Validation and Benchmark Protocol

This page specifies planned comparisons. It does not present a completed benchmark or a demonstrated performance advantage.

Separate Tasks

Measure circumference and area evaluation separately from boundary generation, rasterisation, and three-dimensional modelling. Equal sector counts alone do not make different tasks comparable.

Accuracy and Cost

Compare runtime at the same achieved error, and error at the same runtime. Report arithmetic format, rounding, memory, hardware, software versions, warm-up, repetitions, timing variability, setup cost, and precomputation.

Baselines

Include geometric bisection with inner–outer bounds, comparable weighted or extrapolated kernels, and direct analytical evaluation where appropriate. Give every method the same target and include its full computational cost.

Data and References

Begin with the circle kernels whose hypotheses are documented in the current formulation. Validate other shapes and three-dimensional methods separately. Publish reference precision and how it is obtained.

Convergence

The current regular-sector proofs distinguish second-order arithmetic kernels from fourth-order weighted kernels. These rates must not be transferred automatically to Cartesian trapezoids, endpoint-singular integrands, general shapes, or finite-precision implementations.

Reporting

Publish executable scripts, inputs, raw CSV or JSON, version identifiers, plots, and the conditions of every comparison. Former sample timing rows and schematic plots are not retained as measured results.