Multidimensional quadrature evidence

This page connects each public Phase B 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 a predeclared optimization trigger fire?	performance baseline	A dimension-16 analytic memory proxy exceeded the family-median threshold	An observed process/device-memory bottleneck

Estimator meanings¶

Family	`QuadError.kind`	Interpretation
Fixed tensor	`UNAVAILABLE`	No truncation-error estimate is supplied
Adaptive tensor	`SUCCESSIVE_LEVEL`	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`	Fixed-look Student-t or bounded sequential empirical-Bernstein evidence

Replay and quantity boundary¶

Replay differentiates

\widehat{I}(\theta) = \sum_{i=1}^{N_{\mathrm{accepted}}} w_i(\theta)f(\boldsymbol{x}_i(\theta),\theta),

(1)

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:

\frac{36{,}864\ \mathrm{bytes}}{16{,}384\ \mathrm{bytes}} =2.25.

(2)

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.

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

The exhaustive test, documentation, clean-wheel, and observed-memory campaign remain separate release gates.