Seeded partition kernel comparison (PR #258, step 3)

Production uses the specialized stack-seed suffix automaton. Both candidates passed independent exhaustive comparisons of raw Z, complete boundary partitions and every pair numerator: all ten unrounded theory fixtures and 100 deterministic heterogeneous-weight cases with missing edges, forbidden boundaries, mixed and singleton occurrences, asymmetric spans and noLP. The tolerance is 2e-12 relative; the oracle accumulates in long double. Mathematical fixture accessibility remains unrounded, independently of native integer ED tests.

Reproduce

GCC 14.4.0, Linux x86-64, release Autotools configuration, Z_type=double, -O3 -DNDEBUG, Kokkos mdspan. The hidden Catch case contains every input and uses deterministic weights and identical callback/checked-arithmetic contracts.

OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 /usr/bin/time -v \
  ./tests/runApiTests '[SeededBenchmark]'

Single-run milliseconds on the development host (these are kernel timings, not native full-program speedups; rerun to account for shared-host noise):

Case	Stack Z	Suffix Z	Stack Z+outside	Suffix Z+outside
none	0.000	0.000	0.009	0.000
sparse	59.462	43.934	156.972	140.072
overlap	109.494	77.083	304.623	249.862
dense	207.217	96.059	554.614	302.839
long-stack	1.003	0.879	3.057	1.466
mixed	196.146	99.959	522.997	310.235
asymmetric	65.849	37.285	182.743	121.412

The outside increment is the difference between each combined and partition-only time. All corresponding Z values agree within 2e-12; pair masses were checked before timing. The numerical kernels do not include native seed preprocessing. Ordinary cases use 45 x 45 positions, spans 30 x 30, seed length four and loop limits two. The long-stack case uses a 90-position diagonal (L up to 30); mixed lengths are one through four; asymmetric spans are 12 x 24. No-seed input exits before DP allocation. Sparse input has one seed. These are synthetic stress cases; end-to-end native measurements belong to the final integration gate.

Memory and decision

For a per-start dense rectangle of A cells and c=max(2, maximum seed length), the suffix implementation stores (c+4)A partition values, or 2(c+4)A with the outside pass, plus A bytes of validity and A size_t ending lengths. For c=4 and A=900 this is 65,700 bytes partition-only and 123,300 with outside (eight-byte Z_type/size_t). Maximal stacks use 4A or 8A partition values, A validity bytes and up to 3L scratch partition values for the outside pass. The output matrix adds nmsizeof(Z_type) for either kernel. Occurrences/eligible-start boxes are separate O(number of retained seeds) metadata; neither candidate retains run lists or boundary coefficients globally. These are physical rectangular-cell counts, not just complementary vertices. Allocator overhead is not included.

The suffix candidate generally improves throughput, especially partition-only and long-stack work. The extra bounded-span memory is acceptable for the intended workload, so only suffix states ship in the library. Maximal stacks remain in a test-only header for independent comparisons. This is not a claim of universal speedup or lower memory use. Final integration also accounts for the global pair matrix, private regional result, and legacy boundary-map storage when trackers are enabled.