The result.
And what it establishes.

The supplied campaign reports dimension-dependent reduction time and a 90-second cap at dimension 64. The result checking was strengthened after a numerical issue was identified. These are reported campaign results, not a new evaluation of your basis.

Reduction does not guarantee an exact shortest vector. The supplied campaign reached a 90-second cap at dimension 64. A matching determinant alone does not prove lattice equivalence; that claim requires the corresponding relationship evidence.

The supplied campaign reproduced a 52-digit determinant for a 40×40 matrix. Its approximate-arithmetic comparison began missing the exact integer at dimension 14 in the studied matrix family. That threshold is not universal.

The reported 52-digit, 40×40 determinant is a specific campaign result, not an unlimited matrix-size guarantee. Exact-result semantics, supported inputs and execution capacity must match the delivered release.

The supplied campaign reports recall of 0.821 on five million vectors in 36.85 seconds. The dataset, dimensions, query count, k and timing boundary must accompany any comparison.

Approximate retrieval is not an exact-neighbor guarantee for every query. The supplied 0.821 recall on five million vectors belongs to its specific campaign settings; production comparisons need the dataset, dimensions and timing scope.

The supplied campaign processed 2.05 billion elements on an A10G. The reported frequency check compared 5,000 keys with exact counts; none undercounted and all stayed within the stated bound. That is not a validation of every distinct-count estimate.

Frequency and distinct-count estimates have different statistical properties. They are not interchangeable exact counts. The reported 2.05-billion-element run and 5,000-key check belong to the supplied campaign, not a universal throughput guarantee.

The three reported graph algorithms consumed 4.2 seconds of compute on the roughly-billion-edge workload. Graph500 searches validated on the tested roots. Compute time is not total ingestion, transfer and verification latency.

The reported billion-edge, 4.2-second total compute result has its own timing boundary. It is not a blanket end-to-end promise. GraphForge supplies graph operators, not a full graph-database replacement.

The supplied campaign reports 6,494 checked satisfying models with no failed assignment check. This is witness-checking evidence, not universal SAT completeness or an independent UNSAT proof for every input.

The supplied campaign reports 6,494 checked models without a failed assignment check. That does not establish unrestricted SAT performance or independently checked UNSAT proofs for every result.

The supplied results matched brute force at all six tested sizes and reported a closed zero gap for those supported knapsack cases. They do not establish general MIP performance.

This is the documented 0/1 knapsack scope, not a universal MIP solver. An interrupted or incomplete run must not be described as a proved optimum. The reported brute-force agreement covers six tested sizes.

The supplied campaign reports an error certificate matching the true error on the tested cases. That observation belongs to the studied model and is not a universal equality for every planning problem.

The campaign’s tight error result belongs to its tested model. It does not guarantee accurate real-world transition models. certnum: MDP is a separately qualified upgrade.

The supplied campaign reports a billion-unknown Poisson workload fitting on an H100. The new Krylov track targets execution overhead identified in that campaign; no unmeasured successor speedup is inferred.

The billion-unknown Poisson result is a specific reported operator and H100 configuration. It does not establish capacity for arbitrary stored matrices. A small residual does not alone guarantee a small solution error for an ill-conditioned problem.

A reported 256-million-point Poisson computation agreed with the closed-form answer at round-off error. This is a particular reference problem and numerical setting, not general PDE qualification.

The reported 256-million-point Poisson example is a particular closed-form comparison. Consistency checks are not proof that every scientific model is physically correct or that all PDE classes are supported.

The supplied study records a reconstruction-error transition in its measurement setup. Its matrix-free path was not exercised on GPU. The example is not evidence of clinical performance or universal recovery conditions.

The supplied campaign did not exercise the matrix-free path on GPU. The product page does not claim validated GPU performance for that path, clinical suitability or a medical-device approval. Data fit is not automatically ground-truth accuracy.

The supplied campaign compared the transport result with an exact reference across studied regularization settings. Its observed error trend is specific to those cases and does not replace marginal or objective checks.

Marginal feasibility is not itself proof of unregularized optimality. The observed regularization trend belongs to the supplied campaign. Optimal transport is distinct from vehicle-routing or logistics-route planning; CertOT is its separately qualified upgrade.

The supplied campaign reports 2.56 million states on an A10G and comparison with an exact reference filter in the studied setup. These are not universal forecast-accuracy or memory-capacity guarantees.

The supplied 2.56-million-state A10G result and convergence trend are configuration-specific. They do not establish forecast accuracy across arbitrary models. The independent check contract is specific to the delivered release.

The reported one-billion-path interval included the Black–Scholes reference price. Achieving the stated certified interval required about four times the paths of the ordinary interval at the same width in that study.

Confidence coverage is probabilistic, not certainty that every interval contains the truth. The reported one-billion-path Black–Scholes comparison is one model test, not financial advice or a guarantee of real-world valuation accuracy.

The reported estimates matched exact enumeration on the evaluated instances. The newer log-Z track has a separate two-sided-bound scope; neither is the general exact-counting module.

This is not exact counting for arbitrary discrete models. The supplied summary does not establish universal confidence coverage. certnum: log-Z and certnum: Exact counting are separate tracks with different output requirements.