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    "headline": "Topology Guided Long-Horizon Reasoning",
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    "dek": "SAGE combined algebraic sparsification and hyperbolic guidance across 12 benchmarks and seven model families.",
    "summary": "SAGE combined algebraic sparsification and hyperbolic guidance across 12 benchmarks and seven model families.",
    "body_text": "The framework treats long reasoning as a branching-space problem: locally plausible paths can be structurally unstable, and small deviations compound before a sparse reward arrives. SAGE projects candidates into operator-indexed subspaces and embeds reasoning states in negatively curved space to provide depth-wise guidance. The authors report gains over competing baselines, including up to an eightfold improvement on their Andrews-Curtis task. The result is benchmark evidence for these structural priors, not a solution to the underlying open mathematical problem.",
    "why_it_matters": "SAGE combined algebraic sparsification and hyperbolic guidance across 12 benchmarks and seven model families.",
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      "The result is benchmark evidence for these structural priors, not a solution to the underlying open mathematical problem."
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    "tags": [
      "long-horizon reasoning",
      "topology",
      "structural guidance"
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    {
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      "title": "arXiv preprint 2609.30192",
      "publisher": "arXiv",
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      "published_at": "2026-09-24T13:33:29.000-04:00",
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    "title": "Topology Guided Long-Horizon Reasoning",
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