Carrying exact longest-common-prefix (LCP) lengths through both the three-way target sampler and its parent builder reduces complete COLA build time on these long-prefix fixtures. The direct before/after measurement has 4,096-byte-prefix medians 77.0–85.2% lower, with disjoint observed ranges in all four cases. Short-key ranges overlap; their lower medians do not establish a separate short-key speedup.

Direct combined comparison

The direct run compares 77507b8 with 6cc772a (accepted as ac5d4c4). Both versions retain the same aligned comparator, native inputs, output format and checked public APIs. This is the measured combined result; it is not a product of the separate stage percentages below.

The metric throughout is nanoseconds per augmented occurrence of the newly built node, including builder construction, stepping and finalization. Each cell is median [minimum, maximum], from 15 timed observations. These are complete build measurements, not timers around individual selectors.

Unit	K	Prefix bytes	Before	Both frontiers	Median change
byte	3	0	161.5 [154.6, 177.8]	161.2 [155.0, 171.2]	-0.2%
byte	15	0	173.6 [166.6, 183.1]	171.1 [161.6, 185.8]	-1.4%
bit	3	0	251.3 [246.0, 270.1]	241.2 [235.6, 260.2]	-4.0%
bit	15	0	298.7 [280.2, 320.8]	261.9 [250.8, 314.8]	-12.3%
byte	3	4096	984.7 [940.0, 1036.6]	164.2 [155.2, 174.8]	-83.3%
byte	15	4096	1154.5 [1112.9, 1194.5]	170.8 [167.2, 197.3]	-85.2%
bit	3	4096	1083.8 [1062.4, 1115.3]	249.0 [236.5, 269.3]	-77.0%
bit	15	4096	1261.4 [1230.5, 1302.3]	254.9 [250.4, 284.5]	-79.8%

Sampler frontier

This comparison changes only cola_sample_cursor in cola_index.h: 77507b8 to 0ba3ee3 (accepted as d1d74e7). Each live head carries its exact bit LCP with the preceding emitted occurrence. Unequal frontiers select the next head without rescanning their shared prefix; equal frontiers compare only their suffixes. The selected stream advances with profile_cursor::advance_comparison, and the losing heads retain the ordered-LCP minimum. Native/main/secondary tie order and sampled occurrence positions stay unchanged.

Measured by itself, this stage lowers long-prefix medians by 47.0–57.1%, with all four observed range pairs disjoint. All short-key range pairs overlap.

Unit	K	Prefix bytes	Before	Sampler frontier	Median change
byte	3	0	154.9 [150.9, 374.2]	152.3 [145.3, 325.3]	-1.7%
byte	15	0	180.8 [166.5, 337.7]	165.8 [153.9, 293.5]	-8.3%
bit	3	0	257.4 [245.6, 416.1]	248.9 [234.8, 384.8]	-3.3%
bit	15	0	301.6 [279.1, 431.1]	265.6 [260.3, 350.8]	-11.9%
byte	3	4096	1000.5 [951.1, 1127.5]	504.1 [472.6, 640.3]	-49.6%
byte	15	4096	1162.1 [1119.3, 1201.9]	498.8 [483.9, 549.4]	-57.1%
bit	3	4096	1102.2 [1052.3, 1161.7]	584.0 [557.8, 612.1]	-47.0%
bit	15	4096	1283.4 [1246.7, 1355.4]	608.1 [599.8, 698.2]	-52.6%

Builder frontier

The second comparison, 0ba3ee3 to 6cc772a, holds the improved sampler fixed and carries the same exact-bit frontiers through the parent builder. The sampler returns the minimum adjacent LCP across the K occurrences it advances. The builder can then select its next native/main/secondary head and update each cut LCP without comparing against a separate full previous-key buffer. It retains the previous key's length for equality detection; strict native ordering is checked while advancing native cursors.

The four long-prefix medians fall another 56.7–66.6%, with disjoint ranges. Short-prefix median changes span −5.2% to +6.2%, with every range pair overlapping. This is an incremental comparison against the sampler-only version; its percentages must not be multiplied into a claimed overall measurement.

