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Chapter 5 — Cathedral Probe

Act III — Understanding · Synthesis chapter · Requires all prior chapters

Core Question

How do you diagnose a renderer that produces wrong pixels without crashing — when you can't afford to run the full oracle on every frame?

Cathedral Probe — six-layer contact sheet

All six Cathedral Probe diagnostic layers rendered individually. Left to right: beauty render · wireframe · transport ownership · risk probe markers · spacetime transport · continuity vectors. Source: Docs/assets/cathedral_probe/cathedral_probe_contact_sheet_row_0015.png

What to look at

Inspect: The resonance heatmap — compare the stride=1 row (26% band coverage) against the stride=4 row (0.22%). The collapse is a factor of 100× from a single parameter change. Then look at the continuity vector overlay: the high-magnitude clusters appear at rows ~58 and ~122 — the same instability bands Chapter 4's oracle identified.

Contradiction: The intuitive debug response to banding artifacts is "increase integration precision." The DOE shows this makes the banding worse at stride=1 (finer steps expose more transport boundary structure). The actual fix is changing the traversal schedule, not the integration precision.

What would make it stronger: A four-panel stride comparison (stride=1, 2, 4, 8) rendered at the same step length side-by-side, with band coverage percentages annotated on each panel. The DOE dataset has the numbers; the missing piece is the composite visual.

What the Visitor Sees

The Entry Finding: Scheduler Resonance

DOE Scheduler Resonance Heatmap

Band-by-row-mod-stride heatmap. Stride=1: ~26% band coverage. Stride=4: 0.22% coverage. The collapse is deterministic — the same stride always produces the same resonance. Source: output/doe_scheduler_resonance/20260503T002804Z/

The 68-cell DOE Scheduler Resonance experiment revealed a counterintuitive finding: transport banding is controlled by traversal stride, not by integration precision.

Step length Stride=1 band % Stride=2 band % Stride=4 band % Stride=8 band %
0.00625 22.0% 26.8% 0.6% 0.3%
0.0125 33.0% 18.1% 0.2% 0.2%
0.013 32.6% 11.8% 0.5% 0.2%

Band coverage collapses at stride≥4 regardless of step length. Making integration finer increases band coverage because finer steps expose more transport boundary structure, which the row-major scheduler then amplifies. This inverts naive debugging intuition.

The heatmap makes the periodic structure visible: band pixels at stride=2 align with row-mod-2 patterns; at stride=4 the pattern disappears (the band collapses entirely rather than becoming a periodic stripe).

The fix: Scheduler decorrelation. The tile scheduler breaks the row-alignment that enables resonance. Band coverage drops from 20% (row, stride=1) to ~10% (tile). Corner instability (topological) persists unchanged across all modes.

The Six-Layer Cathedral Probe

Cathedral Probe — six-layer composite overlay

Six-layer Cathedral Probe composite. Domain resolver stress scene, step=0.015, row traversal. Transport ownership boundaries are visible as high-density continuity vector clusters. 6,619 high-discontinuity vectors (score ≥ 1.0). All shape regions: boundary_aligns_with_high_vector_density = true.

The Cathedral Probe is not a single tool — it is a layered methodology. Six passive instrumentation passes assembled into a composite that makes transport coherence structure legible as a visual space.

Transport continuity vectors

Layer 5: Transport continuity vector field. High-discontinuity vectors cluster at ownership boundaries. These are the same instability zones Chapter 4 identified via the oracle — but found here from the rendered output alone.

The six layers:

Layer Code Name What it shows
1 Beauty render Raw integration output — the baseline
2 Cartesian wireframe Geometric boundary structure
3 Transport ownership map Per-pixel domain ownership coloring
4 Risk probe markers High-risk transport nodes from oracle sampling
5 Spacetime transport diagram Ray-path topology in scene space
6 Continuity vectors Per-pixel transport disagreement across 6 dimensions

Layer 6 (continuity vectors) is the key non-oracle proxy. Each vector encodes pixel-to-pixel disagreement across collider ownership, domain, hit distance, normal angle, path length, and boundary event. High-magnitude vector clusters appear at the same locations as the Chapter 4 oracle's 289 instability regions — without requiring a separate oracle run.

All six identified transport shape regions confirmed: boundary_aligns_with_high_vector_density = true. The proxy works.

The corner instability visible in the traversal comparison persists across all four traversal modes at 468 ownership-change samples. It is mode-independent — it is the same topological feature Chapter 4's coherence basin oracle identified. The Cathedral Probe finds it; the oracle confirms it; the coherence basin maps it.

Three independent methodologies, same finding.

Artifacts

Promoted (in misterylabs_artifacts/):

Artifact File
Resonance heatmap visuals/doe-scheduler-resonance-heatmap.png
Stride plot visuals/doe-scheduler-resonance-stride-plot.png
DOE dataset (68 cells) datasets/doe-scheduler-resonance.csv
Card cards/doe-scheduler-resonance.md

Canonical images (in Docs/assets/cathedral_probe/):

Image Notes
cathedral_probe_overlay_row_0015.png Six-layer composite — the primary diagnostic image
cathedral_probe_contact_sheet_row_0015.png All six layers individually
continuity_vectors_row_0015.png Layer 6 standalone — the non-oracle instability proxy
traversal_contact_sheet_4mode_0015.png Four traversal modes at step=0.015
band_support_by_mode_0015.png Band coverage reduction: row → tile → checkerboard

Sample World

cathedral_probe_world — design proposal

Scene: test-domain-resolver-stress.tscn

The world provides individual layer toggles for all six Cathedral Probe components plus a stride selector. The visitor can build the composite progressively or jump to the full overlay. Switching stride from 1 to 4 shows the band-coverage collapse in the step-budget-allocation heatmap before it appears as visible banding in the beauty render.

Build priority: 4. Runtime per-layer toggling requires new implementation.

Validation Question

At stride=4, step=0.015, row traversal: what percentage of pixels should fall in the high-curvature band?

Expected: 0.22–0.45% (from the 68-cell DOE at varying step lengths). At stride=1: 20–33%.

Layer 6 check: Are the high-continuity-vector clusters in the composite aligned with the Chapter 4 instability bands (rows ~58 and ~122)? Expected: yes. The proxy and the oracle should identify the same zones.

Key Insight

Transport instability is not globally smoothable. It is localized, topological, and scheduler-amplified. The right response is scheduler decorrelation first, local precision management second, global smoothing never.

Chapter Synthesis

Chapter 5 closes the Atlas arc.

  • Chapter 1 showed that curved transport is beautiful and real.
  • Chapter 2 showed it is measurably different from straight transport.
  • Chapter 3 showed that "measurably different" is not the same as "measurably correct."
  • Chapter 4 showed that some transport regions cannot be corrected by brute force.
  • Chapter 5 showed how to find those regions systematically and how the scheduler was amplifying them into global banding.

What comes after Chapter 5: The recursive mirror ghost portal (pending Phase 2 scene build) is the first exhibit requiring all five chapters to interpret. Discrete mirror reflection events + continuous GRIN integration between bounces + hermetic validation + coherence basin mapping + Cathedral Probe diagnosis. It becomes Chapter 6 when its benchmark image exists.