Skip to content

Curvature Domain Ownership

Domain ownership describes which transport regime — near-side, bridge, or far-side — owns each observer position on the wormhole ladder. The research analysis estimates these regimes from transport metrics; renderer-integrated domain maps are heuristic diagnostics and may include fixture/runtime signals such as hit classification, remap/crossing counts, boundary confidence, selection flips, and normal discontinuity. Treat the integrated maps as inspection aids, not proof of metric-only domain ownership.

Core Finding

Visible banding correlates with curvature-domain boundary transitions in the audited fixtures, not with final-hit selection artifacts alone.

Supporting evidence from the six-checkpoint wormhole observer ladder. These metrics motivate the diagnostics; they are not validation evidence for every renderer-integrated domain map:

Evidence type Metric Value
Multi-metric anomaly rank Bridge z-score 4.40 (top ranked)
Multi-metric anomaly rank Bridge isolation forest 0.616
Multi-metric anomaly rank Bridge LOF 1.35
Automatic clustering Best-fit k 3 (ARI = 0.5946, silhouette = 0.5547)
Bridge isolation Singleton cluster yes — bridge occupies cluster 1 alone
Segments per crossing Bridge value 366 (vs 50–153 for all others)
Phase-coherence gap Mouth band vs outside 0.162 (coherence drops at band locations)
Radial slope at aperture Throat value 0.025 (strongest feature at throat, not bridge)

Regime Decomposition

The k = 3 automatic partition (agglomerative + k-means, same result) recovers the following structure:

Cluster Checkpoints Transport character
Near-side (cluster 2) mouth, mouth-to-throat, throat Continuously increasing density; decreasing cost; interpolation-valid
Bridge (cluster 1, singleton) post-throat backstep Sparse, expensive; maximum segments-per-crossing; minimum OPL mean
Far-side (cluster 0) exit-approach, exit-lookback Re-densified; maximum portal density; tangential orientation dominant

The throat is classified with the near-side family, not with the bridge. Clustering evidence disagrees with a naive spatial reading that would place the throat as the boundary between near-side and bridge. The throat extends the near-side trend; the actual transport discontinuity occurs at the bridge.

Domain Boundaries vs Banding

Band-boundary alignment was measured by testing whether the visible-band mask and the phase-incoherence signal concentrate at the same locations:

  • Visible-band / incoherence correlation was reduced by −0.033 after phase-guided hit selection, but the visible-band phase-boundary fraction changed by only −0.007. This suggests bands and incoherence share structural causes rather than one causing the other.

  • Neighbour-normal-delta discontinuity strongly aligns with visible bands. First-hit divergence originates before stored-hit refinement. Orientation fields remain globally persistent while morphology fragments locally. These are consistent with a domain-boundary origin for banding rather than a sampling or precision origin.

Checkpoint Feature Table

Full metrics from derived_metrics.json and clustering_summary.md:

Checkpoint Manual regime Cluster OPL mean portal density crossings/px segments/crossing
mouth near-side 2 9.96 0.147 0.650 153
mouth-to-throat near-side 2 9.73 0.163 0.699 140
throat throat 2 9.51 0.175 0.748 128
bridge (backstep) bridge 1 7.59 0.096 0.210 366
exit-approach far-side 0 8.12 0.180 1.654 50
exit-lookback far-side 0 8.43 0.256 1.420 61

The bridge is anomalous across all five characterisation features simultaneously — not merely extreme in one dimension. This multi-metric outlier character distinguishes it from a checkpoint that is simply at one end of a continuous gradient.

Interpolation Validity by Domain

Domain Interpolation verdict Reason
Near-side (mouth → throat) Valid Smooth continuous progression in all metrics
Throat Extends near-side; interpolation-valid across throat hinge Throat is a transition hinge, not a discontinuity
Bridge Invalid for world-space interpolation Multi-metric outlier; dense-to-sparse collapse; no smooth path from near-side metrics to bridge metrics
Far-side (exit-approach → exit-lookback) Valid within far-side Smooth re-densification
Bridge → far-side Requires discovered checkpoints No interpolation path exists through the bridge transport anomaly

Future Work

  • Full six-checkpoint phase-coherence scoring (currently only mouth and bridge are measured).
  • Geometric primitive inventory (Hough line/arc events) for all six checkpoints — currently only available at mouth and bridge.
  • Cross-checkpoint persistence tracking: which curvature-centre candidates recur across domains (attractor behaviour) vs which are bridge-only (transition events).

Cross-References