Dissertation/Thesis
Προβολή σε EDS

00: The Recursive Zero and the Layered Abstraction of Number

Λεπτομέρειες βιβλιογραφικής εγγραφής
Τίτλος: 00: The Recursive Zero and the Layered Abstraction of Number
Συγγραφείς: Bolter, Barry Brian
Συνεισφορές: Bolter, Barry Brian
Στοιχεία εκδότη: Zenodo
Έτος έκδοσης: 2025
Συλλογή: Zenodo
Θεματικοί όροι: 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
Περιγραφή: Title:00: The Recursive Zero and the Layered Abstraction of Number Description:This paper introduces a structurally distinct mathematical entity: recursive zero, denoted as 00. Unlike classical zero (0), which marks termination and nullity, 00 functions as a recursive neutral — a boundary that enables logical recombination and transformation rather than collapse. We demonstrate the operational distinction between 0 and 00 through two formal models: a recursive logic engine and an automata-based system. The paper also explores the implications of this distinction across computation, formal logic, automata theory, algebra, quantum systems, and programming language design. The extended number line is revealed to possess a structural asymmetry across the 00|0 boundary, where the domain left of 00 remains abstract and open, and the domain right of 0 is operationally closed. This asymmetry offers a new lens through which to understand definability, closure, and recursion in foundational mathematics. This is a foundational contribution intended for researchers in mathematics, theoretical computer science, formal logic, and symbolic systems. It may also be of interest to philosophers of mathematics and AI theorists exploring machine-structured reasoning.
Τύπος εγγράφου: Thesis
Γλώσσα: unknown
Relation: https://zenodo.org/records/15667175; oai:zenodo.org:15667175; https://doi.org/10.5281/zenodo.15667175
DOI: 10.5281/zenodo.15667175
Διαθεσιμότητα: https://doi.org/10.5281/zenodo.15667175
https://zenodo.org/records/15667175
Rights: Creative Commons Attribution 4.0 International ; cc-by-4.0 ; https://creativecommons.org/licenses/by/4.0/legalcode
Αριθμός Καταχώρησης: edsbas.FDC38688
Βάση Δεδομένων: BASE
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://doi.org/10.5281/zenodo.15667175#
    Name: EDS - BASE (ns324271)
    Category: fullText
    Text: View record from BASE
Header DbId: edsbas
DbLabel: BASE
An: edsbas.FDC38688
RelevancyScore: 892
AccessLevel: 3
PubType: Dissertation/Thesis
PubTypeId: unknown
PreciseRelevancyScore: 891.935607910156
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: 00: The Recursive Zero and the Layered Abstraction of Number
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Bolter%2C+Barry+Brian%22">Bolter, Barry Brian</searchLink>
– Name: Author
  Label: Contributors
  Group: Au
  Data: Bolter, Barry Brian
– Name: Publisher
  Label: Publisher Information
  Group: PubInfo
  Data: Zenodo
– Name: DatePubCY
  Label: Publication Year
  Group: Date
  Data: 2025
– Name: Subset
  Label: Collection
  Group: HoldingsInfo
  Data: Zenodo
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Recursive+zero%22">Recursive zero</searchLink><br /><searchLink fieldCode="DE" term="%22Double+zero+%2800%29%22">Double zero (00)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+abstraction%22">Mathematical abstraction</searchLink><br /><searchLink fieldCode="DE" term="%22Logic+boundary%22">Logic boundary</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+recursion%22">Structural recursion</searchLink><br /><searchLink fieldCode="DE" term="%22Formal+systems%22">Formal systems</searchLink><br /><searchLink fieldCode="DE" term="%22Zero+asymmetry%22">Zero asymmetry</searchLink><br /><searchLink fieldCode="DE" term="%22Automata+theory%22">Automata theory</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+logic%22">Computational logic</searchLink><br /><searchLink fieldCode="DE" term="%22Recursive+computation%22">Recursive computation</searchLink><br /><searchLink fieldCode="DE" term="%22Meta-neutral+element%22">Meta-neutral element</searchLink><br /><searchLink fieldCode="DE" term="%22Type+theory%22">Type theory</searchLink><br /><searchLink fieldCode="DE" term="%22Recursive+mathematics%22">Recursive mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Non-standard+number+systems%22">Non-standard number systems</searchLink><br /><searchLink fieldCode="DE" term="%22Closure+and+abstraction%22">Closure and abstraction</searchLink><br /><searchLink fieldCode="DE" term="%22Symbolic+logic%22">Symbolic logic</searchLink><br /><searchLink fieldCode="DE" term="%22Foundations+of+Mathematics%22">Foundations of Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Logic+and+Set+Theory%22">Logic