","unstructured":"Genuys, F. (1968). Cooperating sequential processes. Programming Languages, Academic Press."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"666","DOI":"10.1145\/359576.359585","article-title":"Communicating sequential processes","volume":"21","author":"Hoare","year":"1978","journal-title":"Commun. ACM"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1086\/286788","article-title":"Behavior, purpose and teleology","volume":"10","author":"Rosenblueth","year":"1943","journal-title":"Philos. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1145\/360933.360975","article-title":"Guarded commands, nondeterminacy and formal derivation of programs","volume":"18","author":"Dijkstra","year":"1975","journal-title":"Commun. ACM"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Back, R.-J., and Wright, J. (1998). Refinement Calculus: A Systematic Introduction, Springer.","DOI":"10.1007\/978-1-4612-1674-2"},{"key":"ref_37","first-page":"57","article-title":"High-performance deterministic concurrency using Lingua Franca","volume":"20","author":"Lohstroh","year":"2023","journal-title":"ACM Trans. Arch. Code Optim."},{"key":"ref_38","unstructured":"Plotkin, G.D. (1981). A Structural Approach to Operational Semantics. Tech. Rep. DAIMI FN-19, Aarhus University."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Milner, R. (1980). A Calculus of Communicating Systems, Springer.","DOI":"10.1007\/3-540-10235-3"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1145\/828.833","article-title":"A theory of communicating sequential processes","volume":"31","author":"Brookes","year":"1984","journal-title":"J. ACM"},{"key":"ref_41","unstructured":"Milner, R. (1999). Communicating and Mobile Systems: The Pi Calculus, Cambridge University Press."},{"key":"ref_42","first-page":"395","article-title":"Solving games without determinization","volume":"LNCS 4207","author":"Henzinger","year":"2006","journal-title":"Proceedings of the 15th Annual Conference of the European Association for Computer Science Logic (CSL 2006)"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1109\/43.736561","article-title":"A framework for comparing models of computation","volume":"17","author":"Lee","year":"1998","journal-title":"IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0304-3975(00)00056-6","article-title":"Universal coalgebra: A theory of systems","volume":"249","author":"Rutten","year":"2000","journal-title":"Theor. Comput. Sci."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1145\/564585.564601","article-title":"Brewer\u2019s conjecture and the feasibility of consistent, available, partition-tolerant web services","volume":"33","author":"Gilbert","year":"2002","journal-title":"ACM SIGACT News"}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/5\/547\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T04:57:27Z","timestamp":1779339447000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/5\/547"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,11]]},"references-count":45,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["systems14050547"],"URL":"https:\/\/doi.org\/10.3390\/systems14050547","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,11]]}}}