MethodFile availableToward a Unified Information Science: The Mathematical Principles of RongzhiXueAugust 2026DOI:10.13140/RG.2.2.19916.78726Xiaohui ZouOPL (16)Unified Information Science.pdf详细内容的英文版以下是简要内容英汉双语融智学信息科学原理的完整数学公式体系以2026年8月RG预印本《融智学信息科学体系——基于双重五信与信智序位的新范式》为基准Complete Mathematical Formula System of RongzhiXue Information Science PrinciplesXiaohui Zou0000-0002-5577-8245(based on the RG preprint of August 2026)AbstractThis document presents the complete set of mathematical formulas and definitions that constitute the foundational framework of RongzhiXue Information Science, as established in the 2026 RG preprint “RongzhiXue Information Science System-A New Paradigm Based on Dual Five-Xin and Xin-Zhi Sequence-Position”. The system spans ontological definitions, core intelligence equations,information measures,the Tao function, three fundamental laws of sequence-position logic, dual five-xin coupling dynamics, a universal multi-dimensional number formula, and physical boundary constraints.摘要本文呈现了构成“融智学信息科学”基础框架的完整数学公式和定义集该框架系基于2026年RG预印本《融智学信息科学系统一种基于“双五信”与“信智序位”的新范式》而确立。该系统涵盖本体论定义、核心智方程、信息度量、道函数、序位逻辑的三个基本定律、双五信耦合动力学、通用多维信息公式以及物理边界约束。1.OntologicalDefinitions1.1 Five-DimensionalVector Space(Ontological Skeleton of Information)I〈Ip,Iv,Is,IL,Im〉(1)where:Ip physical space-time (hardware carrier,non-information)Ivvirtual objects(software ontology,algorithms/logic gates)Isintentional class(intention/cognitive representation;meaning belongs to IM, intention to Is)ILsymbolic class(eight forms:characters,formulas,charts,tables,audio,images, 3D,living)Immeta-rule class (principles,meanings,laws,methods,sequence-positions)一、本体论定义五维向量空间信息的本体论骨架I 〈IP, IV, IS, IL, IM〉 1其中·I_P 质能时空物理层硬件载体非信息·I_V 虚拟物类软件本体算法/逻辑门·I_S 意类意图/认知表征义归 I_M、意归 I_S·I_L 文类符号层八大形式字式图表音像立活·I_M 理义法序位类元规则集1.2Meta-Rule Set(Mathematization of the Fifth Category)Im{λ|λ:(I×T)→{0,1}}(2)which assigns validity and priority judgments.元规则集第五范畴的数学化I_M {λ|λ: (I × T)→{0,1}}赋予有效性与优先级判定。2.CoreFormulas2.1 Intelligence Generation MechanismIntelligence InformationProcessingIntentional Selection(3)Information processing operations on the five information components (Ip→Iv→Is→IL→Im).Intentional selection driven by the five beliefs (credibility,trust,confidence,reputation,faith).二、核心公式2.1.智的生成机制智 信息处理 选择用意信息处理信息五信I_P→I_V→I_S→I_L→I_M的操作选择用意信念五信信用/信任/信心/信誉/信仰的驱动2.2UnificationofThreeIntelligencesHI⊕AICI(4)where:AIstrong information processingbutlacks intentionalselection(only pseudo-confidence).HI(Human Intelligence)naturalintentional selectiondriving biological neural networks.CI(Collaborative Intelligence) higher-order wisdom emerging fromhuman-machineinteractiongoverned bysequence-position order-positionOPlogic.2.2.三智统一HI⊕AI CI·AI人工智能 强信息处理缺选择用意仅有伪置信度·HI人类智力 天然选择用意驱动生物神经网络·CI协同之智 人机在序位逻辑统摄下涌现的高阶智慧3InformationMeasures3.1 Narrow Information Equation(Extension of Shannon Entropy)(5)3.2 General Information Equation(Rongzhi Entropy)(6)Physicalmeaning:conservativeflowofinformationamongmatter,intention,symbols,Tao,and methods.