Research-Stack/4-Infrastructure/shim/imports/mathxml_domains.graphml
2026-05-11 22:18:31 -05:00

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<?xml version="1.0" encoding="UTF-8"?>
<graphml xmlns="http://graphml.graphdrawing.org/xmlns"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns
http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd">
<key id="d0" for="node" attr.name="category" attr.type="string"/>
<key id="d1" for="node" attr.name="priority" attr.type="string"/>
<key id="d2" for="node" attr.name="connections" attr.type="string"/>
<key id="d3" for="node" attr.name="number" attr.type="int"/>
<key id="d4" for="edge" attr.name="relationship" attr.type="string"/>
<key id="d5" for="edge" attr.name="strength" attr.type="string"/>
<graph id="MathematicalFields" edgedefault="directed">
<!-- Category 1: Foundational Extensions -->
<node id="n1">
<data key="d0">Foundational Extensions</data>
<data key="d1">HIGH</data>
<data key="d2">Genus-3 surfaces, branch-cut defects, topological RAM, FAMM basins, PIST witness surfaces</data>
<data key="d3">1</data>
</node>
<node id="n2">
<data key="d0">Foundational Extensions</data>
<data key="d1">HIGH</data>
<data key="d2">Particle spectrum, four forces, spin quantization, winding numbers, OTOM bind</data>
<data key="d3">2</data>
</node>
<node id="n3">
<data key="d0">Foundational Extensions</data>
<data key="d1">HIGH</data>
<data key="d2">Topological RAM classification, manifold vector bundles, quantum foam, fractional unified field</data>
<data key="d3">3</data>
</node>
<node id="n4">
<data key="d0">Foundational Extensions</data>
<data key="d1">HIGH</data>
<data key="d2">Quantum foam, fractional derivatives, topological RAM, FAMM frustration, OTOM formalization</data>
<data key="d3">4</data>
</node>
<!-- Category 2: Deep Theoretical Connections -->
<node id="n5">
<data key="d0">Deep Theoretical Connections</data>
<data key="d1">HIGH</data>
<data key="d2">Lean 4 formalization, OTOM bind primitive, topological RAM, manifold classification</data>
<data key="d3">5</data>
</node>
<node id="n6">
<data key="d0">Deep Theoretical Connections</data>
<data key="d1">MEDIUM</data>
<data key="d2">OTOM formalization, FAMM composition, PIST transformations, bind primitive</data>
<data key="d3">6</data>
</node>
<node id="n7">
<data key="d0">Deep Theoretical Connections</data>
<data key="d1">MEDIUM</data>
<data key="d2">Local-to-global principles, FAMM memory, OTOM as topos, data manifold as site</data>
<data key="d3">7</data>
</node>
<node id="n8">
<data key="d0">Deep Theoretical Connections</data>
<data key="d1">MEDIUM</data>
<data key="d2">Quantum foam, fractional field, topological RAM, OTOM, compression moduli</data>
<data key="d3">8</data>
</node>
<!-- Category 3: Analysis and PDE Deep Dive -->
<node id="n9">
<data key="d0">Analysis and PDE Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">Fractional derivatives, quantum foam, branch cuts, FAMM frustration, compression</data>
<data key="d3">9</data>
</node>
<node id="n10">
<data key="d0">Analysis and PDE Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">Fractal dimensions, topological RAM, FAMM basins, compression entropy, recursive structures</data>
<data key="d3">10</data>
</node>
<node id="n11">
<data key="d0">Analysis and PDE Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">Torsional cosmology, particle spectrum, eigenvector clustering, FAMM, compression</data>
<data key="d3">11</data>
</node>
<node id="n12">
<data key="d0">Analysis and PDE Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">Torsional unwinding, FAMM frustration, topological RAM, fractional field, compression</data>
<data key="d3">12</data>
</node>
<!-- Category 4: Probability and Statistics Deep Dive -->
<node id="n13">
<data key="d0">Probability and Statistics Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">FAMM memory cycles, search space exploration, compression entropy, distributed systems</data>
<data key="d3">13</data>
</node>
<node id="n14">
<data key="d0">Probability and Statistics Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">FAMM frustration as stochastic process, quantum foam, topological RAM, compression</data>
<data key="d3">14</data>
</node>
<node id="n15">
<data key="d0">Probability and Statistics Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">Compression, FAMM optimization, search space, OTOM, Bayesian inference</data>
<data key="d3">15</data>
</node>
<node id="n16">
<data key="d0">Probability and Statistics Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">FAMM frustration, compression, search space, distributed systems, topological RAM</data>
<data key="d3">16</data>
</node>
<!-- Category 5: Algebra and Number Theory Deep Dive -->
<node id="n17">
<data key="d0">Algebra and Number Theory Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">Integer arithmetic, mass numbers, fractional field, compression, OTOM</data>
<data key="d3">17</data>
</node>
<node id="n18">
<data key="d0">Algebra and Number Theory Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">Fractional unified field, mass numbers, compression, OTOM, quantum foam</data>
<data key="d3">18</data>
</node>
<node id="n19">
<data key="d0">Algebra and Number Theory Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">Topological RAM, FAMM, OTOM, compression, manifold classification</data>
<data key="d3">19</data>
</node>
<node id="n20">
<data key="d0">Algebra and Number Theory Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">Integer arithmetic, OTOM modules, compression, topological RAM, fractional field</data>
<data key="d3">20</data>
</node>
<!-- Category 6: Geometry and Topology Deep Dive -->
<node id="n21">
<data key="d0">Geometry and Topology Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">Torsional cosmology, topological RAM, FAMM, compression, genus-3 surfaces</data>
<data key="d3">21</data>
</node>
<node id="n22">
<data key="d0">Geometry and Topology Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">Torsional unwinding, FAMM, compression, OTOM, quantum foam</data>
<data key="d3">22</data>
</node>
<node id="n23">
<data key="d0">Geometry and Topology Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">Fractional unified field, torsional cosmology, compression, OTOM, topological RAM</data>
<data key="d3">23</data>
</node>
<node id="n24">
<data key="d0">Geometry and Topology Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">Braid theory, genus-3 surfaces, topological RAM, FAMM, OTOM</data>
<data key="d3">24</data>
</node>
<!-- Category 7: Mathematical Physics Deep Dive -->
<node id="n25">
<data key="d0">Mathematical Physics Deep Dive</data>
<data key="d1">MEDIUM</data>
