<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-05045749</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-04T09:01:09+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Infinity Algebra: A Foundational Framework for Symbolic Computation with Infinite Quantities</title>
            <author role="aut">
              <persName>
                <forename type="first">Antonios</forename>
                <surname>Valamontes</surname>
              </persName>
              <email type="md5">64acb5da5d8c17669acf81e78ed524d1</email>
              <email type="domain">kapodistrian.edu.gr</email>
              <idno type="idhal" notation="string">antonios-valamontes</idno>
              <idno type="idhal" notation="numeric">1535629</idno>
              <idno type="halauthorid" notation="string">3494874-1535629</idno>
              <idno type="ORCID">https://orcid.org/0009-0008-5616-7746</idno>
              <idno type="ARXIV">https://arxiv.org/a/valamontes_a_1</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=AifUEgIAAAAJ</idno>
              <affiliation ref="#struct-1246210"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Antonios</forename>
                <surname>Valamontes</surname>
              </persName>
              <email type="md5">9d67ba3862323b2c557d53c127ebc898</email>
              <email type="domain">valamontes.com</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2025-04-24 14:55:34</date>
              <date type="whenModified">2025-05-07 16:54:00</date>
              <date type="whenReleased">2025-05-07 16:54:00</date>
              <date type="whenProduced">2025-04-24</date>
              <date type="whenEndEmbargoed">2025-04-24</date>
              <ref type="file" target="https://hal.science/hal-05045749v1/document">
                <date notBefore="2025-04-24"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-05045749v1/file/Infinity_Algebra__A_Foundational_Framework_for_Symbolic_Computation_with_Infinite_Quantitiesv2.pdf" id="file-5045749-4368961">
                <date notBefore="2025-04-24"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="1573398">
                <persName>
                  <forename>Antonios</forename>
                  <surname>Valamontes</surname>
                </persName>
                <email type="md5">9d67ba3862323b2c557d53c127ebc898</email>
                <email type="domain">valamontes.com</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-05045749</idno>
            <idno type="halUri">https://hal.science/hal-05045749</idno>
            <idno type="halBibtex">valamontes:hal-05045749</idno>
            <idno type="halRefHtml">2025</idno>
            <idno type="halRef">2025</idno>
            <availability status="restricted">
              <licence target="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0 - Attribution<ref corresp="#file-5045749-4368961"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt/>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Infinity Algebra: A Foundational Framework for Symbolic Computation with Infinite Quantities</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Antonios</forename>
                    <surname>Valamontes</surname>
                  </persName>
                  <email type="md5">64acb5da5d8c17669acf81e78ed524d1</email>
                  <email type="domain">kapodistrian.edu.gr</email>
                  <idno type="idhal" notation="string">antonios-valamontes</idno>
                  <idno type="idhal" notation="numeric">1535629</idno>
                  <idno type="halauthorid" notation="string">3494874-1535629</idno>
                  <idno type="ORCID">https://orcid.org/0009-0008-5616-7746</idno>
                  <idno type="ARXIV">https://arxiv.org/a/valamontes_a_1</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=AifUEgIAAAAJ</idno>
                  <affiliation ref="#struct-1246210"/>
                </author>
              </analytic>
              <monogr>
                <imprint>
                  <date type="datePub">2025-04-16</date>
                </imprint>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Infinity Algebra Symbolic Computation Infinite Calculus Black Hole Entropy Non-Standard Analysis Singularity Modeling Symbolic Field Theory</term>
                <term xml:lang="en">Infinity Algebra</term>
                <term xml:lang="en">Symbolic Computation</term>
                <term xml:lang="en">Infinite Calculus</term>
                <term xml:lang="en">Black Hole Entropy</term>
                <term xml:lang="en">Non-Standard Analysis</term>
                <term xml:lang="en">Singularity Modeling</term>
                <term xml:lang="en">Symbolic Field Theory</term>
              </keywords>
              <classCode scheme="halDomain" n="sdu">Sciences of the Universe [physics]</classCode>
              <classCode scheme="halDomain" n="math">Mathematics [math]</classCode>
              <classCode scheme="halDomain" n="nlin">Nonlinear Sciences [physics]</classCode>
              <classCode scheme="halDomain" n="sdu">Sciences of the Universe [physics]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Infinity Algebra is a new mathematical framework designed to treat infinity not as a limit, asymptotic value, or conceptual extremum, but as a fully operable and symbolic algebraic entity. This paper introduces the foundational axioms of Infinity Algebra, including explicit rules for infinite addition, subtraction, multiplication, division, inverse operations, and exponentiation. By establishing a closed and internally consistent algebraic system, we enable symbolic manipulation of infinite quantities without reliance on traditional limit-based calculus or set-theoretic extensions. We formally define Infinity Groups, Rings, and Fields that incorporate ∞ as computable operands, allowing for structured algebraic interactions with real and infinite values. These structures serve as the basis for extended domains such as Infinity Calculus, Infinity Linear Algebra, and Infinity-Valued Function Spaces, including ∞-matrices, ∞-tensors, and symbolic derivatives evaluated at ∞. Applications span multiple disciplines: from theoretical mathematics to black hole entropy modeling, from quantum field singularities to symbolic AI systems operating over infinite-depth architectures. The symbolic entropy matrix and ∞-Einstein equations demonstrate how Infinity Algebra can reframe gravitational singularities and divergent field interactions in physics. The framework is supported by a Python-based symbolic computation engine that enables experimentation, visualization, and application of Infinity Algebra to real and abstract problems. Ultimately, this system offers a robust and extensible language for engaging with infinite structure, both as a formal tool and as a philosophical reorientation. Infinity Algebra not only complements existing approaches to divergence but provides a symbolic foundation for future exploration of the infinite in mathematics and physics.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="institution" xml:id="struct-1246210" status="INCOMING">
          <orgName>Kapodistrian Academy of Science</orgName>
          <orgName type="acronym">KAS</orgName>
          <desc>
            <address>
              <country key="US"/>
            </address>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>