field results
the proving ground
Public datasets, hard problems, and numbers that were checked against something other than our own output. Every figure below was independently reverified.
the public record: QPLIB 2036
QPLIB is the public library of hard quadratic programs; its listed best-known value for instance 2036 stood until we submitted a better one. The maintainer independently verified the improved objective and is updating the published figure. Separately, instances 2017, 2029, and 2036 are absent from Hans Mittelmann's seven-solver benchmark table, meaning all seven fail within the hour; they fall in 58.3, 57.0, and 96.8 seconds here.
Hardware honesty: Mittelmann's benchmark machine is a 12-core Ryzen 9 5900X; ours is a 40-core Xeon Gold 5218R, roughly 3.3x the cores. Discounting fully by core count still leaves about a fivefold margin, and the instances nobody solves stay unsolved regardless of hardware.
the open problem: G-set MaxCut G22
Nobody has ever proven the optimum of G22, a 2,000-node MaxCut instance whose best-known cut has stood through a decade of specialized research. The suite's stock annealer, called through the same CLI a customer would use with zero instance tuning, lands one edge from that record on desk hardware, reproduced twelve times across 22 restarts.
Every one of the 22 reported objectives was reverified by recomputing the cut from the returned assignment against the raw edge list. 22 of 22 matched exactly. This is not a record and does not close the problem; it is a stock solver within one edge of one.
the allocation engine: baskets that prove their work
Pick the best basket of trades under a risk budget and a position cap: an NP-hard selection every commercial optimizer handles with heuristics and hands back without proof. Here the exact solver picks it, a full enumeration of the combination space re-verifies it, and the answer ships with the certificate. Five risk levels, five provably optimal baskets, rotating from cyclicals to defensives exactly as the arithmetic demands.
The regime detector under it is held to the same standard: a claimed market break must be the provably best split of the recent window and must beat the 99th percentile of the same statistic on shuffles of that very window. When the evidence is not there, the report says so, with the margin and the bar it failed to clear. Stress replays of 2018, 2020, and 2022 print in every report, including the losses.
the intake test: 7,043 real telecom customers
The classic messy customer dataset hides eleven blank values as single spaces inside a numeric column. The auto intake profiled every column correctly, caught and logged all eleven, and surfaced something better: those eleven are exactly the tenure-zero customers, never billed, so the blank means something and the cleaning log makes that reviewable.
The reported median, smoothed final, top-k, and histogram were each recomputed independently from the raw file. All matched exactly, and the histogram conserved all 7,043 rows.
the hard business decision: retail bundle selection
From half a million real e-commerce rows: pick the ten products to co-promote that maximize co-purchase affinity. On a slice small enough to prove, three independent methods agree exactly: exhaustive enumeration of all 4,368 candidates, the exact tier reporting optimal, and the annealer. At full scale the annealer beats a greedy baseline by 8.8 percent, and the winning bundle is the store's tightest real co-purchase clique.
The proof structure is the product: exact where proof is possible, heuristic where it is not, and the same answer where the two regimes overlap.
Method details beyond standard technique names are deliberately absent from this page. Bring a problem you already know the answer to and check us: subscribe on AWS.