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全域测序定位系统： 基于孪生图灵机双列表的八大形式体系与三类理想系统

• October 2026

• DOI: 

• 10.13140/RG.2.2.25667.16166

• Shunpeng Zou

• Lijun Ke

• Xiaohui Zou

Global Sequencing-Positioning System, GSPS twin-list Turing machine, TTMD GSPS = + GSPS GSPS-CR BNF GSPS [EN] We present a Global Sequencing-Positioning System (GSPS) for formal information systems. GSPS uses a twin-list Turing machine (TTMD) with an object list and a morphism list. Eight formal systems-character, formula, graph, table, sound, image, solid and life-are formalized as independent sub-universes; each admits three ideal set kinds (singleton, stratified, classified), three ideal mappings (tuple morphism, level functor, natural transformation) and one extensible ideal system. Ideal systems are further divided into ideal simple, ideal complex and ideal wise systems, all sequencable and positionable inside GSPS. Particles and chemical elements are assigned to solid forms, genomes to life forms, software ontologies to character forms as information-primary entities, and hardware carriers as energy-spacetime instances derived from software. Miscellaneous collections, cross-mappings and disordered states are not an independent ontological domain; they are modeled as errors in call-selection and are decomposed, located and judged by GSPS. The full BNF grammar and example code tables of the GSPS Coordinate Rule (GSPS-CR) are given, together with finite-step reduction results on four case studies. The framework supports an information-first foundation for information science.

摘要

针对形式信息系统中语言、符号、模型与载体混杂导致的不可判定、不可测序定位与不可归约问题，本文提出全域测序定位系统（Global Sequencing–Positioning System, GSPS）。以孪生图灵机双列表（twin-list Turing machine, TTMD）为计算内核，将字、式、图、表、音、像、立、活八大形式体系分别形式化为独立子全域；每体系定义三类理想集合（单一、分层、分类）、三类理想映射（元组态射、层级函子、自然变换）与一类可扩展理想系统。进一步将理想系统分为理想简单系统、理想复杂系统与理想智慧系统，并证明三者均可由 GSPS 在统一坐标下测序、定位与判定。基本粒子与化学元素归于“立”，基因归于“活”，软件本体归于“文”并作为形式信息第一性本体=实体+关系，硬件载体作为由软件本体派生的质能时空实例。杂多集合、交叉映射与混乱状态不构成本体论独立域，而建模为调用选择中的差错集合，由 GSPS 按手术刀分解、全域坐标系测序定位与标准语法判定予以纠正或剔除。本文给出全域测序定位坐标编码规则（GSPS-CR）的完整 BNF 范式与八体系示例码表，并证明对任意理想碎片存在唯一坐标编码、对任意非理想碎片可有限步判定。在汉字偏旁—词项、分子结构、基因调控与硬件描述语言四类实例上给出归约流程与编码结果，结果表明 GSPS 可对非理想输入进行有限步判定。本文为信息科学超越单纯物理还原提供形式本体论框架。

关键词：全域测序定位；孪生图灵机；双列表；八大形式体系；理想简单系统；理想复杂系统；理想

智慧系统；信息第一性；软件本体；硬件派生；坐标编码

现有信息系统形式化面临三类缺口：第一，语言、数值、图形、音频、图像、几何与生物模型等分置不同数学框架， 缺乏统一测序定位坐标；第二，物理载体与软件模型常混为一谈，数字孪生多依赖物理实体奠基， 而信息第一性假设未获严格形式化；第三，非理想输入（杂多、交叉、混乱）缺乏可判定归约规则。

本文贡献：（i）给出TTMD双列表公理化；（ii）给出八形式体系每体系的三类集合、三类映射与系统判定； （iii）将理想系统扩展为简单、复杂、智慧三类并被GSPS统摄；（iv）规定软件本体信息第一性、硬件派生及非理想差错模型； （v）提出全域测序定位坐标编码规则GSPS-CR的完整BNF与码表；（vi）给出有限步判定算法与四类实例。

对字式图表音像立活每一形式体系建立独立TTMD，互不设映射。摘要总表见表1：

八体系理想结构总表

粒子与化学元素仅在“立”中作形式模型（原子坐标、键合元组、晶体格点），不在物理质能层作TTMD； 基因仅在“活”中作形式模型（碱基序列、调控弧、表达时间序列）。

<GSPS-Coordinate> ::= <SysID>·<SubID>·<Kind>·<Layer>·<MapType>·<RelID><SysID>           ::= "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8"                       -- 1=字 2=式 3=图 4=表 5=音 6=像 7=立 8=活<SubID>           ::= <digit>+                       -- 字体系: 1=文中 2=文英 3=数 4=符                       -- 其他体系: 1=默认主子系统<Kind>            ::= "S" | "T" | "C"                       -- S=单一集合(原子) T=分层集合(元组关系) C=分类集合<Layer>           ::= "L" ("0"..."6")<MapType>         ::= "∅" | "μ" | "F" | "α"                       -- ∅=纯元素(无映射) μ=元组态射 F=层级函子 α=自然变换<RelID>           ::= ("R"|"M"|"N"|"E") <digit>+                       -- R=对象列表元组 M=态射算子 N=自然变换 E=差错标记

GSPS以TTMD双列表统一字式图表音像立活八大形式体系与三类理想系统，给出GSPS-CR完整BNF与码表，将软件本体置于信息第一性、硬件载体物作为派生，非理想仅作调用差错。该框架可为形式信息科学、数字孪生语义建模与跨模态形式本体提供标准与法。后续可接入工业本体、RAMI/OPC UA语义层与可计算物理仿真，扩展并加载为工程化全域测序定位智慧系统应用平台。

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