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00: The Recursive Zero and the Layered Abstraction of Number

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Title: 00: The Recursive Zero and the Layered Abstraction of Number
Authors: Bolter, Barry Brian
Contributors: Bolter, Barry Brian
Publisher Information: Zenodo
Publication Year: 2025
Collection: Zenodo
Subject Terms: Recursive zero, Double zero (00), Mathematical abstraction, Logic boundary, Structural recursion, Formal systems, Zero asymmetry, Automata theory, Computational logic, Recursive computation, Meta-neutral element, Type theory, Recursive mathematics, Non-standard number systems, Closure and abstraction, Symbolic logic, Foundations of Mathematics, Logic and Set Theory, Number Theory (Non-standard number systems), Formal Languages and Automata Theory, Theory of Computation, Programming Languages (Semantics, Type Systems), Philosophy of Mathematics, Ontology of Abstraction, Symbolic Reasoning, Recursive Representation Models
Description: This document is a preprint of the paper titled:"Recursive Neutrality in Automata and Arithmetic: A Formal Model of the Double Zero Operator"It has been made publicly available on Zenodo for the purposes of early community access and peer feedback. The work is currently under consideration for formal peer review and academic journal publication.This paper introduces a formal distinction between two types of computational neutrality, represented by the classical zero (0) and a recursive-neutral operator (00). The structure defines a novel binary operation ⊕ over an extended domain X = ℕ₀ ∪ {00}, accompanied by an automaton model extended with a recursive modifier δ₀₀. The paper demonstrates that 00 behaves as a structurally distinct, non-halting transformation operator — not as an identity element — and proposes a layered ordering framework that distinguishes recursion from halting.Readers are encouraged to treat this version as a theoretical preprint. Feedback is welcome and may inform the final peer-reviewed submission.License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Document Type: report
Language: unknown
Relation: https://zenodo.org/records/15714877; oai:zenodo.org:15714877; https://doi.org/10.5281/zenodo.15714877
DOI: 10.5281/zenodo.15714877
Availability: https://doi.org/10.5281/zenodo.15714877
https://zenodo.org/records/15714877
Rights: Creative Commons Attribution 4.0 International ; cc-by-4.0 ; https://creativecommons.org/licenses/by/4.0/legalcode
Accession Number: edsbas.77D57C70
Database: BASE
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  Data: 00: The Recursive Zero and the Layered Abstraction of Number
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  Data: 2025
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  Data: This document is a preprint of the paper titled:"Recursive Neutrality in Automata and Arithmetic: A Formal Model of the Double Zero Operator"It has been made publicly available on Zenodo for the purposes of early community access and peer feedback. The work is currently under consideration for formal peer review and academic journal publication.This paper introduces a formal distinction between two types of computational neutrality, represented by the classical zero (0) and a recursive-neutral operator (00). The structure defines a novel binary operation ⊕ over an extended domain X = ℕ₀ ∪ {00}, accompanied by an automaton model extended with a recursive modifier δ₀₀. The paper demonstrates that 00 behaves as a structurally distinct, non-halting transformation operator — not as an identity element — and proposes a layered ordering framework that distinguishes recursion from halting.Readers are encouraged to treat this version as a theoretical preprint. Feedback is welcome and may inform the final peer-reviewed submission.License: Creative Commons Attribution 4.0 International (CC BY 4.0)
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  Data: https://zenodo.org/records/15714877; oai:zenodo.org:15714877; https://doi.org/10.5281/zenodo.15714877
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        Value: 10.5281/zenodo.15714877
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    Subjects:
      – SubjectFull: Recursive zero
        Type: general
      – SubjectFull: Double zero (00)
        Type: general
      – SubjectFull: Mathematical abstraction
        Type: general
      – SubjectFull: Logic boundary
        Type: general
      – SubjectFull: Structural recursion
        Type: general
      – SubjectFull: Formal systems
        Type: general
      – SubjectFull: Zero asymmetry
        Type: general
      – SubjectFull: Automata theory
        Type: general
      – SubjectFull: Computational logic
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      – SubjectFull: Recursive computation
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      – SubjectFull: Meta-neutral element
        Type: general
      – SubjectFull: Type theory
        Type: general
      – SubjectFull: Recursive mathematics
        Type: general
      – SubjectFull: Non-standard number systems
        Type: general
      – SubjectFull: Closure and abstraction
        Type: general
      – SubjectFull: Symbolic logic
        Type: general
      – SubjectFull: Foundations of Mathematics
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      – SubjectFull: Logic and Set Theory
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      – SubjectFull: Number Theory (Non-standard number systems)
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      – SubjectFull: Formal Languages and Automata Theory
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      – SubjectFull: Theory of Computation
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      – SubjectFull: Programming Languages (Semantics
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      – SubjectFull: Type Systems)
        Type: general
      – SubjectFull: Philosophy of Mathematics
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      – SubjectFull: Ontology of Abstraction
        Type: general
      – SubjectFull: Symbolic Reasoning
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      – SubjectFull: Recursive Representation Models
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      – TitleFull: 00: The Recursive Zero and the Layered Abstraction of Number
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              Y: 2025
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