Unit	K	Prefix bytes	Sampler only	Sampler + builder	Median change
byte	3	0	156.3 [146.7, 168.5]	158.3 [153.4, 208.2]	+1.3%
byte	15	0	159.1 [154.9, 177.7]	169.0 [162.0, 198.6]	+6.2%
bit	3	0	243.8 [234.5, 263.0]	244.7 [236.0, 272.5]	+0.4%
bit	15	0	267.2 [260.3, 287.7]	253.2 [248.2, 270.1]	-5.2%
byte	3	4096	481.1 [469.2, 516.7]	163.9 [156.1, 183.1]	-65.9%
byte	15	4096	503.3 [483.9, 521.3]	167.9 [162.6, 178.3]	-66.6%
bit	3	4096	578.1 [565.7, 611.2]	250.5 [235.6, 265.6]	-56.7%
bit	15	4096	620.6 [607.0, 634.2]	264.8 [249.1, 292.6]	-57.3%

Method and limits

The C++ fixture is unchanged from the comparison-layout experiment. The new node has 2,048 native records and samples a main node with 4,096 native records plus borrowed samples, and a 4,096-record terminal secondary. The main node's two routes share a native leaf. Keys have an ordered four-byte suffix after either zero or 4,096 common bytes. Bit policies append three meaningful bits. Values are variable-width; K is 3 or 15, W defaults to K, and the bit/K=3 case uses Golomb-3 controls. This fixture contains overlapping native and borrowed keys.

The M2 Max host runs Apple Clang 21.0.0 with -O3 -DNDEBUG -std=c++20 under the exclusive host CPU resource lease. Each variant runs in five fresh processes, alternating baseline/candidate order; each process warms up every fixture and then records three timed rounds. Baseline runs first in three of the five trials. No affinity was requested. Construction of the input fixture, serialization and result/builder destruction are outside the timer.

Every process writes its eight warm-up IX03 files. The runner compares all bytes across both variants and all trials. Each timed result is serialized after timing and checked against its process's warm-up CRC; the CSV also records exact output size. All sizes, occurrence counts and CRCs agree across versions. This is wire-equivalence evidence against the existing implementation, not an independent semantic oracle or a cryptographic equality check for each timed output. The separate COLA tests supply original-key/query oracles. Both sampler-only and final builder candidates passed the strict O3 ASan/UBSan core suite; the final candidate also passed the mapped-store guide example.

Ranges are observations, not confidence intervals. All outliers are retained. These measurements cover owning, in-memory construction and the tested input shapes on this compiler/host. They do not measure mapped I/O, sealing, SQLite publication, a scheduler, or a portable bound on key-comparison work. The alignment decision from the preceding experiment is held fixed in both variants.

Reproduction and raw evidence

Run the runner under the host's CPU resource gate. It copies both committed header trees into a new build directory; it does not compile against changing working-tree headers. The build directory must not exist.

python3 bench/cola_frontier.py --baseline 77507b8 --candidate ac5d4c4 \
  --trials 5 --rounds 3 --build-dir build-world-frontier-overall
python3 bench/cola_frontier.py --baseline 77507b8 --candidate d1d74e7 \
  --trials 5 --rounds 3 --build-dir build-world-sampler-frontier
python3 bench/cola_frontier.py --baseline d1d74e7 --candidate ac5d4c4 \
  --trials 5 --rounds 3 --build-dir build-world-builder-frontier

The original measured fixture SHA-256 is 8757aad627c34e9622a07ec5ef420680a477a698abbbd91121570207f4df0a27; the original runner SHA-256 is 39811b608c7ddd801cf6fd63db5154e35a5a47e455aa99de4c834c51344cc206. Each run retains all 240 timed observations and its measurement metadata, with source and path names normalized:

Direct combined result: CSV, metadata.
Sampler stage: CSV, metadata.
Builder stage: CSV, metadata.

The metadata records full measured source revisions, every header hash, compile commands, compiler/platform, binary hashes, execution order, whole-file hashes and start/completion times. Accepted revision spellings in the reproduction commands retain every measured header in this fixture's include closure. Their multiverse.h differs from the recorded tree, but this fixture does not include that facade.