<data key="d2">Fractional unified field, quantum foam, FAMM, OTOM, topological RAM</data>
<data key="d3">25</data>
</node>
<node id="n26">
<data key="d0">Mathematical Physics Deep Dive</data>
<data key="d1">LOW</data>
<data key="d2">Fractional unified field, quantum foam, genus-3 surfaces, topological RAM, OTOM</data>
<data key="d3">26</data>
</node>
<node id="n27">
<data key="d0">Mathematical Physics Deep Dive</data>
<data key="d1">LOW</data>
<data key="d2">Quantum foam, torsional cosmology, topological RAM, FAMM, fractional field</data>
<data key="d3">27</data>
</node>
<node id="n28">
<data key="d0">Mathematical Physics Deep Dive</data>
<data key="d1">LOW</data>
<data key="d2">Fractional unified field, torsional cosmology, compression, OTOM, quantum foam</data>
<data key="d3">28</data>
</node>
<!-- Category 8: Computational and Applied Mathematics -->
<node id="n29">
<data key="d0">Computational and Applied Mathematics</data>
<data key="d1">LOW</data>
<data key="d2">Fractional derivatives, torsional cosmology, FAMM, topological RAM, compression</data>
<data key="d3">29</data>
</node>
<node id="n30">
<data key="d0">Computational and Applied Mathematics</data>
<data key="d1">MEDIUM</data>
<data key="d2">FAMM, search space, compression, OTOM, topological RAM</data>
<data key="d3">30</data>
</node>
<node id="n31">
<data key="d0">Computational and Applied Mathematics</data>
<data key="d1">LOW</data>
<data key="d2">Compression, FAMM, search space, OTOM, topological RAM</data>
<data key="d3">31</data>
</node>
<node id="n32">
<data key="d0">Computational and Applied Mathematics</data>
<data key="d1">LOW</data>
<data key="d2">Compression algorithms, search space, OTOM, FAMM, topological RAM</data>
<data key="d3">32</data>
</node>
<!-- Category 9: Interdisciplinary Connections -->
<node id="n33">
<data key="d0">Interdisciplinary Connections</data>
<data key="d1">LOW</data>
<data key="d2">PIST biological shifter, genetics, FAMM, compression, OTOM</data>
<data key="d3">33</data>
</node>
<node id="n34">
<data key="d0">Interdisciplinary Connections</data>
<data key="d1">LOW</data>
<data key="d2">FAMM, topological RAM, compression, OTOM, search space</data>
<data key="d3">34</data>
</node>
<node id="n35">
<data key="d0">Interdisciplinary Connections</data>
<data key="d1">LOW</data>
<data key="d2">Stochastic processes, FAMM, optimization, risk management, compression</data>
<data key="d3">35</data>
</node>
<node id="n36">
<data key="d0">Interdisciplinary Connections</data>
<data key="d1">LOW</data>
<data key="d2">Quantum foam, topological RAM, FAMM, compression, OTOM</data>
<data key="d3">36</data>
</node>
<!-- Category 10: Specialized and Cutting-Edge Fields -->
<node id="n37">
<data key="d0">Specialized and Cutting-Edge Fields</data>
<data key="d1">LOW</data>
<data key="d2">Integer arithmetic, compression, FAMM, OTOM, topological RAM</data>
<data key="d3">37</data>
</node>
<node id="n38">
<data key="d0">Specialized and Cutting-Edge Fields</data>
<data key="d1">LOW</data>
<data key="d2">OTOM transformations, FAMM, compression, topological RAM, search space</data>
<data key="d3">38</data>
</node>
<node id="n39">
<data key="d0">Specialized and Cutting-Edge Fields</data>
<data key="d1">LOW</data>
<data key="d2">Eigenvector clustering, FAMM, compression, OTOM, quantum foam</data>
<data key="d3">39</data>
</node>
<node id="n40">
<data key="d0">Specialized and Cutting-Edge Fields</data>
<data key="d1">LOW</data>
<data key="d2">OTOM, FAMM, compression, quantum foam, topological RAM</data>
<data key="d3">40</data>
</node>
<node id="n41">
<data key="d0">Specialized and Cutting-Edge Fields</data>
<data key="d1">LOW</data>
<data key="d2">Compression, FAMM, search space, topological RAM, OTOM</data>
<data key="d3">41</data>
</node>
<node id="n42">
<data key="d0">Specialized and Cutting-Edge Fields</data>
<data key="d1">LOW</data>
<data key="d2">FAMM, search space, ENE, compression, OTOM</data>
<data key="d3">42</data>
</node>
<node id="n43">
<data key="d0">Specialized and Cutting-Edge Fields</data>
<data key="d1">MEDIUM</data>
<data key="d2">Compression, FAMM, topological RAM, manifold classification, OTOM</data>
<data key="d3">43</data>
</node>
<node id="n44">
<data key="d0">Specialized and Cutting-Edge Fields</data>
<data key="d1">MEDIUM</data>
<data key="d2">OTOM, FAMM, quantum foam, compression, topological RAM</data>
<data key="d3">44</data>
</node>
<node id="n45">
<data key="d0">Specialized and Cutting-Edge Fields</data>
<data key="d1">LOW</data>
<data key="d2">OTOM, FAMM, topological RAM, compression, quantum foam</data>
<data key="d3">45</data>
</node>
<node id="n46">
<data key="d0">Specialized and Cutting-Edge Fields</data>
<data key="d1">LOW</data>
<data key="d2">Topological RAM, fractional derivatives, OTOM, FAMM, quantum foam</data>
<data key="d3">46</data>
</node>
<node id="n47">
<data key="d0">Specialized and Cutting-Edge Fields</data>
<data key="d1">LOW</data>
<data key="d2">Quantum foam, topological RAM, torsional cosmology, FAMM, OTOM</data>
<data key="d3">47</data>
</node>
<node id="n48">
<data key="d0">Specialized and Cutting-Edge Fields</data>
<data key="d1">LOW</data>
<data key="d2">Compression, FAMM, OTOM, search space, topological RAM</data>
<data key="d3">48</data>
</node>
<node id="n49">
<data key="d0">Specialized and Cutting-Edge Fields</data>
<data key="d1">LOW</data>
<data key="d2">Braid theory, fractional unified field, FAMM, OTOM, topological RAM</data>
<data key="d3">49</data>
</node>
<node id="n50">
<data key="d0">Specialized and Cutting-Edge Fields</data>
<data key="d1">LOW</data>
<data key="d2">Topological RAM, FAMM, OTOM, compression, manifold classification</data>
<data key="d3">50</data>
</node>
<!-- Edges showing relationships and prerequisites -->
<!-- Algebraic Topology connections -->
<edge source="n1" target="n5">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n1" target="n7">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n1" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n1" target="n24">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n1" target="n43">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<!-- Representation Theory connections -->
<edge source="n2" target="n6">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n2" target="n25">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n2" target="n11">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- K-Theory connections -->
<edge source="n3" target="n1">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n3" target="n4">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n3" target="n25">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Non-Commutative Geometry connections -->
