This page connects each public multidimensional-quadrature claim to the artifact that owns it. Passing one row does not promote the other rows, and none establishes universal superiority over another library.
Evidence map¶
| Question | Evidence owner | What it warrants | What it does not warrant |
|---|---|---|---|
| Do values and work records match independent truths? | truth artifact | Declared analytic and numerical cases at recorded tolerances | Accuracy for unresolved discontinuities or arbitrary integrands |
| Does first-order replay match the accepted formula? | replay artifact | Declared parameter, bound, measure, and quantity derivatives | Derivatives of discrete refinement or higher derivatives |
| Do randomized intervals meet the declared calibration experiment? | RQMC artifact | Real-scalar fixed-look and bounded sequential coverage in the frozen campaign | Per-integral certainty or complex/vector confidence intervals |
| How were external capabilities compared? | comparison artifact | Only the recorded exact, strong-match, node-match, family-match, or capability label | Algorithmic identity from a broad family label |
| Did observed replay memory warrant optimization? | observed-memory artifact | No frozen CPU replay case exceeded its matched primal RSS by the 10 GiB materiality criterion | A separate device-memory measurement or a universal memory claim |
Estimator meanings¶
| Family | QuadError.kind | Interpretation |
|---|---|---|
| Fixed tensor | UNAVAILABLE | No truncation-error estimate is supplied |
| Adaptive tensor | REFINEMENT_DIFFERENCE | Difference between accepted global nested levels |
| Adaptive cubature | EMBEDDED_RULE | Shared-node high/low Genz-Malik disagreement |
| Sparse grid | SPARSE_GRID_SURPLUS | Hierarchical frontier or accepted-index evidence |
| Deterministic Sobol | UNAVAILABLE | No randomization, therefore no confidence interval |
| Randomized Sobol | CONFIDENCE_INTERVAL_HALF_WIDTH | Fixed-look Student-t or bounded sequential empirical-Bernstein evidence |
Replay and quantity boundary¶
Replay differentiates
with the accepted structure frozen. Opt-in quantity normalization may use
heterogeneous coordinate units and restores the result unit after the raw JAX
kernel. It remains alpha: downstream package adoption and direct
Quantity-PyTree quotient-unit Jacobians are not implied.
Performance disposition¶
The immutable baseline fired only the analytic memory-proxy trigger at dimension 16:
This is expected linear coordinate storage and a small absolute proxy, not an observed peak-memory failure. The optimization addendum therefore authorizes no runtime change until a measured campaign demonstrates a material case.
The frozen fresh-process CPU campaign subsequently measured 72 supported primal/replay cases over dimensions 2, 4, 8, and 16 and Sobol levels 8, 12, and 16. Its largest matched replay increment was 45,973,504 bytes (43.8 MiB), for scalar eight-replicate scrambled Sobol at dimension 16 and level 16. That is below the predeclared 10 GiB materiality threshold, so it authorizes no runtime optimization. The remaining 24 randomized array-payload cases are an intentional rejection: calibrated randomized intervals are real-scalar only. The active CPU backend exposes no reliable separate device-memory metric.
Reproduce the focused evidence¶
The following checks are intentionally narrower than the full release gate:
uv run --no-sync python scripts/generate_quad_multidim_evidence.py --check
uv run --no-sync python scripts/generate_quad_rqmc_evidence.py --check
uv run --no-sync python scripts/benchmark_quad_multidim.py --suite baseline --check
uv run --no-sync python scripts/measure_quad_multidim_memory.py --checkThe exhaustive test, documentation, clean-wheel, and observed-memory campaign remain separate release gates.