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Capability inventory

The package is developed as vertical, independently testable slices. A capability is complete only when its public API, CLI, provenance schema, wheel/sdist contents, anchors, and clean-install tests pass.

Public operations converge on a small typed model layer: Generator, CoefficientProblem, RadiusProblem, EvidenceState, Certificate, and LiteratureVerdict. Canonical problem identity preserves direction, normalization, functional parameters, claim type, and provenance. JSON schemas and CLI exit codes are versioned public contracts; internal expression-DAG nodes and search implementation details are not.

Exact generator and Fekete–Szegő operations

Status: shipped.

  • Immutable generator definitions with bibliographic provenance (39 catalog keys, 38 distinct generator formulas). janowski_A0_B-1 and order_0.5 are the same exact function 1/(1-z); keep both public keys for compatibility and historical source locators.
  • Exact Taylor coefficients B_1, …, B_n via generator_series.
  • Exact Ma–Minda Fekete–Szegő constants under declared assumptions via fekete_szego.
  • Classical starlike anchors and JSON-capable CLI.

Function verification, class screens, and witness replay

Status: shipped.

  • Tiered verification (screen / symbolic / rigorous) of normalized functions from coefficients or preconstructed SymPy closed forms. Numerical screens are never presented as proofs.
  • Ma–Minda class operations: admissibility checks, membership screens, containment screens, and exact extremal coefficients. Screens are labelled as screens unless a certified theorem is attached.
  • Counterexample witness replay and grid-search-plus-interval-certification via verify_counterexample and find_counterexample.

Plot reproduction

Status: shipped.

  • Dependency-free SVG plots: conformal domain grids, coefficient magnitudes, real-part heatmaps, and phase portraits, from built-in generators or custom coefficients. Plots visualize a finite Taylor polynomial; they are not proofs of the full image domain.

Optional application labs

Status: shipped behind the lab extra (NumPy).

  • Cryptography Lab: S-box construction and benchmark metrics (bijection, nonlinearity, SAC, BIC, differential uniformity, linear probability) with deterministic AES and identity anchors. Crypto outputs are benchmark metrics, never security claims.
  • Image Lab: full-reference quality metrics (MSE, RMSE, MAE, PSNR, PCC, SSIM, GMSD) and convolution transforms (smooth, sharpen, edge) on deterministic generated arrays. Image outputs are empirical.

Registry snapshots and reconciliation

Status: shipped as a user-supplied snapshot boundary. The registry database is not bundled in the wheel and this package does not currently publish a canonical snapshot URL. Users install a database plus matching manifest with gfa snapshot install SOURCE DESTINATION --manifest MANIFEST; the manifest records hashes, populations, and an optional HTTPS source_url. Snapshot selection and integrity checks are local and fail closed. Typed verdicts (known general, specific known, candidate improvement, contradiction, no extracted claim, unresolved) remain separate from computational evidence, and no automated novelty declaration is emitted.

Paper-level reproduction

Planned. A future command will reproduce every lightweight quantitative table and figure input, with a manifest identifying operations that require expensive computation, external literature access, or human review.

Publication and long-term hosting

Recommended public stack:

  • source and issue tracking: GitHub;
  • Python releases: PyPI;
  • immutable research releases and DOI: Zenodo linked to GitHub releases;
  • API documentation: Read the Docs or GitHub Pages;
  • large registry snapshots: Zenodo release assets or an S3-compatible object store with checksums;
  • live registry: separately deployable web frontend/API consuming a versioned public snapshot.

The Python package must remain useful without the live website. The website must display the package and snapshot versions used for every computed claim.

Deliberately excluded from the reusable package

OCR, OpenAlex/arXiv harvesting, metadata cleanup, literature-PDF storage, review-ledger mutation, usefulness/expert sign-off, reviewer-deck generation, submission packaging, site baking, and deployment remain repository or service operations. The package may contain a pure deterministic comparator for structured claims, but it must not perform editorial decisions or automatically declare literature novelty.