<edge source="n4" target="n3">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n4" target="n9">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n4" target="n25">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<!-- Homotopy Type Theory connections -->
<edge source="n5" target="n6">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n5" target="n8">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n5" target="n44">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<!-- Category Theory connections -->
<edge source="n6" target="n5">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n6" target="n7">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n6" target="n38">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n6" target="n44">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<!-- Sheaf Theory connections -->
<edge source="n7" target="n1">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n7" target="n6">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n7" target="n43">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Derived Algebraic Geometry connections -->
<edge source="n8" target="n1">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n8" target="n6">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n8" target="n18">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<!-- Microlocal Analysis connections -->
<edge source="n9" target="n12">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n9" target="n11">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n9" target="n4">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<!-- Geometric Measure Theory connections -->
<edge source="n10" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n10" target="n1">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n10" target="n43">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Harmonic Analysis connections -->
<edge source="n11" target="n2">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n11" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n11" target="n39">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Nonlinear PDE connections -->
<edge source="n12" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n12" target="n9">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n12" target="n29">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Ergodic Theory connections -->
<edge source="n13" target="n15">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n13" target="n14">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n13" target="n42">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Stochastic Calculus connections -->
<edge source="n14" target="n13">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n14" target="n16">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n14" target="n35">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<!-- Information Geometry connections -->
<edge source="n15" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n15" target="n30">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n15" target="n31">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Large Deviations connections -->
<edge source="n16" target="n14">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n16" target="n15">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<!-- Algebraic Number Theory connections -->
<edge source="n17" target="n20">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n17" target="n18">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<!-- Arithmetic Geometry connections -->
<edge source="n18" target="n17">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n18" target="n20">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n18" target="n23">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Homological Algebra connections -->
<edge source="n19" target="n1">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n19" target="n6">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n19" target="n50">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<!-- Commutative Algebra connections -->
<edge source="n20" target="n19">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n20" target="n17">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<!-- Riemannian Geometry connections -->
<edge source="n21" target="n1">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n21" target="n22">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n21" target="n23">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n21" target="n10">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<!-- Symplectic Geometry connections -->
<edge source="n22" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n22" target="n2">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n22" target="n25">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Complex Geometry connections -->
<edge source="n23" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n23" target="n22">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n23" target="n18">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Low-Dimensional Topology connections -->
<edge source="n24" target="n1">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n24" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n24" target="n49">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n24" target="n25">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- QFT connections -->
<edge source="n25" target="n2">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n25" target="n4">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n25" target="n9">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<!-- String Theory connections -->
<edge source="n26" target="n25">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n26" target="n23">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n26" target="n24">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<!-- Loop Quantum Gravity connections -->
<edge source="n27" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n27" target="n2">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n27" target="n47">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Twistor Theory connections -->
<edge source="n28" target="n23">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n28" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<!-- Numerical Analysis connections -->
<edge source="n29" target="n12">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n29" target="n9">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n29" target="n11">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Optimization connections -->
<edge source="n30" target="n15">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n30" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n30" target="n42">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<!-- Machine Learning Theory connections -->