三、信息度量方程3.1.狭义信息方程香农熵扩展I_nar(X) logP(X|O)/P(X|T)3.2.广义信息方程融智熵I_gen ∫_R (O⨂I⨂T)·delta∆(L∘N)物理意义信息在“物、意、文、道、理义法序位”间的守恒流动。3.3 InformationIdentityI_nar I_gentr (Ψ○Q)(7)Meaning:totalinformation processingisjointlydeterminedbythethinkingcoordinate(Tao function Ψ) and database query (Q).3.3.信息恒等式I_{nar} I_{gen} tr(Ψ∘Q)意义信息处理总量由思维坐标道函数Ψ与数据库查询Q共同决定。4 TaoFunctionandThinkingCoordinates4.1DefinitionoftheTaoFunctionΨT×L→R³(8)Ψ(x)(Image(x),Abstraction(x),Intuition(x))(9)This is the mathematical expression of “joint subject-object meaning assignment”—the subject perceives the GE band and activates the corresponding sequence-position of the ID band via intentional selection;the object computes the ID band and outputs the GE band through a coupling function.四、道函数与思维坐标4.1.道函数定义Ψ: T×L→R^3Ψ(x) (形象(x),抽象(x),直觉(x))这是主客体联合赋义的数学表达——主体感知GE格带并通过意图选择激活ID格带的对应序位客体计算ID格带并通过联动函数输出GE格带。5 Three FundamentalLawsof Sequence-PositionLogic5.1 First Law(Rigid:UniqueConservation of Sequence-PositionRelations)∀u∈U,∃!id(u),id(φ(u))id(u)(10)Every element u has a unique sequence-position identifier id(u),which remains invariant under any legitimate natural transformation φ.Newtons conservation laws are a special case in the information domain.5.2 Second Law(Rigid:Synonymy Parallel Correspondence Con- version-Seeking Truth){id(a1),...,id(am)}{id(b₁),...,id(bn)}(11)Two tuples are synonymous if their sets of element sequence-positions are identical.This ensures semantic equivalence among different symbolic forms(characters,formulas,charts, tables,audio,images,3D,living).5.3 Third Law(Flexible:Agreeable Parallel Correspondence Conversion-Seeking Goodness and Beauty)(12)In a specific context c,intentional selection follows this distribution.It characterises the mathematical essence of “intentional selection”,controlled by the five extensions(generalised language, text, bilingual, translation, interpretation).五、序位逻辑三大基本定律第一定律刚性·序位关系唯一守恒∀u∈U,∃! id(u),id(φ(u)) id(u)任意元子 u具有唯一序位标识 id(u)且在合法自然变换φ下序位不变,牛顿守恒律是其在信息领域的特例。第二定律刚性·同义并列对应转换·求真{id(a_1),...,id(a_m)} {id(b_1),...,id(b_n)}两个元组同义当且仅当其元子序位集合一致。保证不同符号形式字式图表音像立活间的语义等价。第三定律柔性·同意并列对应转换·求善求美P(s|c) {exp((sφ,c))}/{∑exp(φ(s,c))}在具体语境 c 中意图的选择服从该分布。刻画选择用意的数学本质由五广广义语言/文本/双语/翻译/解释控制。6DualFive-XinCouplingDynamics6.1 CouplingDynamicsEquation(13)where:I vector of the five information components,B vector of the five beliefs,Φ cooperative potential function,Cdualdual five-xin coupling coefficient,ξ(t)stochastic fluctuation.Meaning:flexible judgments(beliefs)are not a “soft”thing floating outside the rigid framework,but are dynamical variables precisely anchored by the information components.六、双重五信耦合动力学耦合动力学方程d/dt(I⨂B) C_dual·∇Φ(I, B) ξ(t)其中·I 信息五信向量·B 信念五信向量·Φ 协同势能函数·C_dual 双重五信耦合系数·ξ(t) 随机涨落含义柔性判断信念五信不是游离在刚性框架之外的软东西而是被信息五信精确锚定的动力学变量。7Universal Multi-DimensionalNumber Formula(Patent Mathematical Kernel,2000)7.1GeneralForm(abi...)