and Set Theory</searchLink><br /><searchLink fieldCode="DE" term="%22Number+Theory+%28Non-standard+number+systems%29%22">Number Theory (Non-standard number systems)</searchLink><br /><searchLink fieldCode="DE" term="%22Formal+Languages+and+Automata+Theory%22">Formal Languages and Automata Theory</searchLink><br /><searchLink fieldCode="DE" term="%22Theory+of+Computation%22">Theory of Computation</searchLink><br /><searchLink fieldCode="DE" term="%22Programming+Languages+%28Semantics%22">Programming Languages (Semantics</searchLink><br /><searchLink fieldCode="DE" term="%22Type+Systems%29%22">Type Systems)</searchLink><br /><searchLink fieldCode="DE" term="%22Philosophy+of+Mathematics%22">Philosophy of Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Ontology+of+Abstraction%22">Ontology of Abstraction</searchLink><br /><searchLink fieldCode="DE" term="%22Symbolic+Reasoning%22">Symbolic Reasoning</searchLink><br /><searchLink fieldCode="DE" term="%22Recursive+Representation+Models%22">Recursive Representation Models</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: Title:00: The Recursive Zero and the Layered Abstraction of Number Description:This paper introduces a structurally distinct mathematical entity: recursive zero, denoted as 00. Unlike classical zero (0), which marks termination and nullity, 00 functions as a recursive neutral — a boundary that enables logical recombination and transformation rather than collapse. We demonstrate the operational distinction between 0 and 00 through two formal models: a recursive logic engine and an automata-based system. The paper also explores the implications of this distinction across computation, formal logic, automata theory, algebra, quantum systems, and programming language design. The extended number line is revealed to possess a structural asymmetry across the 00|0 boundary, where the domain left of 00 remains abstract and open, and the domain right of 0 is operationally closed. This asymmetry offers a new lens through which to understand definability, closure, and recursion in foundational mathematics. This is a foundational contribution intended for researchers in mathematics, theoretical computer science, formal logic, and symbolic systems. It may also be of interest to philosophers of mathematics and AI theorists exploring machine-structured reasoning.
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Thesis
– Name: Language
  Label: Language
  Group: Lang
  Data: unknown
– Name: NoteTitleSource
  Label: Relation
  Group: SrcInfo
  Data: https://zenodo.org/records/15667175; oai:zenodo.org:15667175; https://doi.org/10.5281/zenodo.15667175
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.5281/zenodo.15667175
– Name: URL
  Label: Availability
  Group: URL
  Data: https://doi.org/10.5281/zenodo.15667175<br />https://zenodo.org/records/15667175
– Name: Copyright
  Label: Rights
  Group: Cpyrght
  Data: Creative Commons Attribution 4.0 International ; cc-by-4.0 ; https://creativecommons.org/licenses/by/4.0/legalcode
– Name: AN
  Label: Accession Number
  Group: ID
  Data: edsbas.FDC38688
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.FDC38688
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.5281/zenodo.15667175
    Languages:
      – Text: unknown
    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
        Type: general
      – SubjectFull: Recursive computation
        Type: general
      – 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
        Type: general
      – SubjectFull: Logic and Set Theory
        Type: general
      – SubjectFull: Number Theory (Non-standard number systems)
        Type: general
      – SubjectFull: Formal Languages and Automata Theory
        Type: general
      – SubjectFull: Theory of Computation
        Type: general
      – SubjectFull: Programming Languages (Semantics
        Type: general
      – SubjectFull: Type Systems)
        Type: general
      – SubjectFull: Philosophy of Mathematics
        Type: general
      – SubjectFull: Ontology of Abstraction
        Type: general
      – SubjectFull: Symbolic Reasoning
        Type: general
      – SubjectFull: Recursive Representation Models
        Type: general
    Titles:
      – TitleFull: 00: The Recursive Zero and the Layered Abstraction of Number
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Bolter, Barry Brian
      – PersonEntity:
          Name:
            NameFull: Bolter, Barry Brian
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-locals
              Value: edsbas
            – Type: issn-locals
              Value: edsbas.oa
ResultId 1