[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83827-en":3,"doc-seo-83827-105":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},83827,2336464648322,"Aria","https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488",8,"Research & Report","Heaviside Continuity of Rolling Coefficients for Eliminating Epistemic Entropy in Large Language Models","Large language models can produce fluent but incorrect statements because autoregressive decoding lacks mechanisms to verify intermediate reasoning before progressing. Heaviside Continuity of Rolling Coefficients (HCRC) introduces a verification-first execution framework that reformulates inference into predicate-gated state transitions using a Heaviside operator called the Heaviside Gate. A parallel worker architecture generates independent verification signals combined with model confidence so execution advances only when correctness predicates hold. Experiments across software-engineering and reasoning tasks show false completion collapse and safer halting, plus stable production control-plane deployment without changing the underlying model.","Heaviside Continuity of Rolling Coefficients for Eliminating Epistemic Entropy in Large Language  \nModels  \narXiv :2607 .04562v 1 [ cs .AI] 6 Jul 2026  \nMY Pitsane  \nNorth-West University, RSA Mankind Research Labs, Sandton [Yvonne.Pitsane@nwu.ac.za](Yvonne.Pitsane@nwu.ac.za)[ ](Yvonne.Pitsane@nwu.ac.za)[Yvonne@mankindresearch.org](Yvonne@mankindresearch.org)  \nHope Mogale  \nUniversity of Pretoria, RSA Mankind Research Labs, Sandton [Hope.Mogale@cs.up.ac.za](Hope.Mogale@cs.up.ac.za)[ ](Hope.Mogale@cs.up.ac.za)[Hope@mankindresearch.org](Hope@mankindresearch.org)  \nAbstract  \nLarge language models (LLMs) generate fluent outputs which can at times be wrong but unlike humans who often exhibit body cues which makes you detect them when they are giving false information. LLMs, are yet to exhibit such with their fluent outputs which are not easily detectable but remain susceptible to epistemic errors because autoregressive decoding provides no mechanism for verifying intermediate reasoning before state progression. We introduce Heaviside Continuity of Rolling Coefficients (HCRC), a verification-first execution framework that reformulates inference as a sequence of predicate-gated state transitions governed by a Heaviside decision operator we call the Heaviside Gate. HCRC combines model confidence with independent verification signals produced by a parallel worker architecture, allowing execution to advance only when predefined correctness predicates are satisfied. This execution-layer formulation prevents invalid intermediate states from propagating through the reasoning process, reducing epistemic entropy without modifying the underlying model. We evaluate HCRC on software-engineering and reasoning tasks across thirteen proposers from four providers. On capable proposers the gate collapses the false-completion rate (FCR) from 4–7% to 0% while remaining latency-competitive and in some settings faster than the unwrapped model; on weaker proposers it converts residual false completions into honest halts that surface to the operator instead of corrupting downstream state. Beyond the benchmark, HCRC has operated for months as the production control plane of an agentic coding environment, where the same gate authorizes file mutations, drives verification-slaved progress reporting, and licenses memory compaction over session context. These findings establish HCRC as a general framework for verification-driven LLM execution and suggest that reliable reasoning can be achieved through principled execution control rather than through model scale alone.  \n1 Introduction  \nModern LLMs are optimized for next-token likelihood. This objective rewards fluency and stylistic plausibility but has no direct relation to whether a generated artifact corresponds to a verifiable state of the world. A model can confidently report that a file exists, that a test passes, or that a function returns a particular value when none of these are true. This failure mode is widely discussed under the umbrella of hallucination [2, 3] . We take the view that it is not a calibration issue but the consequence of optimizing a divergence over symbol sequences rather than a divergence over external states.  \nPreprint. Under review.  \nIntent Ri = (prompti , Pi)  \nLLM  \nproposer  \nSummary Parser  \nARIAL Worker Pool  \nCitation  \nH  \nC·V ≥ τ  \nHALT  \nappend gaps, retry  \nVi , C  \nH = 0  \npipeline.json  \naccomplished.json  \nFigure 1: System overview. We declare that the LLM acts as a proposer; it never reads predicate outputs. A pool of ARIALAggresive Reinforcement Intelligent Adaptive Learning workers extracts evidence from the repository, tests, and parsed summary, and aggregates into a verification score V. The Heaviside gate H(C · V − τ) converts this into a binary commit/halt decision. On halt, the gap list is appended to the prompt and the step retries.  \nWe focus on the case where the agent’s task is to drive an external system. A repository, a database, a test suite into a","cbCaiiuYFWTvpyHt","https://ap.wps.com/l/cbCaiiuYFWTvpyHt","pdf",1213068,5,1,28,"English","en",105,"# Introduction\n## Contributions\n## System overview","[{\"question\":\"What problem does HCRC target in large language model execution?\",\"answer\":\"HCRC targets epistemic entropy: the divergence between a model’s claimed state and the reference state obtained from querying an external system. It arises because intermediate reasoning is not verified before state progression in autoregressive decoding.\"},{\"question\":\"How does the Heaviside Gate decide whether to commit or halt?\",\"answer\":\"The Heaviside Gate applies a Heaviside step to the product of model confidence and an aggregated verification score, comparing it to a threshold. If the predicate condition fails, execution halts rather than committing invalid intermediate states.\"},{\"question\":\"What results does the paper report when HCRC is enabled?\",\"answer\":\"Across thirteen proposers, unwrapped false-completion rates of 4–7% collapse to 0–3% on capable proposers when HCRC is enabled. On weaker proposers, residual false completions are converted into honest halts that prevent downstream state corruption.\"}]",1784190713,71,{"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},"heaviside-continuity-of-rolling-coefficients-for-eliminating-epistemic-entropy-in-large-language-models","",{"@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/heaviside-continuity-of-rolling-coefficients-for-eliminating-epistemic-entropy-in-large-language-models/83827/",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","2026-07-27","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},"What problem does HCRC target in large language model execution?","Question",{"text":76,"@type":77},"HCRC targets epistemic entropy: the divergence between a model’s claimed state and the reference state obtained from querying an external system. It arises because intermediate reasoning is not verified before state progression in autoregressive decoding.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the Heaviside Gate decide whether to commit or halt?",{"text":81,"@type":77},"The Heaviside Gate applies a Heaviside step to the product of model confidence and an aggregated verification score, comparing it to a threshold. If the predicate condition fails, execution halts rather than committing invalid intermediate states.",{"name":83,"@type":74,"acceptedAnswer":84},"What results does the paper report when HCRC is enabled?",{"text":85,"@type":77},"Across thirteen proposers, unwrapped false-completion rates of 4–7% collapse to 0–3% on capable proposers when HCRC is enabled. On weaker proposers, residual false completions are converted into honest halts that prevent downstream state corruption.","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},[94,98,102,106,110,115,120,123,128,131,135],{"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":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":20,"slug":138},19,"General","general"]