(14)where:Real part aauthentic information (meaning),unique and conservative →corresponds to the First Law.Imaginary part bifirst-dimensional formal identifier of the multi-gene text....extension to other imaginary dimensions for charts,texts,numbers,tables, audio,images,3D,living,etc.7.2 Five Major FunctionsUnified expression(complex/quaternion/octonion/multi-dimensional numbers),sequence- positioning (real part determines position),domain selection and orientation (imaginaryparts determine categories),synonymy parallel translation (coexistence of different multi- dimensional numbers with same real part),and unification of three natures (information processingintentional selection intelligence).七、全域多元数通式2000年专利数学内核通式(a bi ...)实部 a 本真信息义唯一性和守恒性 → 对应第一基本定律虚部 bi 多元基因文本的第一维形式标识... 图、文、数、表、音、像、立、活,等其余虚部的延展通式五大功能统一表达复数/四元数/八元数/多元数、测序定位实部确定序位、选域定向虚部确定类别、同义并列通译实部相同的不同多元数并列共存、三性统一虚部信息处理选择用意智。8PhysicalBoundaryConstraints8.1 Landauers Principle(Physical Lower Bound of Information Processing)△E≥kBTIn2·△I(15)Erasing one bit of information consumes at least kBTln2 energy.This gives a hard constraint at the Ip layer — any information processing must be completed within the physical boundaries of space-time and energy, but information itself(Iv and above)is neither matter nor energy.八、物理边界约束朗道尔原理信息处理的物理底线⊿E≥k_B T ln 2·⊿I擦除一个比特的信息至少消耗k_B T l n 2 的能量。这给出了I_P层的硬约束——任何信息处理都必须在质能时空的物理边界内完成但信息本身I_V及以上不是物质也不是能量。这就是融智学信息科学原理的完整数学公式体系。从五维本体论定义出发经三大定律、道函数、双重五信耦合、全域多元数通式到物理边界约束全部有严格的数学表达。 融智学信息科学原理的完整数学公式体系
MethodFile availableToward a Unified Information Science: The Mathematical Principles of RongzhiXueAugust 2026DOI:10.13140/RG.2.2.19916.78726Xiaohui ZouOPL (16)Unified Information Science.pdf详细内容的英文版以下是简要内容英汉双语融智学信息科学原理的完整数学公式体系以2026年8月RG预印本《融智学信息科学体系——基于双重五信与信智序位的新范式》为基准Complete Mathematical Formula System of RongzhiXue Information Science PrinciplesXiaohui Zou0000-0002-5577-8245(based on the RG preprint of August 2026)AbstractThis document presents the complete set of mathematical formulas and definitions that constitute the foundational framework of RongzhiXue Information Science, as established in the 2026 RG preprint “RongzhiXue Information Science System-A New Paradigm Based on Dual Five-Xin and Xin-Zhi Sequence-Position”. The system spans ontological definitions, core intelligence equations,information measures,the Tao function, three fundamental laws of sequence-position logic, dual five-xin coupling dynamics, a universal multi-dimensional number formula, and physical boundary constraints.摘要本文呈现了构成“融智学信息科学”基础框架的完整数学公式和定义集该框架系基于2026年RG预印本《融智学信息科学系统一种基于“双五信”与“信智序位”的新范式》而确立。该系统涵盖本体论定义、核心智方程、信息度量、道函数、序位逻辑的三个基本定律、双五信耦合动力学、通用多维信息公式以及物理边界约束。