[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82258-en":3,"doc-seo-82258-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},82258,962075114101,"Seraphina","https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165",8,"Research & Report","Co-evolution of self-replication and function in a digital primordial soup","Traditional evolutionary algorithms assume reproduction is predefined, while self-replication can arise spontaneously inside digital “primordial soups”. This preprint studies the joint emergence of self-replication and mathematical problem-solving. A population of random 32-byte Z80 assembly programs is initialized, and reproduction must evolve through random assembly-level mutations and pairwise interactions. Task-based validation links behavior to performance by raising interaction probability when evaluating a polynomial succeeds. Experiments show co-evolution from randomness, compact reproductive architectures, metabolic constraints enabling conditional early halting, and spatial niches producing an emergent learning curriculum.","arXiv :2607 .092 1 1v 1 [ cs .NE] 10 Jul 2026  \nCO-EVOLUTION OF SELF-REPLICATION AND FUNCTION IN A  \nDIGITAL PRIMORDIAL SOUP  \nA PREPRINT  \nFrancesco Cicalaa,1 , Eyvind Niklassona,1 , Ettore Randazzoa,1 , Sami Boukortta , Alessio Bastib , Mayalen Etcheverrya , Rif A. Saurousa , Ben Lauriea , James Manyikaa , Blaise Agüera y Arcasa,c , and Blake A. Richardsa,d,e,f,2  \na Google, Paradigms of Intelligence Team  \nbUniversity “G. D’Annunzio” of Chieti-Pescara  \ndMila-Quebec AI Institute  \neMcGill University  \nfCIFAR  \nJuly 13, 2026  \nABSTRACT  \nWhile traditional evolutionary algorithms hard-code reproduction, self-replication can emerge spontaneously within digital “primordial soups”. This paper investigates the co-evolution of this emergent self-replication alongside problem-solving capabilities. We initialize a population of random 32-byte Z80 assembly programs, requiring self-replication to arise purely through random assembly-level mutations and pairwise program interactions. To link these behaviors, we introduce a task-based validation step: correctly evaluating a polynomial raises a program’s interaction probability above a baseline rate. Our experiments yield four primary findings. First, self-replication and mathematical problem-solving successfully co-evolve from initial randomness. Second, the pressure to compute accelerates the emergence of compact, robust reproductive architectures that preserve memory for task execution. Third, applying metabolic constraints increases the likelihood that programs evolve conditional halting, terminating early during validation while bypassing the halt during interaction to execute block-copy replication. Finally, when programs are partitioned into spatial task niches, spontaneous self-replication generates an emergent learning curriculum, utilizing simple solutions as stepping stones toward complex polynomials. Altogether, these results demonstrate an interactive feedback loop: environmental task demands actively shape the physical architecture of self-replication, while spontaneous replication alters the evolutionary trajectory of functional problem-solving.  \nKeywords Artificial Life · Spontaneous Replication · Computational Evolution · Automated Curricula  \n1 Introduction  \nOrigin of life research has long debated the fundamental drivers required for life to emerge from non-living matter [Preiner et al., 2020] . Genetics-first accounts hold that life began with self-replicating, information-bearing molecules [Gilbert, 1986], whereas metabolism-first accounts posit that energy-harnessing autocatalytic networks preceded genetic replication [Wächtershäuser, 1997, Lancet et al., 2018, Kauffman, 1986, Hordijk and Steel, 2018, Kauffman, 2000] . A complementary tradition treats the two as jointly necessary, with frameworks such as Gánti’s chemoton [Gánti, 2003] and Dyson’s double-origin hypothesis [Dyson, 1999] positing that a minimal living system must couple metabolism with replication. This inquiry extends naturally into Artificial Life (ALife), which seeks to explore the universal principles of living systems across abstract computational substrates [Scharf et al., 2015, Fontana, 1990, Hutton, 2002, Kruszewski  \n1 F.C., E.N., and E.R. contributed equally to this work.  \n2 To whom correspondence should be addressed. E-mail: [blakerichards@google.com](blakerichards@google.com)  \nand Mikolov, 2022] . Across both biological and digital domains, the spontaneous emergence of self-replication marks a critical phase transition from pre-evolutionary interactions to Darwinian evolution [Nowak and Ohtsuki, 2008, Agüera y Arcas et al., 2024, Spiegelman et al., 1965] . However, platforms studying the evolution of complex behaviors—whether via cellular automata, agentic simulators, or assembly-language organisms—typically bypass the stochastic hurdles of this transition by hard-coding reproduction or seeding their environments with hand-crafted ancestral replicators [Neumann and Burks, 1966, Langton,","cbCaipdJlEY6aMcv","https://ap.wps.com/l/cbCaipdJlEY6aMcv","pdf",9406133,5,1,16,"English","en",105,"# Abstract\n# Introduction\n## Origin-of-life drivers and phase transitions\n## Gap between pre-life emergence and evolution of complex behavior\n## Digital primordial soup setup and competence-gated interactions","[{\"question\":\"How does the paper make reproduction emerge rather than being hard-coded?\",\"answer\":\"Programs are initialized as random Z80 assembly code, and reproduction must be discovered through execution-level behavior. Random assembly mutations and pairwise program interactions drive the emergence of self-replication without assuming an explicit reproductive instruction at the system level.\"},{\"question\":\"What role does task-based validation play in linking problem-solving to reproduction?\",\"answer\":\"A program’s chance to interact and potentially reproduce depends on passing a validation step where it evaluates a polynomial. Correct evaluation increases interaction probability above a baseline rate, coupling functional performance to evolutionary opportunities.\"},{\"question\":\"What key evolutionary outcomes are reported from the experiments?\",\"answer\":\"The results show co-evolution of self-replication and mathematical problem-solving from initial randomness. The study also finds pressure toward compact, robust reproductive architectures, effects of metabolic constraints on conditional halting during validation, and spatial task niches that generate an emergent learning curriculum toward more complex polynomials.\"}]",1784179208,40,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"co-evolution-of-self-replication-and-function-in-a-digital-primordial-soup","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/co-evolution-of-self-replication-and-function-in-a-digital-primordial-soup/82258/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-21","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"How does the paper make reproduction emerge rather than being hard-coded?","Question",{"text":76,"@type":77},"Programs are initialized as random Z80 assembly code, and reproduction must be discovered through execution-level behavior. Random assembly mutations and pairwise program interactions drive the emergence of self-replication without assuming an explicit reproductive instruction at the system level.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What role does task-based validation play in linking problem-solving to reproduction?",{"text":81,"@type":77},"A program’s chance to interact and potentially reproduce depends on passing a validation step where it evaluates a polynomial. Correct evaluation increases interaction probability above a baseline rate, coupling functional performance to evolutionary opportunities.",{"name":83,"@type":74,"acceptedAnswer":84},"What key evolutionary outcomes are reported from the experiments?",{"text":85,"@type":77},"The results show co-evolution of self-replication and mathematical problem-solving from initial randomness. The study also finds pressure toward compact, robust reproductive architectures, effects of metabolic constraints on conditional halting during validation, and spatial task niches that generate an emergent learning curriculum toward more complex polynomials.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,110,115,119,122,127,130,134],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":29,"slug":118},7,"Healthcare","healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":20,"slug":137},19,"General","general"]