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Curvature Benchmark

The Curvature Signature Ladder and related contact sheets form the core visual language for demonstrating where and why curved transport diverges from straight-line assumptions.

The Curvature Signature Ladder

What it shows: For a given scene and observer pose, the minimum step length (or precision floor) required for reference integration to converge on a stable diagnostic classification.

  • Every node that reaches the finest available floor (e.g. 0.003125) and does not converge is marked as a "risk node" or "unresolved island."
  • Bands and clusters are not random; they trace high-curvature boundaries in the GRIN field.

Primary Exhibits

  • Atomic Orbital GRIN Ladder (multiple resolutions and pruning variants)
  • output/atomic_orbital_grin_ladder/
  • Contact sheets and parameter ladders.
  • Curved Field Validation Ladder
  • assets/curved_field_validation_ladder/
  • Precision vs. convergence plots and heatmaps.
  • Transport Coherence Basin
  • output/transport_coherence_basin_smoke/ and repeatability runs.
  • visuals/coherence-basin-hero.png and radial risk plots.
  • Every probed node in the band hits the same precision floor — a topological signature.

Contact Sheet Gallery

Use the assets in assets/curved_field_validation_ladder/ and assets/observatory/ for:

  • Full contact sheets (raw render + risk overlay + ladder).
  • 4-mode traversal comparisons (row vs. tile vs. checkerboard) showing how scheduler choice interacts with curvature cost.
  • Normal discontinuity and ownership transition maps around islands.

Falsification Protocol (for every ladder)

  • Run the identical scene at production step length → record risk node count and locations.
  • Increase precision floor by 2× or 4× → the bands must not dissolve if the feature is topological.
  • Change the IOR gradient or field profile → the spatial signature of the bands must move or disappear in a predictable way.

Why This Section Exists

The ladders turn "the field is curved" into a measurable, mappable, falsifiable property. They are the measurable foundation that makes the other exhibits interpretable — curvature has a signal, and the signal can be mapped.

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