<edge source="n31" target="n15">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n31" target="n30">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n31" target="n39">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Computational Complexity connections -->
<edge source="n32" target="n30">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n32" target="n48">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Mathematical Biology connections -->
<edge source="n33" target="n13">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n33" target="n30">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<!-- Mathematical Neuroscience connections -->
<edge source="n34" target="n13">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n34" target="n14">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<!-- Mathematical Finance connections -->
<edge source="n35" target="n14">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n35" target="n16">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<!-- Quantum Information Theory connections -->
<edge source="n36" target="n25">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n36" target="n2">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n36" target="n44">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<!-- Tropical Geometry connections -->
<edge source="n37" target="n20">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n37" target="n30">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<!-- Cluster Algebras connections -->
<edge source="n38" target="n6">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n38" target="n20">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n38" target="n49">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Random Matrix Theory connections -->
<edge source="n39" target="n11">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n39" target="n14">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n39" target="n40">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<!-- Free Probability Theory connections -->
<edge source="n40" target="n4">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n40" target="n39">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n40" target="n6">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Optimal Transport connections -->
<edge source="n41" target="n15">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n41" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n41" target="n30">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Mean Field Games connections -->
<edge source="n42" target="n14">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n42" target="n30">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n42" target="n12">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Topological Data Analysis connections -->
<edge source="n43" target="n1">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n43" target="n7">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n43" target="n31">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<!-- Categorical Quantum Mechanics connections -->
<edge source="n44" target="n6">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n44" target="n36">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n44" target="n2">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Homotopical Algebra connections -->
<edge source="n45" target="n6">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n45" target="n19">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n45" target="n8">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<!-- Synthetic Differential Geometry connections -->
<edge source="n46" target="n7">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n46" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n46" target="n9">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Causal Set Theory connections -->
<edge source="n47" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n47" target="n25">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<!-- Algorithmic Information Theory connections -->
<edge source="n48" target="n15">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n48" target="n32">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<!-- Quantum Groups connections -->
<edge source="n49" target="n2">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n49" target="n6">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n49" target="n24">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<!-- Derived Algebraic Topology connections -->
<edge source="n50" target="n1">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n50" target="n19">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n50" target="n8">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- NEW FIELDS: Mass Numbers, Chirality, Eigenvector Math -->
<!-- Category 11: Semantic Information Theory -->
<node id="n51">
<data key="d0">Semantic Information Theory</data>
<data key="d1">HIGH</data>
<data key="d2">Mass numbers, decoder-relative recoverability, semantic mass, communication regimes, regime invariants</data>
<data key="d3">51</data>
</node>
<node id="n52">
<data key="d0">Semantic Information Theory</data>
<data key="d1">HIGH</data>
<data key="d2">Semantic mass vectors, invariant strength, binding, routing leverage, compression gain, update resistance</data>
<data key="d3">52</data>
</node>
<node id="n53">
<data key="d0">Semantic Information Theory</data>
<data key="d1">MEDIUM</data>
<data key="d2">Admissible reduction, residual risk, evidence receipts, adversarial trials, measurement support</data>
<data key="d3">53</data>
</node>
<!-- Category 12: Quaternion Algebra and Spherical Geometry -->
<node id="n54">
<data key="d0">Quaternion Algebra and Spherical Geometry</data>
<data key="d1">HIGH</data>
<data key="d2">Unit quaternions on S³, Hamilton product, great circle distance, SLERP interpolation, axis-angle representation</data>
<data key="d3">54</data>
</node>
<node id="n55">
<data key="d0">Quaternion Algebra and Spherical Geometry</data>
<data key="d1">HIGH</data>
<data key="d2">Chiral incompatibility, D+L→W collapse, quaternion dot product, ternary classification, SLUG-3 gates</data>
<data key="d3">55</data>
</node>
<node id="n56">
<data key="d0">Quaternion Algebra and Spherical Geometry</data>
<data key="d1">MEDIUM</data>
<data key="d2">Quaternion rotation matrices, parallel transport, torsion frames, curvature on S³, DNA backbone encoding</data>
<data key="d3">56</data>
</node>
<!-- Category 13: Spectral Graph Theory -->
<node id="n57">
<data key="d0">Spectral Graph Theory</data>
