[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84270-en":3,"doc-seo-84270-105":29,"detail-sidebar-cat-0-en-105":90},{"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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84270,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","RetractorDB Deterministic Edge Signal Processing Engine","RetractorDB is an open-source edge signal processing engine for regular time series, providing query semantics grounded in number theory covering systems. Deployed near the signal source, it pre-processes and filters high-frequency measurements on edge devices using a declarative query language, maintains inspectable, partially correctable records of past and scheduled future events, and transmits exact deterministic results upstream. Its differential data model and rational arithmetic rate-conversion operators (interleave/de-interleave) form an algebra tied to Beatty sequences and Fraenkel’s partition theorem, enabling exact deterministic resampling and optimizer-safe rewrites. The paper outlines an end-to-end realization with RQL compilation to a rationally resolved dependency DAG, slot-based scheduling, artifact formats with schema and gap metadata, and validates semantics via deterministic engine tests including a full Pan–Tompkins QRS-detection pipeline over MIT-BIH ECG. A real-time performance evaluation is planned for a later version.","arXiv :2607 .07730v 1 [ cs .DB] 6 Jul 2026  \nRetractorDB: A Deterministic Edge Signal Processing Engine Based on Rational Beatty Sequences and Fraenkel’s Partition  \nMichal Widera  \nIndependent Researcher, Zabrze, Poland  \nORCID: 0000-0002-3578-3792  \n[michal@widera.com.pl](michal@widera.com.pl)  \nJuly 2026  \nAbstract  \nWe present RetractorDB, an open-source edge signal processing engine (ESPE) for regular time series whose query semantics is grounded in the number theory of covering systems. RetractorDB is designed to support, not replace, time-series databases (TSDB) and data stream management systems (DSMS): deployed close to the signal source, it pre-processes and filters high-frequency measurements on the edge device through a declarative signalprocessing query language, maintains a partial, correctable record of past and scheduled future events in inspectable artifacts, and transmits exact, deterministic results upstream, so that only reduced, already-processed streams reach the central architecture. The data model is differential (a stream is a pair (sn , ∆) with a constant rational inter-arrival interval), and the core rate-conversion operators, interleave and de-interleave, are proved to be rational Beatty sequences satisfying the conditions of Fraenkel’s partition theorem. This yields an algebra in which resampling is an exact, deterministic, first-class operator: de-interleaving inverts interleaving bit-for-bit using rational arithmetic alone, and algebraic rewrite rules license query-plan optimization without changing results. We describe the end-to-end realization of this algebra in a working engine: declarative query language (RQL), compilation to a dependency DAG with rational interval resolution, slot-based runtime scheduling, and an inspectable artifact format with schema and null/gap metadata. We validate the semantics on deterministic query examples drawn from the engine’s integration tests, including a complete Pan–Tompkins QRS-detection pipeline over MIT-BIH ECG data expressed entirely within the algebra. A performance evaluation under a real-time operating environment is in progress and deferred to a subsequent version.  \nKeywords. edge signal processing; stream processing; time series; Beatty sequences; Fraenkel’s theorem; covering systems; exact rational arithmetic; deterministic execution; continuous queries; multirate signal processing.  \n1 Introduction  \nContinuous stream systems often face three hard requirements at once: low latency, determinism, and mathematically grounded operator semantics. RetractorDB addresses this combination by connecting number-theoretic covering systems with a practical database query-processing stack.  \nThe system perspective is intentionally simple: users declare source streams and continuous transformations in RQL, compile and execute with xretractor, inspect live outputs via xqry, and validate binary artifacts with xtrdb. Unlike typical best-effort stream runtimes, RetractorDB emphasizes deterministic execution order and reproducible outputs: identical input traces produce identical artifacts.  \nPositioning: an edge companion to TSDB and DSMS. RetractorDB is best understood as an edge signal processing engine (ESPE), not as a replacement for a time-series database (TSDB) or a general-purpose data stream management system (DSMS) . In a typical deployment it sits between the signal source and an upstream store: it ingests regular streams at the edge, applies exact rate conversion and signal operators, and manages a bounded, artifact-based record of the stream. The primary operational motivation is offloading. High-frequency sources such as biomedical, industrial, or acoustic sensors saturate links and ingestion pipelines when shipped raw; because RQL expresses complete signal-processing pipelines declaratively (filtering, decimation, feature extraction; see the Pan–Tompkins pipeline of Section 6.4), the processing happens where the data is recorded, and only rate-reduced","cbCaiipJAZOBuU3G","https://ap.wps.com/l/cbCaiipJAZOBuU3G","pdf",445196,1,18,"English","en",105,"# Introduction\n## Positioning and Operational Motivation\n## Distinguishing Data Model and Semantics\n# Abstract","[{\"question\":\"What problem does RetractorDB target in edge deployments?\",\"answer\":\"It addresses the combined requirements of low latency, determinism, and mathematically grounded operator semantics by performing exact pre-processing at the edge and transmitting only rate-reduced, already-processed streams upstream.\"},{\"question\":\"How does RetractorDB model a time series stream?\",\"answer\":\"It uses a differential stream model (sn, ∆), where ∆ is a constant rational inter-arrival interval, enabling known slot timelines and deterministic event scheduling.\"},{\"question\":\"Why can RetractorDB perform rate conversion and resampling exactly?\",\"answer\":\"Its core rate-conversion operators interleave and de-interleave are proven to correspond to rational Beatty sequences satisfying conditions from Fraenkel’s partition theorem, allowing deterministic bit-for-bit inversion using rational arithmetic without floating-point approximation.\"}]",1784194507,45,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"retractordb-deterministic-edge-signal-processing-engine","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/retractordb-deterministic-edge-signal-processing-engine/84270/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What problem does RetractorDB target in edge deployments?","Question",{"text":74,"@type":75},"It addresses the combined requirements of low latency, determinism, and mathematically grounded operator semantics by performing exact pre-processing at the edge and transmitting only rate-reduced, already-processed streams upstream.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does RetractorDB model a time series stream?",{"text":79,"@type":75},"It uses a differential stream model (sn, ∆), where ∆ is a constant rational inter-arrival interval, enabling known slot timelines and deterministic event scheduling.",{"name":81,"@type":72,"acceptedAnswer":82},"Why can RetractorDB perform rate conversion and resampling exactly?",{"text":83,"@type":75},"Its core rate-conversion operators interleave and de-interleave are proven to correspond to rational Beatty sequences satisfying conditions from Fraenkel’s partition theorem, allowing deterministic bit-for-bit inversion using rational arithmetic 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