1.OntologicalDefinitions1.1 Five-DimensionalVector Space(Ontological Skeleton of Information)I〈Ip,Iv,Is,IL,Im〉(1)where:Ip physical space-time (hardware carrier,non-information)Ivvirtual objects(software ontology,algorithms/logic gates)Isintentional class(intention/cognitive representation;meaning belongs to IM, intention to Is)ILsymbolic class(eight forms:characters,formulas,charts,tables,audio,images, 3D,living)Immeta-rule class (principles,meanings,laws,methods,sequence-positions)一、本体论定义五维向量空间信息的本体论骨架I 〈IP, IV, IS, IL, IM〉 1其中·I_P 质能时空物理层硬件载体非信息·I_V 虚拟物类软件本体算法/逻辑门·I_S 意类意图/认知表征义归 I_M、意归 I_S·I_L 文类符号层八大形式字式图表音像立活·I_M 理义法序位类元规则集1.2Meta-Rule Set(Mathematization of the Fifth Category)Im{λ|λ:(I×T)→{0,1}}(2)which assigns validity and priority judgments.元规则集第五范畴的数学化I_M {λ|λ: (I × T)→{0,1}}赋予有效性与优先级判定。2.CoreFormulas2.1 Intelligence Generation MechanismIntelligence InformationProcessingIntentional Selection(3)Information processing operations on the five information components (Ip→Iv→Is→IL→Im).Intentional selection driven by the five beliefs (credibility,trust,confidence,reputation,faith).二、核心公式2.1.智的生成机制智 信息处理 选择用意信息处理信息五信I_P→I_V→I_S→I_L→I_M的操作选择用意信念五信信用/信任/信心/信誉/信仰的驱动2.2UnificationofThreeIntelligencesHI⊕AICI(4)where:AIstrong information processingbutlacks intentionalselection(only pseudo-confidence).HI(Human Intelligence)naturalintentional selectiondriving biological neural networks.CI(Collaborative Intelligence) higher-order wisdom emerging fromhuman-machineinteractiongoverned bysequence-position order-positionOPlogic.2.2.三智统一HI⊕AI CI·AI人工智能 强信息处理缺选择用意仅有伪置信度·HI人类智力 天然选择用意驱动生物神经网络·CI协同之智 人机在序位逻辑统摄下涌现的高阶智慧3InformationMeasures3.1 Narrow Information Equation(Extension of Shannon Entropy)(5)3.2 General Information Equation(Rongzhi Entropy)(6)Physicalmeaning:conservativeflowofinformationamongmatter,intention,symbols,Tao,and methods.三、信息度量方程3.1.狭义信息方程香农熵扩展I_nar(X) logP(X|O)/P(X|T)3.2.广义信息方程融智熵I_gen ∫_R (O⨂I⨂T)·delta∆(L∘N)物理意义信息在“物、意、文、道、理义法序位”间的守恒流动。3.3 InformationIdentityI_nar I_gentr (Ψ○Q)(7)Meaning:totalinformation processingisjointlydeterminedbythethinkingcoordinate(Tao function Ψ) and database query (Q).3.3.信息恒等式I_{nar} I_{gen} tr(Ψ∘Q)意义信息处理总量由思维坐标道函数Ψ与数据库查询Q共同决定。4 TaoFunctionandThinkingCoordinates4.1DefinitionoftheTaoFunctionΨT×L→R³(8)Ψ(x)(Image(x),Abstraction(x),Intuition(x))(9)This is the mathematical expression of “joint subject-object meaning assignment”—the subject perceives the GE band and activates the corresponding sequence-position of the ID band via intentional selection;the object computes the ID band and outputs the GE band through a coupling function.四、道函数与思维坐标4.1.道函数定义Ψ: T×L→R^3Ψ(x) (形象(x),抽象(x),直觉(x))这是主客体联合赋义的数学表达——主体感知GE格带并通过意图选择激活ID格带的对应序位客体计算ID格带并通过联动函数输出GE格带。5 Three FundamentalLawsof Sequence-PositionLogic5.1 First Law(Rigid:UniqueConservation of Sequence-PositionRelations)∀u∈U,∃!id(u),id(φ(u))id(u)(10)Every element u has a unique sequence-position identifier id(u),which remains invariant under any legitimate natural transformation φ.Newtons conservation laws are a special case in the information domain.5.2 Second Law(Rigid:Synonymy Parallel Correspondence Con- version-Seeking Truth){id(a1),...,id(am)}{id(b₁),...,id(bn)}(11)Two tuples are synonymous if their sets of element