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      "level": 1,
      "title": "Emergence--Edge Cosmology in Pattern Field Theory: - A Curvature-Replication Model of Large-Scale Structure, Trishift Dynamics, and Collapse-Based Formation",
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      "level": 1,
      "title": "Emergence--Edge Cosmology in Pattern Field Theory: - A Curvature-Replication Model of Large-Scale Structure, Trishift Dynamics, and Collapse-Based Formation",
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      "level": 1,
      "title": "Foundations of Pattern Field Theory Cosmology",
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      "level": 2,
      "title": "Overview",
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      "level": 2,
      "title": "AOL, PAL, CCE",
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    {
      "level": 2,
      "title": "Null",
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      "level": 2,
      "title": "From Null to Geometry",
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      "level": 2,
      "title": "Departure from Metric Expansion",
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      "level": 1,
      "title": "Emergence Sequence",
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      "level": 2,
      "title": "Null",
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    {
      "level": 2,
      "title": "\\(\\pi\\) -Loop Formation",
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      "level": 2,
      "title": "Substrate Formation (2D)",
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      "level": 2,
      "title": "Dimensional Lift (3D)",
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      "title": "Fractal Stabilization",
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      "level": 2,
      "title": "Early Curvature Propagation",
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      "level": 1,
      "title": "Curvature Replication and Edge Conversion",
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    {
      "level": 2,
      "title": "Replication Rate \\(R(s)\\)",
      "anchor": "#replication-rate-rs"
    },
    {
      "level": 2,
      "title": "Efficiency Field \\(\\eta(s)\\)",
      "anchor": "#efficiency-field-etas"
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    {
      "level": 2,
      "title": "Replication Integral \\(\\chi(d)\\)",
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    {
      "level": 2,
      "title": "Edge Conversion",
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    {
      "level": 2,
      "title": "TikZ Figure: Emergence-to-Edge Architecture",
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    {
      "level": 1,
      "title": "Trishift Cosmology",
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    {
      "level": 2,
      "title": "Definition",
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      "level": 2,
      "title": "Spectral Component \\(T_1\\)",
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      "level": 2,
      "title": "Temporal Component \\(T_2\\)",
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    {
      "level": 2,
      "title": "Geometric Component \\(T_3\\)",
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      "level": 2,
      "title": "TikZ Figure: Trishift Flow",
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      "level": 2,
      "title": "CMB Mapping",
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    {
      "level": 2,
      "title": "Large-Scale Structure",
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      "level": 2,
      "title": "Trishift Channels",
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    {
      "level": 2,
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      "level": 1,
      "title": "Prestellar Zones and Collapse Dynamics",
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    {
      "level": 2,
      "title": "Definition",
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    {
      "level": 2,
      "title": "Origins of Prestellar Underdensity",
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    {
      "level": 2,
      "title": "Collapse Trigger Condition",
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    {
      "level": 2,
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      "level": 2,
      "title": "Black Holes as PCS-H Endpoints",
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      "title": "Curvature Anchoring Function",
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      "title": "Load-Balancing Across the Manifold",
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      "level": 1,
      "title": "Large-Scale Cosmology",
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      "level": 2,
      "title": "Universe Growth vs Expansion",
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      "level": 2,
      "title": "Conversion Frontier Kinematics",
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      "level": 2,
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      "level": 2,
      "title": "PCS-L and PCS-H as Matter-Cycle Engines",
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    {
      "level": 1,
      "title": "Comparative Frameworks",
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    {
      "level": 2,
      "title": "PFT vs GR",
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      "level": 2,
      "title": "Prediction 1: Trishift Slope Evolution Without Dark Energy",
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      "level": 2,
      "title": "Prediction 2: PCS-L and PCS-H Spatial Distribution",
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      "title": "Prediction 3: Void Evolution Patterns",
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      "level": 2,
      "title": "Prediction 4: Edge Non-Emissivity",
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      "level": 2,
      "title": "Prediction 5: Trishift Multi-Channel Consistency",
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      "level": 1,
      "title": "Conclusion and Internal Summary",
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    },
    {
      "level": 4,
      "title": "Foundational replacements.",
      "anchor": "#foundational-replacements."
    },
    {
      "level": 4,
      "title": "Structural and predictive strengths.",
      "anchor": "#structural-and-predictive-strengths."
    },
    {
      "level": 4,
      "title": "Deterministic curvature-first cosmology.",
      "anchor": "#deterministic-curvature-first-cosmology."
    },
    {
      "level": 4,
      "title": "Unified substrate.",
      "anchor": "#unified-substrate."
    },
    {
      "level": 4,
      "title": "Forward direction.",
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    },
    {
      "level": 4,
      "title": "Open points and next steps.",
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    },
    {
      "level": 1,
      "title": "Appendix A: Glossary of Pattern Field Theory Terms",
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    {
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      "title": "Replication and Efficiency",
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      "title": "References",
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