Reproduce and cite a calculation

A reproducible answer identifies the mathematical object and global form, representation category, chosen map, input, convention profile, and mathematical implementation. A displayed dimension or decomposition is one part of that record.

Share inputs and save the result

Each supported workbench provides a calculation link, LaTeX output, and JSON export. The link restores inputs with the currently deployed engine. Save the JSON when using a result in research: it preserves the calculated output and the version evidence even after the live site changes.

Version	What it identifies in this edition
Application	6.0.0: website and exported-result integration.
Dataset	2026.11-workbench.4: released mathematical records and provenance.
Schema	2.0.0: the common structural contract.
Algorithm	The particular mathematical engine used; see below.
Convention profile	A stable ID and version for category, numbering, normalization, charges, or map.

The release-level umbrella version is groups-workbench-4.0.0. A calculation’s own algorithm field is more specific:

Mathematical implementation	Algorithm version
Original five calculators	groups-design-1.0.0
Finite character arithmetic and decompositions	finite-characters-1.0.0
Weyl dimensions, SU(3) tensor products, and SU(3) branching	lie-representations-1.0.0
SU(N) matter and central quotients	su-n-matter-kernel-1.0.0
SU(N) Littlewood–Richardson tensor products	su-n-tensors-1.0.0
Charge-refined SU(N) block restriction	su-n-block-branching-1.0.0
Product SU factors, one U(1), and embedded quotients	product-gauge-1.0.0
Local scalar/Weyl polynomial invariants	local-operators-1.0.0

The character-table resource additionally names its data version, small-characters-1.0.0. Convention profiles and the method manifest make these choices inspectable independently of the interface.

Named saved calculations

The operator enumerator accepts groups.qft.org/operator-enumeration/1 inventories and exports groups.qft.org/operator-enumeration-calculation/1 envelopes. Its algorithm is operator-enumeration-1.0.0, with the underlying local-operator and gauge algorithms recorded separately. Imports validate and recompute; cached counts are ignored and changed algorithm versions are reported. Six worked inventories include downloadable requests and results.

The local-operator tool adds groups.qft.org/physical-setup/1 inputs and groups.qft.org/physical-calculation/1 result envelopes. A setup records Lorentzian spacetime, the exact gauge quotient, scalar/Weyl species, flavors, and a fixed monomial with its algebraic equivalence convention. A calculation retains those inputs and the method/version evidence. Loading either file validates the semantics and recomputes; cached results are ignored. Eleven worked files and the schema reference make this contract inspectable.

The three Workbench II tools provide Save calculation and Load calculation. A groups.qft.org/model-calculation/1 file retains its setup name, single-tool inputs, exact result, convention profile, sources, and versions. Loading validates its inputs and recomputes using the current implementation; the stored answer is not trusted as an unchecked result. A changed algorithm version is reported. These local files require no account and are not uploaded.

Download a worked calculation file, open its indicated tool, and choose Load calculation. The saved ranks field in product-group files contains SU factor sizes $N_i$, not algebra ranks $N_i-1$. These older single-tool files do not carry Lorentz or statistics data. The new physical setup schema supplies those fields for its bounded domain; the complete proposed physical model remains broader.

The charged branching tool can transfer its multiplets to the product-group tool together with the actual block-map kernel. In the color-first SU(5) example the transfer uses $Q_Y=6Y=-X$; other supported splits use $Q=X$. The receiving tool applies its own input limits and recomputes descent.

Operator enumeration runs in a local background worker with progress and cancellation. The result includes nonzero monomial sectors, exact invariant dimensions, subtotals by canonical dimension, and necessary-filter diagnostics. An obstruction or resource failure never becomes a partial total presented as complete.

Exact values and independent checks

The new engines use arbitrary-precision integers and reduced rational arithmetic. Nonintegral finite characters are encoded in the exact fields specified by their tables. JSON preserves large integers and coefficients as strings; a decimal approximation is not a replacement for those exact values.

Character orthogonality, degree sums, class power maps, full-character reconstruction, dimension conservation, central charges, and map-kernel constraints are checked where relevant. Independent mathematical fixtures test selected known results and entire bounded families. These checks establish their stated properties; they do not amount to an independent human proof or approval of every page.

Reconstruct the mathematical choices

Keep the original highest-weight ordering and Cartan matrix with a Lie result. Keep class representatives and exact character fields with finite tables. A branching calculation requires the named homomorphism, image, kernel, and torus action. A symmetric or exterior power requires its statistics interpretation. A global-form result needs the actual central subgroup, not just a Lie algebra name.

The root-system snapshot, finite character tables, and convention manifest support local reconstruction. The tools execute local JavaScript implementations. An upstream GAP or SageMath reference records a source or verification target; it does not mean that software executed the website’s calculation.

Download a verification script

Four tools generate scripts for an independently installed environment: GAP for finite characters, SageMath for highest-weight invariants and SU(3) tensor products, and standard-library Python for matter quotients. The generator version is reproduction-scripts-1.0.1. The SU(3) branching tool, the three Workbench II tools, and the local-operator tool have no external-script export in this edition. Script downloads supplement the result JSON; they do not replace its conventions and provenance.

The GAP script verifies the serialized table and operations using exact cyclotomics, without independently identifying the group or assuming an upstream class order. SageMath scripts reconstruct the stated Cartan type and coroot labels. Python matter scripts independently recompute dimensions, charges, common kernels, and quotient obstructions. Scripts include expected results and verification assertions.

The site does not execute these external environments. On 2026-11-09, local development checks executed 12 standard-library Python scripts and 39 generated SageMath scripts using SageMath 9.7. The Sage fixtures cover all 32 supported root systems, rank-one edge cases, a large exact E8 dimension, and three SU(3) tensor products. The 93 GAP fixtures were generated and serialization-checked; native GAP execution remains unverified. These checks concern the recorded fixtures, not arbitrary future downloads or a live computational backend.

Cite a record or calculation

For a reference property, retain its entity and claim identifiers, source locator, dataset version, and available content fingerprint. The canonical URL identifies the subject; the version and fingerprint identify the content inspected. Record pages supply BibTeX citations and JSON.

For a calculation used in research, cite its mathematical sources, preserve the exported result alongside the work, and state any changed normalization or physical interpretation. Include that export and the affected claim identifiers in an evidence-backed correction packet if a discrepancy appears. Correction packets are prepared locally; the current site does not send them to a public inbox automatically.