With a ten-second solver allowance, the largest tested knapsack size proved optimal in both repetitions rises from 32 to 384 binary variables in each of two fixed distributions. That is a 12-fold increase in tested size, not a speed ratio or an estimate of the solver's maximum size. The assignment control remains at 256 variables. Both versions reach their time limit at the 512-variable knapsack stress point.

This study measures the existing bounded exact capacity optimization from the algorithm checkpoint. No solver algorithm, option or ABI changed for this measurement. The broader commercial-parity roadmap remains incomplete.

Largest tested size

A size counts only if both repetitions return independently verified Optimal results within the internal ten-second allowance. Every tested point, including the 512-variable stress case, participates in this calculation.

Family	Tested binary variables	Before	Current	Ratio of tested sizes
Uncorrelated capacity	8, 32, 128, 384, 512	32	384	12
Correlated capacity	8, 32, 128, 384	32	384	12
Assignment	9, 25, 81, 256	256	256	1

There is one seeded instance at each size. The two repetitions measure the same instance, not two independent samples. Sizes between the listed points were not tested. In particular, the before result does not establish that 32 is its largest solvable size, and the current correlated result gives no upper limit.

Complete outcome census

All 52 required observations completed and returned an independently valid original-model witness. Before proves 16/26 optima and reaches its time limit in 10/26 runs; current proves 24/26 and reaches its time limit in 2/26. No failed or capped result is removed. The whole invocation takes 150.1307507 seconds, including two separate loader probes and preparation.

Each table cell reports the number of proved optima out of two repetitions. 0/2, limit means both runs return TimeLimit with feasible incumbents, not that the model is infeasible. Objectives minimize negative profit for capacity models and positive cost for assignment.

Family	Variables	Reference objective	Before	Current
Uncorrelated capacity	8	-337	2/2	2/2
Uncorrelated capacity	32	-1,096	2/2	2/2
Uncorrelated capacity	128	-4,318	0/2, limit	2/2
Uncorrelated capacity	384	-13,832	0/2, limit	2/2
Uncorrelated capacity, stress	512	-18,731	0/2, limit	0/2, limit
Correlated capacity	8	-62	2/2	2/2
Correlated capacity	32	-312	2/2	2/2
Correlated capacity	128	-1,211	0/2, limit	2/2
Correlated capacity	384	-3,648	0/2, limit	2/2
Assignment	9	87	2/2	2/2
Assignment	25	162	2/2	2/2
Assignment	81	146	2/2	2/2
Assignment	256	145	2/2	2/2

The complete public record retains all individual statuses, incumbent objectives, bounds and internal/external times, plus the frozen models and reference witnesses. A speed ratio is left absent whenever either version has an unfinished repetition. Sub-millisecond solves and two repetitions do not support a general timing claim; the primary result here is the difference in proved sizes.

Frozen inputs and independent references

The 13 cases, sizes, distributions, seeds and order were fixed and hashed before measurement. There are no planted optima or selected replacement instances.

Capacity tiers contain 8, 32, 128 and 384 Binary variables with weights drawn uniformly from 1 through 31. Capacity is 6*n. Uncorrelated profits are uniform from 1 through 100 with seed 20260906; correlated profits are weight + uniform(0,10) with seed 20260907. Each family uses nested item prefixes. The 512-item uncorrelated stress case continues the same prefix.
Assignment uses 3, 5, 9 and 16 tasks, encoded as 9, 25, 81 and 256 Binary variables. Costs are uniform from 1 through 100, using the top-left square of one 16-by-16 master matrix with seed 20260908. Row and column equalities are represented by pairs of lower-bounded sparse rows: 4*q rows and 4*q*q nonzeros for q tasks. This control is outside the single-row DP.
Capacity reference optima use exact minimum-weight-by-profit dynamic programming, independently of the product's weight-indexed objective DP. Assignment references use exact column-subset dynamic programming. Small subset/permutation enumeration tests cross-check both oracles. The measured phase verifies frozen identities and original witnesses without recomputing the references. Solver TXT files contain incumbent 0; no reference objective or reference assignment enters solve options.

The product's work depends on capacity as well as variable count. Its complete table has (n+1)*(capacity+1) cells and is capped at one million cells, with a separate capacity limit of 65,536. The 384-item cases use 887,425 cells; the 512-item case would need 1,576,449, so it deliberately exercises the unchanged ordinary-search fallback. Both cohorts return incumbent -11,574 in both stress repetitions without proving the reference optimum -18,731. This visible limit prevents extrapolating the 12-fold size result to arbitrary capacities, larger models or additional constraints.

Execution and provenance

The runner makes two alternating paired repetitions: before/current for every case in the first repetition and current/before in the second. Each call uses ordinary Native/BAB, Exact, one thread, seed zero, zero gap tolerances and a 10-second internal limit. Capture allows 11 seconds per child, plus at most 0.5 seconds for cleanup; the invocation has a cooperative 600-second allowance. Internal limits include native compilation/search/checking but not the driver's sparse model construction. External times additionally include startup, parsing, construction and output. Cooperative cleanup can make a time-limited result's reported duration slightly exceed ten seconds.

One adjacent pair of recorded UTC start times implies an apparent 51.3 ms overlap. The runner executes sequentially and reaps each child before launching the next; elapsed durations use monotonic clocks. UTC timestamps therefore do not independently establish nonoverlap or machine quietness.

Before libraries are the preserved source 530a3b783 / compiled product c2fabb78f1. Current libraries contain the accepted capacity algorithm and all five runtime library hashes match the prior algorithm-checkpoint candidate. Two loader probes verify the actual cohorts. The same freshly frozen executable serves both versions; its sole driver change raises the accepted time-limit argument ceiling from five to ten seconds. The earlier study's frozen driver remains unchanged.

The measured source/tooling head is f76dd776af77d2b416d58ea164099b8fdca22dc5. The frozen model manifest SHA256 is ce41bc1e75e35c6dbe708b65ff3f97904533aa66c9f57b1e10d9534b55ff13d3. Model, source, executable, baseline-manifest and loaded-library integrity checks all pass. Eighteen new generator/runner tests pass in 1.430 seconds, including reference isolation, hash rejection, ten-second classification, stress-point inclusion and structured failed-probe preservation. These are tooling checks; the existing solver product and its prior correctness gates are unchanged.

Reproduction uses experiments/optimize/benchmark_capacity_scaling.py: first --freeze-only --freeze-dir NEW_DIRECTORY, then a separate measurement with the printed --manifest-sha256, a ten-second-capable frozen driver, the preserved and current library directories, and a new output directory. Local evidence is under build/capacity-scaling/; the public JSON above includes the report, summary, models and validation record without workstation paths.