sequence-positions are identical.This ensures semantic equivalence among different symbolic forms(characters,formulas,charts, tables,audio,images,3D,living).5.3 Third Law(Flexible:Agreeable Parallel Correspondence Conversion-Seeking Goodness and Beauty)(12)In a specific context c,intentional selection follows this distribution.It characterises the mathematical essence of “intentional selection”,controlled by the five extensions(generalised language, text, bilingual, translation, interpretation).五、序位逻辑三大基本定律第一定律刚性·序位关系唯一守恒∀u∈U,∃! id(u),id(φ(u)) id(u)任意元子 u具有唯一序位标识 id(u)且在合法自然变换φ下序位不变,牛顿守恒律是其在信息领域的特例。第二定律刚性·同义并列对应转换·求真{id(a_1),...,id(a_m)} {id(b_1),...,id(b_n)}两个元组同义当且仅当其元子序位集合一致。保证不同符号形式字式图表音像立活间的语义等价。第三定律柔性·同意并列对应转换·求善求美P(s|c) {exp((sφ,c))}/{∑exp(φ(s,c))}在具体语境 c 中意图的选择服从该分布。刻画选择用意的数学本质由五广广义语言/文本/双语/翻译/解释控制。6DualFive-XinCouplingDynamics6.1 CouplingDynamicsEquation(13)where:I vector of the five information components,B vector of the five beliefs,Φ cooperative potential function,Cdualdual five-xin coupling coefficient,ξ(t)stochastic fluctuation.Meaning:flexible judgments(beliefs)are not a “soft”thing floating outside the rigid framework,but are dynamical variables precisely anchored by the information components.六、双重五信耦合动力学耦合动力学方程d/dt(I⨂B) C_dual·∇Φ(I, B) ξ(t)其中·I 信息五信向量·B 信念五信向量·Φ 协同势能函数·C_dual 双重五信耦合系数·ξ(t) 随机涨落含义柔性判断信念五信不是游离在刚性框架之外的软东西而是被信息五信精确锚定的动力学变量。7Universal Multi-DimensionalNumber Formula(Patent Mathematical Kernel,2000)7.1GeneralForm(abi...)(14)where:Real part aauthentic information (meaning),unique and conservative →corresponds to the First Law.Imaginary part bifirst-dimensional formal identifier of the multi-gene text....extension to other imaginary dimensions for charts,texts,numbers,tables, audio,images,3D,living,etc.7.2 Five Major FunctionsUnified expression(complex/quaternion/octonion/multi-dimensional numbers),sequence- positioning (real part determines position),domain selection and orientation (imaginaryparts determine categories),synonymy parallel translation (coexistence of different multi- dimensional numbers with same real part),and unification of three natures (information processingintentional selection intelligence).七、全域多元数通式2000年专利数学内核通式(a bi ...)实部 a 本真信息义唯一性和守恒性 → 对应第一基本定律虚部 bi 多元基因文本的第一维形式标识... 图、文、数、表、音、像、立、活,等其余虚部的延展通式五大功能统一表达复数/四元数/八元数/多元数、测序定位实部确定序位、选域定向虚部确定类别、同义并列通译实部相同的不同多元数并列共存、三性统一虚部信息处理选择用意智。8PhysicalBoundaryConstraints8.1 Landauers Principle(Physical Lower Bound of Information Processing)△E≥kBTIn2·△I(15)Erasing one bit of information consumes at least kBTln2 energy.This gives a hard constraint at the Ip layer — any information processing must be completed within the physical boundaries of space-time and energy, but information itself(Iv and above)is neither matter nor energy.八、物理边界约束朗道尔原理信息处理的物理底线⊿E≥k_B T ln 2·⊿I擦除一个比特的信息至少消耗k_B T l n 2 的能量。这给出了I_P层的硬约束——任何信息处理都必须在质能时空的物理边界内完成但信息本身I_V及以上不是物质也不是能量。这就是融智学信息科学原理的完整数学公式体系。从五维本体论定义出发经三大定律、道函数、双重五信耦合、全域多元数通式到物理边界约束全部有严格的数学表达。