Website → package parity

The package is the local reproduction layer for the Geometric Function Atlas website. Each capability represented in this table has one short gfa command and a Python function backed by the same implementation. Browser-only panels and a separate GUI are out of scope.

Website capability	Local package interface	State
Browse/search function families	gfa generators, gfa classes	available
Inspect facts, instances, evidence, and verification runs	gfa verify, gfa class-check	available
Re-check a supplied counterexample witness	gfa verify-counterexample	available
Verify a function from a closed form or coefficients	gfa verify	available
Search for a violation and certify it	gfa find-counterexample	available
Reproduce generator Taylor coefficients	gfa coefficients	available
Reproduce Fekete–Szegő values and bounds	gfa fekete-szego	available
Query other coefficient bounds and expansions	gfa coefficient-bound, gfa expansion	available
Reproduce function-domain and coefficient plots	gfa plot	available
Query, identify, audit, or bounded-recompute directed inclusion radii	gfa radius, gfa radius-identify, gfa radius-audit, gfa radius-recompute, gfa radius-attainment	available
Re-run a stored proof or certificate	gfa verify-certificate	available
Compare classes and hierarchy	gfa compare	available
Inspect class application tags	gfa applications	available
Inspect papers and reconciliation records	gfa papers, gfa reconciliation	available
Export citation formats	gfa citation	available
Query legacy functions, paper facets, and tags	gfa function, gfa functions, gfa paper-facets, gfa tags	available
Export domain plots as SVG, PNG, or TikZ	gfa plot domain ... --output ...	available
Replay the website's 435-row cryptography metric snapshot	gfa crypto-lab leaderboard --scope website	available (reported metrics only; no S-box payload)
Reproduce the Image Lab's finite coefficient-derived filters and metrics	gfa image-lab	available (lab extra; no analytic or conformal-warp claim)
Reproduce Cryptography Lab benchmark metrics	gfa crypto-lab	available (lab extra; no security claim)
Report registry snapshot statistics	gfa stats	available

Completion rule

A row is complete only when:

1. the command is simple enough to copy from the webpage;
2. the Python API performs the same scientific operation;
3. a parity test compares it with a frozen website/API result;
4. the output clearly distinguishes a proof, a certified enclosure, a numerical screen, and an unresolved result.

The registry database remains a separately versioned snapshot. The package does not bundle it and does not currently publish a canonical snapshot URL. Users provide the database and matching manifest explicitly; gfa snapshot install verifies hashes, populations, and SQLite integrity before installation, while paper facets can search citation metadata as well as claims and tags.

The package ships the complete lightweight parity surface represented by this table: deterministic generator/class computations, SVG visualizations, baked scientific-artifact queries and certificate replay, directed-radius queries and reviewed replay, and local immutable-snapshot queries. Heavy proof search, full radius discovery, OCR/literature harvesting, and deployment remain outside ordinary package commands. Their absence is an explicit boundary, not a release-stage label.

Image Lab parity covers finite, non-empty 2D (H×W) and RGB (H×W×3) inputs. For GMSD, the package mirrors the website's 2×2 prefilter exactly, including discarding trailing rows or columns on odd-sized inputs.

Website panel

Each implemented scientific item should display a small Run locally panel, not a custom launcher or desktop application:

Install once   [macOS/Linux] [Windows]
Reproduce      gfa <task-oriented command>

The install buttons copy the commands in docs/getting-started.md. The reproduce button copies the exact command for that page item. Human-readable output is the default; --json is an optional advanced action.