Curved Minimal Subtile Granularity¶

Scope¶

Phase 1.5 characterizes the existing tile-metrics scaffold on the curved_minimal validation path without changing scheduler behavior.

Runs used:

Reference artifacts:

The scaled film width on this path is effectively 80px, so widths below 4 would likely over-fragment without adding meaningful spatial signal.

Width	Unique Subtiles	Active	Empty	Hit Concentration	Mean Spread	Max Spread	Active-Band Top Stability
64	2	1	1	one subtile owns `100%` of hits	`0.0392`	`0.1880`	`100%` same subtile
32	3	1	2	one subtile owns `100%` of hits	`0.0783`	`0.3750`	`100%` same subtile
16	5	1	4	one subtile owns `100%` of hits	`0.1566`	`0.7500`	`100%` same subtile
8	10	2	8	hits split `53.3% / 46.7%` across two neighbors	`0.1671`	`0.7500`	`66.6% / 33.4%` between two neighbors
4	20	4	16	hits split `40.0% / 36.7% / 13.3% / 10.1%` across four neighbors	`0.2504`	`1.0000`	`66.6% / 33.4%` between two neighbors

Widths 64, 32, and 16 are too coarse for scheduler experiments on this scene. They collapse the active region into a single subtile, so prioritization would have little to choose between.
Width 8 is the first setting that exposes more than one active subtile while still keeping the active region compact.
Width 4 reveals more structure, but most subtiles remain empty and the active region becomes noticeably more fragmented.

Coarse widths hide internal structure by assigning all hits to one container.
At width 8, the scene resolves into two adjacent active subtiles around x=32 and x=40, with a near-even split in hit share.
At width 4, that same region breaks into four active subtiles, but the outer two carry much less signal than the inner pair.

Yield spread rises as width narrows, which is expected and desirable up to a point.
Width 8 increases spatial contrast relative to 16 while still preserving a compact active set.
Width 4 pushes max spread to 1.0, which is strong discrimination but also a sign of sparse, highly localized occupancy.

Important note:

counting the top subtile across all bands is misleading here because many bands are zero-hit and therefore tie at 0
the useful signal is top-subtile stability across active bands only

Using active bands only:

widths 64, 32, and 16 are trivially stable because only one subtile ever carries hits
width 8 remains stable enough for prioritization: the best subtile stays within the same two-neighbor region, with a 66.6% / 33.4% split
width 4 keeps the same core region, but becomes more spike-prone and fragmented

Recommended initial subtile width for first scheduler experiments: 8

Why:

it is the first width that exposes non-trivial horizontal structure
it keeps the active region narrow and interpretable
it avoids the over-fragmentation and one-pixel-like spikes seen at width 4
it should give a scheduler enough spatial choice to test prioritization without making bookkeeping dominate the experiment

Recommended first experiment: reorder-only

Why:

it isolates the effect of tile ordering from the effect of reduced work
it preserves the current budget envelope, which is safer for output-stability comparisons
it makes validation easier to interpret because any change in results comes from traversal order, not fewer rays or fewer candidate checks

reorder plus budget reduction should be deferred until reorder-only shows: