Guidelines

Sep 14, 2025

GRG Documentation Guidelines

Describe the construction through its geometric definitions. Use plain language, explicit hypotheses, and reproducible evidence.

Current Formulas

Use geometric lengths and ratios. Keep circular constants outside the construction’s formulas and numerical kernel. Explicit computational comparisons may use reference constants, with their role clearly stated.

Claims and Evidence

Distinguish definitions, proved statements, numerical observations, proposals, and applications. Do not claim efficiency, numerical stability, exact hardware arithmetic, or originality without supporting evidence.

Versioning

Identify historical formulations and retain their provenance. The binary radial formulation is the current two-dimensional reference.

Presentation

Keep site content in English. Provide accessible diagram descriptions, readable mathematical displays, and verified links. Avoid polemical slogans and comparisons that imply an unmeasured advantage.

Publications

Publications

Sep 13, 2025

Publications and Research References

This page identifies documented GRG material and distinguishes it from publication plans. Website articles are research documentation; they are not, by themselves, evidence of peer review.

Current Formulation

External Research Records

GRG community on Zenodo and Stefano Ferragina’s ORCID record provide entry points to external records. A community link or an ORCID identifier is not a DOI for this formulation.

Citation

For a website citation, use the author, exact article title, article URL, access date, and the version being discussed. Use a publication DOI only when its landing page has been checked against the actual work and version.

Publication Status

Previous manuscript lists and citation templates have been withdrawn from this page as unverified placeholders. Manuscripts, datasets, and software releases will be listed with their actual status and persistent links after verification.

Results

Results

Sep 13, 2025

Results and Verification

This page separates analytical results from numerical illustrations and performance measurements.

Analytical Results

The current binary radial formulation defines regular chord–tangent sectors and gives exact-arithmetic proofs of second-order error for arithmetic kernels and fourth-order error for the weighted circumference and area kernels. It also proves an area bracket for the defined regular sectors.

These statements have specific geometric hypotheses. They do not establish numerical exactness at finite resolution, hardware stability, originality, or superiority over other methods.

Numerical Checks

Numerical evaluations may check consistency with the analytical results. A publishable record must include the generating procedure, radius, sector count, precision, reference definition, raw output, and executable code.

Performance Results

The former gallery mixed example cards with timing figures and incomplete dataset records. Those figures are not retained as validated performance results. No measured efficiency advantage is established by this page.

Performance results will be added when complete reproducible evidence is available under the comparison protocol.

Roadmap

Roadmap

Sep 13, 2025

Research Roadmap

This page records work to be completed rather than retaining expired milestones or unsupported delivery promises.

Documentation

Align the current formulation, area-kernel article, notation, historical methods, and references. Consolidate duplicate content and preserve versions.

Implementation

Trace dependencies in every interactive tool. Specify which operations construct geometry, evaluate measures, compute comparison references, and draw the visualisation.

Verification

Review domains, normalisations, error proofs, rounding, cancellation, and stopping conditions. Validate general shapes and three-dimensional methods independently.

Benchmarks and Releases

Publish actual scripts, datasets, environments, licences, and measured results. Assess equal-accuracy performance before reporting a speed advantage.

Publication

List manuscripts and releases with verified status and persistent links. No release date, throughput target, or completed milestone is implied until evidence is available.

Reproducibility

Reproducibility

Sep 13, 2025

Reproducibility and Research Artifacts

This page defines the evidence required to reproduce a GRG result. It is a protocol, not a declaration that every artifact is already available.

Available Documentation

Required Record

Each numerical result should identify the construction version, input geometry, sector count, sampling convention, arithmetic format, rounding policy, software version, reference definition, and raw output.

Code and Environment

Provide executable source, a documented environment, test cases, and a release identifier. State the actual licence; do not imply an open-source release before one is published.

Measurement Protocol

Archive inputs, outputs, timing methodology, hardware details, memory measurements, and comparison methods. Include setup and precomputation costs. Compare complete implementations at equal achieved accuracy.

Verification Status

Previous completion checkmarks and sample commit identifiers were templates. They have been removed. Repository, continuous-integration, dataset, and DOI availability must be verified individually before being marked complete.

Use Publications and Research References for documented external records.