The tiled builder is correct, but this comparison does not support replacing the existing default. Complete-path medians were lower in 7 of 12 fixtures and higher in 5; observed process-median ranges overlap in 9. The three disjoint ranges favor tiling. The existing default and its frozen cutover calibration remain unchanged.

What changed

A workgroup constructs 256 prefix-min-tree leaves and all their interior heap nodes in shared memory. Further passes process 256 completed roots at a time. The resulting tree has exactly the same nodes and padding as the levelwise builder; inherited-prefix queries are unchanged. This reduces tree dispatches from 1 + log2(bit_ceil(input_records)) to max(1, ceil(log2(bit_ceil(input_records))/8)). No scratch pooling, input reconstruction, output approximation, or timing-scope change is introduced.

Use optimized-tiles for candidate correctness, optimized-tiles-bench for the original benchmark set, or cutover-tiles CASE TRIALS for one existing calibration fixture. The corresponding modes without -tiles retain the levelwise builder. These modes do not automatically select a production runtime backend.

Checks

All 14 optional CTests passed in 7.59 s: the existing 13 plus the tiled optimized corpus. The new whole-tree oracle runs 42 fixtures through both builders, comparing every node, padding, node-zero/tail guards, descriptor immutability and exact validation flags. It covers one-record inputs, both empty-side directions, source boundaries around 256, malformed retention/source labels, and 65,537 records requiring two upper reduction passes. The tiled complete merge also retains the 81 whole-file adversarial cases and existing EF, packed-word and index-rank oracles. DXC compilation, SPIR-V validation and Metal compilation passed.

Paired measurements

Each cell is the median [minimum–maximum] of three fresh-process medians; each process contributes three measured trials after one verified warmup. The 12 fixture IDs were fixed before collection, pair order was shuffled, and which builder ran first alternated across repetitions. All 72 processes passed complete canonical output bytes, mapped scans and CRC checks. All 216 measured CPU/GPU pairs are retained in the raw case logs. Each process also checks one warmup, whose timing is excluded and not printed. Fixture/result fields agree across modes and repetitions.

Case	Records A / B	Prefix bytes	Ties %	Value bytes	Levelwise total ms	Tiled total ms	Tiled change	Ranges
0	256 / 256	32	50	8	5.581 [5.036–5.614]	2.720 [1.871–4.686]	51.3% lower	disjoint
1	1024 / 1024	32	50	8	5.276 [2.030–5.562]	5.065 [3.067–5.534]	4.0% lower	overlap
2	4096 / 4096	32	50	8	4.243 [2.546–6.379]	3.480 [2.477–3.489]	18.0% lower	overlap
3	16384 / 16384	32	50	8	5.366 [4.238–6.627]	3.714 [3.004–4.118]	30.8% lower	disjoint
4	65536 / 65536	32	50	8	4.954 [4.691–8.155]	6.691 [4.340–6.769]	35.1% higher	overlap
5	262144 / 262144	32	50	8	8.731 [8.306–10.661]	9.032 [8.194–10.204]	3.4% higher	overlap
9	4096 / 4096	256	50	8	6.936 [4.020–8.154]	6.025 [5.209–8.288]	13.1% lower	overlap
11	4096 / 4096	32	100	8	4.894 [4.215–5.856]	3.605 [2.925–3.781]	26.3% lower	disjoint
13	4096 / 4096	32	50	512	5.500 [3.817–6.919]	5.254 [4.469–5.530]	4.5% lower	overlap
34	2048 / 2048	64	25	32	3.016 [2.822–4.966]	3.279 [3.157–3.962]	8.7% higher	overlap
38	8192 / 8192	64	25	32	3.399 [2.994–4.301]	3.627 [3.222–6.996]	6.7% higher	overlap
44	32768 / 4096	0	0	512	6.122 [5.774–6.858]	7.374 [6.190–10.048]	20.4% higher	overlap

The parse stage contains input import, descriptor/tree allocation, GPU framing/tree construction, completion waiting and validation. Its process-median comparisons are:

Case	Levelwise parse ms	Tiled parse ms
0	1.100 [1.061–1.104]	0.513 [0.492–1.108]
1	1.116 [0.581–3.222]	1.020 [0.943–1.052]
2	1.226 [0.996–2.442]	1.219 [0.947–1.317]
3	1.677 [1.395–3.368]	1.185 [1.044–2.325]
4	1.142 [1.114–1.495]	1.395 [1.073–1.733]
5	2.777 [2.342–3.069]	2.383 [2.253–2.400]
9	1.203 [0.948–1.251]	1.212 [1.139–1.248]
11	2.090 [1.556–2.091]	0.939 [0.841–1.393]
13	1.469 [1.203–1.501]	1.607 [1.349–2.034]
34	1.062 [0.823–1.361]	0.977 [0.943–1.180]
38	1.038 [0.742–1.094]	1.033 [1.025–1.300]
44	1.725 [1.292–1.823]	2.158 [1.221–2.730]

These ranges describe observed runs, not confidence intervals. Unchanged later phases also vary; whole-path differences cannot be attributed solely to eliminated dispatch cost. GPU command timestamps cover command intervals, not isolated kernel instructions. Stage medians need not add to the total median.

Both paths start with the same warm compressed mmap inputs and end with a complete checksummed scratch file. Timing includes imports, all scratch/output allocation, GPU input parsing, prefix tree/cache, merge/compaction, exact sizing/scans, direct packed payload and EF output, all host waits, output mapping, directory and CRC. It excludes pipeline creation, fixture generation, correctness oracles, final local-object destruction, fsync and catalog publication. The five blocking host/GPU handoffs remain.

Identity and raw data

Measured source: ac6e05665946bd74827f6e97da6ea2911715df03. One executable and one shader library contain both paths, so a mode flag is the only comparison selection.

Executable SHA-256: 762a6a649207ff710e2d0baf2f6d2770100856b82aec876f33fd823fb7107886
Shader library SHA-256: d452e21f9caa9ec6552ac85e30d16d273de36e1aa6b2105c304c551aaf34315c
Collection: 2026-09-16T06:09:29Z to 2026-09-16T06:09:45Z on the same Apple M2 Max used by the existing calibration.

Raw rows, process summaries and frozen source/artifact hashes retain the measured values. The old 50-case rule has not been fitted to these 12 cases and does not identify this executable. Default CPU fallback on identity mismatch still applies.