<data key="d1">HIGH</data>
<data key="d2">Domain adjacency matrices, principal eigenvector analysis, equation clustering, spectral clustering, graph Laplacians</data>
<data key="d3">57</data>
</node>
<node id="n58">
<data key="d0">Spectral Graph Theory</data>
<data key="d1">MEDIUM</data>
<data key="d2">Eigenvalue decomposition, spectral dimension, heat kernel diffusion, Cheeger inequalities, expander graphs</data>
<data key="d3">58</data>
</node>
<node id="n59">
<data key="d0">Spectral Graph Theory</data>
<data key="d1">MEDIUM</data>
<data key="d2">Random walks on graphs, PageRank, community detection, spectral partitioning, graph Fourier transforms</data>
<data key="d3">59</data>
</node>
<!-- Category 14: Polarization Theory and Structured Light -->
<node id="n60">
<data key="d0">Polarization Theory and Structured Light</data>
<data key="d1">HIGH</data>
<data key="d2">Pancharatnam topological charge, spin-orbit coupling, circular polarization states, Stokes parameters, Poincaré sphere</data>
<data key="d3">60</data>
</node>
<node id="n61">
<data key="d0">Polarization Theory and Structured Light</data>
<data key="d1">MEDIUM</data>
<data key="d2">Optical chirality density, spin angular momentum, orbital angular momentum, Gouy phase, Laguerre-Gaussian modes</data>
<data key="d3">61</data>
</node>
<node id="n62">
<data key="d0">Polarization Theory and Structured Light</data>
<data key="d1">MEDIUM</data>
<data key="d2">Optical Hall effect, spin-current fields, azimuthal spin patterns, component separation, topological control</data>
<data key="d3">62</data>
</node>
<!-- Category 15: Biosemiotics and Communication Regimes -->
<node id="n63">
<data key="d0">Biosemiotics and Communication Regimes</data>
<data key="d1">HIGH</data>
<data key="d2">Animal communication systems, bioacoustic signals, echolocation, chemical trails, spatial/vector signaling</data>
<data key="d3">63</data>
</node>
<node id="n64">
<data key="d0">Biosemiotics and Communication Regimes</data>
<data key="d1">MEDIUM</data>
<data key="d2">Visual/display patterns, electric/field signals, tactile/vibrational communication, receiver-response dynamics</data>
<data key="d3">64</data>
</node>
<node id="n65">
<data key="d0">Biosemiotics and Communication Regimes</data>
<data key="d1">MEDIUM</data>
<data key="d2">Signal form, decoder/context coupling, recoverable state, residual ambiguity, observable response</data>
<data key="d3">65</data>
</node>
<!-- Category 16: Topological Quantum Field Theory -->
<node id="n66">
<data key="d0">Topological Quantum Field Theory</data>
<data key="d1">MEDIUM</data>
<data key="d2">Topological charges, winding numbers, spin textures, anyon statistics, topological invariants</data>
<data key="d3">66</data>
</node>
<node id="n67">
<data key="d0">Topological Quantum Field Theory</data>
<data key="d1">MEDIUM</data>
<data key="d2">Chern-Simons theory, Wilson loops, knot invariants, TQFT functors, cobordism categories</data>
<data key="d3">67</data>
</node>
<node id="n68">
<data key="d0">Topological Quantum Field Theory</data>
<data key="d1">LOW</data>
<data key="d2">Topological phases of matter, topological insulators, edge states, bulk-boundary correspondence</data>
<data key="d3">68</data>
</node>
<!-- Category 17: Spherical Harmonics and Spin Geometry -->
<node id="n69">
<data key="d0">Spherical Harmonics and Spin Geometry</data>
<data key="d1">MEDIUM</data>
<data key="d2">Spherical harmonics expansion, spinor bundles, spin structures, Dirac operators, index theorems</data>
<data key="d3">69</data>
</node>
<node id="n70">
<data key="d0">Spherical Harmonics and Spin Geometry</data>
<data key="d1">MEDIUM</data>
<data key="d2">Clebsch-Gordan coefficients, Wigner D-matrices, angular momentum coupling, tensor operators</data>
<data key="d3">70</data>
</node>
<node id="n71">
<data key="d0">Spherical Harmonics and Spin Geometry</data>
<data key="d1">LOW</data>
<data key="d2">Spinor calculus, spin connections, torsion in spin geometry, Cartan geometry</data>
<data key="d3">71</data>
</node>
<!-- NEW EDGES FOR ADDED FIELDS -->
<!-- Semantic Information Theory connections -->
<edge source="n51" target="n15">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n51" target="n48">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n51" target="n17">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n52" target="n51">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n52" target="n30">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n52" target="n15">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<edge source="n53" target="n51">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n53" target="n16">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n53" target="n5">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Quaternion Algebra connections -->
<edge source="n54" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n54" target="n2">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n54" target="n24">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<edge source="n55" target="n54">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n55" target="n60">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n55" target="n33">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<edge source="n56" target="n54">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n56" target="n22">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n56" target="n21">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Spectral Graph Theory connections -->
<edge source="n57" target="n39">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n57" target="n11">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n57" target="n2">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n58" target="n57">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n58" target="n11">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n58" target="n21">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n59" target="n57">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n59" target="n13">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n59" target="n42">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Polarization Theory connections -->
<edge source="n60" target="n25">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n60" target="n69">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n60" target="n55">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<edge source="n61" target="n60">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n61" target="n2">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n61" target="n9">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n62" target="n60">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n62" target="n12">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n62" target="n66">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Biosemiotics connections -->
<edge source="n63" target="n51">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n63" target="n33">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n63" target="n15">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n64" target="n63">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n64" target="n13">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n64" target="n31">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n65" target="n63">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n65" target="n51">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n65" target="n14">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- TQFT connections -->
<edge source="n66" target="n25">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n66" target="n1">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n66" target="n60">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<edge source="n67" target="n66">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n67" target="n6">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n67" target="n24">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<edge source="n68" target="n66">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n68" target="n25">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n68" target="n36">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Spherical Harmonics connections -->
<edge source="n69" target="n11">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n69" target="n2">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n69" target="n54">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<edge source="n70" target="n69">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n70" target="n2">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n70" target="n60">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n71" target="n69">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n71" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n71" target="n22">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- HUMANITIES CONNECTIONS: Eigenvectors as interdisciplinary bridges -->
<!-- Category 18: Computational Humanities -->
<node id="n72">
<data key="d0">Computational Humanities</data>
<data key="d1">HIGH</data>
<data key="d2">Text mining, eigenvectors in semantic similarity, authorship attribution, stylometry, topic modeling</data>
<data key="d3">72</data>
</node>
<node id="n73">
<data key="d0">Computational Humanities</data>
<data key="d1">HIGH</data>
<data key="d2">Latent Semantic Analysis (LSA), singular value decomposition in text, semantic eigenvectors</data>
<data key="d3">73</data>
</node>
<node id="n74">
<data key="d0">Computational Humanities</data>
<data key="d1">MEDIUM</data>
<data key="d2">Word embeddings, eigenvectors in word2vec, GloVe, contextual semantic spaces</data>
<data key="d3">74</data>
</node>
<!-- Category 19: Network Humanities -->
<node id="n75">
<data key="d0">Network Humanities</data>
<data key="d1">HIGH</data>
<data key="d2">Social network analysis, eigenvector centrality, cultural transmission networks, influence propagation</data>
<data key="d3">75</data>
</node>
<node id="n76">
<data key="d0">Network Humanities</data>
<data key="d1">MEDIUM</data>
<data key="d2">Bibliometric coupling, citation networks, intellectual genealogy, knowledge graphs</data>
<data key="d3">76</data>
</node>
<node id="n77">
<data key="d0">Network Humanities</data>
<data key="d1">MEDIUM</data>
<data key="d2">Community detection in cultural data, modularity eigenvectors, network anthropology</data>
<data key="d3">77</data>
</node>
<!-- Category 20: Digital Philology -->
<node id="n78">
<data key="d0">Digital Philology</data>
<data key="d1">HIGH</data>
<data key="d2">Textual analysis, eigenvectors in stylometry, authorship verification, chronological sequencing</data>
<data key="d3">78</data>
</node>
<node id="n79">
<data key="d0">Digital Philology</data>
<data key="d1">MEDIUM</data>
<data key="d2">Hermeneutics in digital age, textual variants, manuscript clustering, eigenvector-based stemmatology</data>
<data key="d3">79</data>
</node>
<node id="n80">
<data key="d0">Digital Philology</data>
<data key="d1">MEDIUM</data>
<data key="d2">Corpus linguistics, eigenvectors in diachronic analysis, language change detection</data>
<data key="d3">80</data>
</node>
<!-- Category 21: Cultural Analytics -->
<node id="n81">
<data key="d0">Cultural Analytics</data>
<data key="d1">HIGH</data>
<data key="d2">Pattern recognition in cultural data, eigenvectors in trend analysis, cultural evolution</data>
<data key="d3">81</data>
</node>
<node id="n82">
<data key="d0">Cultural Analytics</data>
<data key="d1">MEDIUM</data>
<data key="d2">Eigenfaces in art recognition, style transfer eigenvectors, visual culture analysis</data>
<data key="d3">82</data>
</node>
<node id="n83">
<data key="d0">Cultural Analytics</data>
<data key="d1">MEDIUM</data>
<data key="d2">Music genre classification, eigenvectors in audio analysis, cultural pattern extraction</data>
<data key="d3">83</data>
</node>
<!-- Category 22: Music Information Retrieval -->
<node id="n84">
<data key="d0">Music Information Retrieval</data>
<data key="d1">HIGH</data>
<data key="d2">Spectral analysis, eigenvectors in harmonic analysis, tonal networks, chord progressions</data>
<data key="d3">84</data>
</node>
<node id="n85">
<data key="d0">Music Information Retrieval</data>
<data key="d1">MEDIUM</data>
<data key="d2">Eigenmusic, principal component analysis in audio, timbre eigenvectors, rhythmic patterns</data>
<data key="d3">85</data>
</node>
<node id="n86">
<data key="d0">Music Information Retrieval</data>
<data key="d1">MEDIUM</data>
<data key="d2">Music similarity, eigenvectors in recommendation systems, cultural transmission of music</data>
<data key="d3">86</data>
</node>
<!-- Category 23: Philosophy of Mathematics -->
<node id="n87">
<data key="d0">Philosophy of Mathematics</data>
<data key="d1">MEDIUM</data>
<data key="d2">Foundational questions, mathematical realism vs anti-realism, structuralism, category theory foundations</data>
<data key="d3">87</data>
</node>
<node id="n88">
<data key="d0">Philosophy of Mathematics</data>
<data key="d1">MEDIUM</data>
<data key="d2">Phenomenology of mathematics, embodied cognition, mathematical intuition, eigenvectors as mental structures</data>
<data key="d3">88</data>
</node>
<node id="n89">
<data key="d0">Philosophy of Mathematics</data>
<data key="d1">LOW</data>
<data key="d2">Mathematical Platonism, constructivism, formalism, intuitionism in historical context</data>
