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<journal-id journal-id-type="publisher">global-journal-of-science-frontier-research-f-mathematics-decision</journal-id>
<journal-title-group>
<journal-title>Global Journal of Science Frontier Research - F: Mathematics &amp; Decision</journal-title>
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<issn publication-format="print">0975-5896</issn>
<issn publication-format="electronic">2249-4626</issn>
<publisher><publisher-name>Global Journals Publishing Group Incorporated</publisher-name></publisher>
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<article-id pub-id-type="publisher-id">115418</article-id>
<title-group>
<article-title>Symbolic Collapse Intractability Hypothesis: P â‰  NP</article-title>
<subtitle>Formal Proof of P != NP via Symbolic Entropy</subtitle>
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<contrib-group>
<contrib contrib-type="author"><name><surname>Kornhaus</surname><given-names>Justin</given-names></name><xref ref-type="aff" rid="aff1" />
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<aff id="aff1">UNITED STATES</aff>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2025-09-03">
<day>03</day>
<month>09</month>
<year>2025</year>
</pub-date>
<volume>25</volume>
<issue>F1</issue>
<fpage>1</fpage>
<lpage>5</lpage>
<abstract><p>The following proof focuses on the Symbolic Collapse Intractability Hypothesis and leverages symbolic entropy, recursive tractability, and structural complexity to argue that NPcomplete problems with high entropy are intractable in polynomial time, implying P ≠ NP.</p></abstract>
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<kwd>Symbolic Collapse Intractability Hypothesis and leverages symbolic entropy.</kwd>
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<title>Full Text</title>
<p>The following proof focuses on the Symbolic Collapse Intractability Hypothesis and leverages symbolic entropy, recursive tractability, and structural complexity to argue that NPcomplete problems with high entropy are intractable in polynomial time, implying P â‰  NP.</p>
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