I remove the redundant 64-bit total from each rank owner and view. The encoded word and checkpoint arrays do not change. rank(g) now requires an existing group, and bitmap rank(p) requires an existing bit. The final boundary is not a rank query. A caller obtains a group's upper prefix from its lower rank plus its class; count() derives the total from the last valid prefix and class or bit, with zero for an empty index.

This is a C++ API change: constructors no longer take a total, owning .total fields are gone, and count() is a bounded payload query rather than a cached noexcept scalar getter. Shape-only mapped opening does not call it. Projection still checks its selected ranks against the authoritative native/borrowed sizes. Raw views retain the builder-or-validated-metadata contract. Packed checked addition now bounds by virtual size; a raw malformed directory is not checked against a separately supplied borrowed total. Full-bitmap arithmetic retains its existing trusted-directory contract. Complete semantic admission stays in explicit scanners.

Measurements

The source and runner compare the final candidate with baseline c31f339321eebd68aa9319db8c31f788572f2538. The raw table records minimum, median and maximum for five rotating trials; metadata records exact compiler flags and source/header hashes. Timing used the working-tree headers subsequently committed as f02434a; the metadata also records that exact match.

Each trial performs 1,048,576 queries. Packed variants share the same arrays; the bitmap shares its words and uses identical directory contents with distinct C++ directory element types. Independent original populations supply the oracle. Dependent queries feed each answer into the next position. Every query is in range, and the pair workload computes 2*rank(g)+class_at(g).

On this M2 Max, Apple Clang 21 used -O3 -DNDEBUG with QOS_CLASS_USER_INITIATED, without CPU affinity. Median nanoseconds:

Workload	Cached total	Bounded
K=15 independent rank	5.568	5.569
K=15 independent rank plus class	7.751	7.639
K=15 dependent rank	16.277	16.371
K=15 dependent rank plus class	17.151	17.229
Bitmap independent rank	6.012	6.133
Bitmap dependent rank	17.998	17.935

The full table includes K=3, 7 and 31 and all observed ranges. These results show similar hot-query costs, not a general speedup. The measured views shrink by exactly eight bytes. Arrays occupy 20,480 / 28,672 / 36,864 / 45,056 bytes for K=3 / 7 / 15 / 31, and 33,800 bytes for the bitmap. The bitmap's reported view_bytes includes a 16-byte benchmark adapter span in both variants. This bounded run does not measure cold mappings, LLC-exceeding data, construction, or count() latency.

Reproduce with the measured header revision using the current normalized fixture and runner, under the host's resource gate:

python3 bench/rank_bounds.py --candidate f02434a94b7c1250c29d6d4e20a1401a0700cd4d \

--build-dir build-rank-bounds --trials 5 --queries 1048576

The runner normalizes both pinned header snapshots. rank_compare.sh and neon_bitmap_rank.py retain their pinned historical headers and original observations. other_rank.py accepts either old constructors or the new API without changing its default historical pins.

-Edward Kmett