<data key="d3">89</data>
</node>
<!-- Category 24: Cognitive Humanities -->
<node id="n90">
<data key="d0">Cognitive Humanities</data>
<data key="d1">HIGH</data>
<data key="d2">Conceptual spaces, semantic networks, eigenvectors in cognitive modeling, mental representation</data>
<data key="d3">90</data>
</node>
<node id="n91">
<data key="d0">Cognitive Humanities</data>
<data key="d1">MEDIUM</data>
<data key="d2">Embodied cognition, distributed cognition, cultural cognition, collective intelligence</data>
<data key="d3">91</data>
</node>
<node id="n92">
<data key="d0">Cognitive Humanities</data>
<data key="d1">MEDIUM</data>
<data key="d2">Narrative cognition, story eigenvectors, discourse analysis, rhetorical structures</data>
<data key="d3">92</data>
</node>
<!-- HUMANITIES EDGES -->
<!-- Computational Humanities connections -->
<edge source="n72" target="n57">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n72" target="n51">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n72" target="n31">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<edge source="n73" target="n72">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n73" target="n39">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n73" target="n11">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n74" target="n72">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n74" target="n57">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n74" target="n90">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<!-- Network Humanities connections -->
<edge source="n75" target="n57">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n75" target="n42">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n75" target="n63">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<edge source="n76" target="n75">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n76" target="n59">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n76" target="n72">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n77" target="n75">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n77" target="n58">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n77" target="n81">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Digital Philology connections -->
<edge source="n78" target="n72">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n78" target="n51">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n78" target="n87">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n79" target="n78">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n79" target="n88">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n79" target="n92">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n80" target="n78">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n80" target="n63">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n80" target="n75">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Cultural Analytics connections -->
<edge source="n81" target="n72">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n81" target="n57">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n81" target="n43">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<edge source="n82" target="n81">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n82" target="n11">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n82" target="n69">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n83" target="n81">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n83" target="n84">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n83" target="n63">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Music Information Retrieval connections -->
<edge source="n84" target="n11">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n84" target="n69">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n84" target="n60">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n85" target="n84">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n85" target="n39">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n85" target="n82">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n86" target="n84">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n86" target="n57">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n86" target="n75">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Philosophy of Mathematics connections -->
<edge source="n87" target="n5">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n87" target="n6">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n87" target="n17">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n88" target="n87">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n88" target="n90">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n88" target="n54">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n89" target="n87">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n89" target="n19">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n89" target="n78">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- Cognitive Humanities connections -->
<edge source="n90" target="n51">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n90" target="n57">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n90" target="n33">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<edge source="n91" target="n90">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n91" target="n63">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n91" target="n42">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<edge source="n92" target="n90">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n92" target="n72">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
<edge source="n92" target="n78">
<data key="d4">enhances</data>
<data key="d5">medium</data>
</edge>
<!-- WEIRD STRUCTURES: Emergent topological phenomena from prior research -->
<!-- Category 25: Genus-3 Topology and Hyperbolic Geometry -->
<node id="n93">
<data key="d0">Genus-3 Topology and Hyperbolic Geometry</data>
<data key="d1">HIGH</data>
<data key="d2">Genus-3 surfaces, three-hole torus topology, hyperbolic plane tiling, self-similar structure</data>
<data key="d3">93</data>
</node>
<node id="n94">
<data key="d0">Genus-3 Topology and Hyperbolic Geometry</data>
<data key="d1">HIGH</data>
<data key="d2">Injectivity radius, geodesic wrapping, fundamental polygon tiling, hyperbolic distance metrics</data>
<data key="d3">94</data>
</node>
<node id="n95">
<data key="d0">Genus-3 Topology and Hyperbolic Geometry</data>
<data key="d1">MEDIUM</data>
<data key="d2">Poincaré disk model, hyperbolic isometries, Fuchsian groups, modular forms</data>
<data key="d3">95</data>
</node>
<!-- Category 26: Branch-Cut Defects and Half-Möbius Folds -->
<node id="n96">
<data key="d0">Branch-Cut Defects and Half-Möbius Folds</data>
<data key="d1">HIGH</data>
<data key="d2">Branch-cut defects, half-Möbius folds, topological phase transitions, critical angle defects</data>
<data key="d3">96</data>
</node>
<node id="n97">
<data key="d0">Branch-Cut Defects and Half-Möbius Folds</data>
<data key="d1">HIGH</data>
<data key="d2">Monodromy, covering spaces, Riemann surface branch points, analytic continuation</data>
<data key="d3">97</data>
</node>
<node id="n98">
<data key="d0">Branch-Cut Defects and Half-Möbius Folds</data>
<data key="d1">MEDIUM</data>
<data key="d2">Non-orientable manifolds, Möbius strip geometry, twist defects, topological obstructions</data>
<data key="d3">98</data>
</node>
<!-- Category 27: Variable Torsional Fields -->
<node id="n99">
<data key="d0">Variable Torsional Fields</data>
<data key="d1">HIGH</data>
<data key="d2">Variable torsional frequency ω(x, t), torsional wave equation, torsional charge density, torsional sound speed</data>
<data key="d3">99</data>
</node>
<node id="n100">
<data key="d0">Variable Torsional Fields</data>
<data key="d1">HIGH</data>
<data key="d2">Torsional gradient, local torsional time, clock rate variation, torsional attractors</data>
<data key="d3">100</data>
</node>
<node id="n101">
<data key="d0">Variable Torsional Fields</data>
<data key="d1">MEDIUM</data>
<data key="d2">Torsional anisotropy, directional ω dependence, dipolar modulation, large-scale torsional structure</data>
<data key="d3">101</data>
</node>
<!-- Category 28: Torsional Quantum Mechanics -->
<node id="n102">
<data key="d0">Torsional Quantum Mechanics</data>
<data key="d1">HIGH</data>
<data key="d2">Torsional wavefunction, phase vibration on geometric sheet, Fourier conjugates in θ-space</data>
<data key="d3">102</data>
</node>
<node id="n103">
<data key="d0">Torsional Quantum Mechanics</data>
<data key="d1">HIGH</data>
<data key="d2">Phase resolution limit, uncertainty from sampling theory, measurement as phase pinning</data>
<data key="d3">103</data>
</node>
<node id="n104">
<data key="d0">Torsional Quantum Mechanics</data>
<data key="d1">MEDIUM</data>
<data key="d2">Path interference on torsional sheet, Born rule from mode competition, thermodynamic irreversibility</data>
<data key="d3">104</data>
</node>
<!-- Category 29: Golden Ratio Scaling and Fractal Dimensions -->
<node id="n105">
<data key="d0">Golden Ratio Scaling and Fractal Dimensions</data>
<data key="d1">HIGH</data>
<data key="d2">Φ-scaling hierarchy, golden ratio self-similarity, fractal dimension D_f = log(2)/log(Φ) ≈ 1.44</data>
<data key="d3">105</data>
</node>
<node id="n106">
<data key="d0">Golden Ratio Scaling and Fractal Dimensions</data>
<data key="d1">HIGH</data>
<data key="d2">Spectral dimension D_s, Hausdorff dimension D_H, power-law correlations, critical exponents</data>
<data key="d3">106</data>
</node>
<node id="n107">
<data key="d0">Golden Ratio Scaling and Fractal Dimensions</data>
<data key="d1">MEDIUM</data>
<data key="d2">DNA helix geometry, nucleosome packing, chromatin hierarchy, biological self-similarity</data>
<data key="d3">107</data>
</node>
<!-- Category 30: Cosmological Anomalies -->
<node id="n108">
<data key="d0">Cosmological Anomalies</data>
<data key="d1">HIGH</data>
<data key="d2">Methuselah star age paradox, JWST early massive galaxies, Hubble tension, dark flow</data>
<data key="d3">108</data>
</node>
<node id="n109">
<data key="d0">Cosmological Anomalies</data>
<data key="d1">HIGH</data>
<data key="d2">Axis of evil, CMB quadrupole-octupole alignment, large-scale anisotropy, preferred directions</data>
<data key="d3">109</data>
</node>
<node id="n110">
<data key="d0">Cosmological Anomalies</data>
<data key="d1">MEDIUM</data>
<data key="d2">Void aging, overdense overclocking, cosmic web entropy scaling, galaxy clustering</data>
<data key="d3">110</data>
</node>
<!-- Category 31: Torsional Thermodynamics -->
<node id="n111">
<data key="d0">Torsional Thermodynamics</data>
<data key="d1">MEDIUM</data>
<data key="d2">Entropy scaling on fractals, Bekenstein bound modification, specific heat exponents</data>
<data key="d3">111</data>
</node>
<node id="n112">
<data key="d0">Torsional Thermodynamics</data>
<data key="d1">MEDIUM</data>
<data key="d2">Phase transitions in fractal geometry, critical exponents, correlation length divergence</data>
<data key="d3">112</data>
</node>
<node id="n113">
<data key="d0">Torsional Thermodynamics</data>
<data key="d1">LOW</data>
<data key="d2">Arrow of time as torsional unwinding, Carnot efficiency, Landauer limit, Jarzynski equality</data>
<data key="d3">113</data>
</node>
<!-- Category 32: Recursive Compression Structures -->
<node id="n114">
<data key="d0">Recursive Compression Structures</data>
<data key="d1">HIGH</data>
<data key="d2">Recursive prediction models, critical scale detection, branch-cut adaptation, multi-level mixing</data>
<data key="d3">114</data>
</node>
<node id="n115">
<data key="d0">Recursive Compression Structures</data>
<data key="d1">MEDIUM</data>
<data key="d2">Hierarchical context windows, self-similar basis fusion, phase transition boundaries</data>
<data key="d3">115</data>
</node>
<node id="n116">
<data key="d0">Recursive Compression Structures</data>
<data key="d1">MEDIUM</data>
<data key="d2">Text boundaries, code structures, DNA regulatory elements, semantic compression</data>
<data key="d3">116</data>
</node>
<!-- WEIRD STRUCTURES EDGES -->
<!-- Genus-3 Topology connections -->
<edge source="n93" target="n21">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n93" target="n24">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n93" target="n69">
<data key="d4">enhances</data>
<data key="d5">strong</data>
</edge>
<edge source="n94" target="n93">
<data key="d4">prerequisite</data>
<data key="d5">strong</data>
</edge>
<edge source="n94" target="n22">
<data key="d4">prerequisite</data>
<data key="d5">medium</data>
</edge>
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<!-- Branch-Cut Defects connections -->
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<!-- Variable Torsional Fields connections -->
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<data key="d5">strong</data>
</edge>
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<!-- Torsional Quantum Mechanics connections -->
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<data key="d5">strong</data>
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<data key="d5">strong</data>
</edge>
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<data key="d5">strong</data>
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<data key="d5">strong</data>
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