Coverage policy

Three mathematical coverage levels

Level	What it promises
Classification	A defined object or parameterized family, its scope, and selected sourced invariants.
Reference	A declared set of curated properties or representation data.
Executable	A named operation over a documented input domain.

A classification entry does not make every property computable. A complete finite list of irreducible dimensions does not supply matrices, character values, modular representations, or basis-dependent coefficients.

Research workbench IV

The current catalogue contains 266 mathematical records, including 62 representation records: all 30 irreducible characters across the seven executable finite groups, and 32 selected Lie representations. There are infinitely many highest weights for every nontrivial compact simple type; the selected representation records are not an exhaustive list. Calculations generate supported results from the declared inputs.

Workbench I tool, retained	Released domain
Finite characters	C₃, S₃, D₈, Q₈, A₄, S₄, A₅; ordinary complex representations; base dimension ≤60, each input multiplicity ≤12; tensor, symmetric, and exterior powers of degree 0–12.
Weyl dimensions	A₁–A₈, B₂–B₈, C₂–C₈, D₄–D₈, E₆, E₇, E₈, F₄, G₂; each Dynkin label 0–30; simply connected compact integration.
SU(3) tensor products	Each input Dynkin label 0–6; complete decomposition, with unrestricted resulting labels within that finite computation.
SU(3) branching	Each input Dynkin label 0–6; regular and principal maps only.
Matter and central quotients	One SU(N) factor, 2≤N≤12, at most 16 multiplets, labels 0–30; all compatible central quotients.
Workbench II addition	Released domain
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SU(N) tensor products	2≤N≤6, labels 0–12, and at most 16 canonical Young boxes across both inputs; complete Littlewood–Richardson decomposition, subject to a 2,000,000-state resource guard.
Branching with U(1) charges	3≤N≤6, 1≤p<N, labels 0–12 and at most 12 canonical parent Young boxes; the specified primitive block map, including its kernel and all charges.
Product gauge groups and matter	One or two SU(N) factors, 2≤N≤8, and one U(1); at most 16 multiplets, labels 0–12, integer charges −24…24; at most 3 quotient generators, phase denominators ≤60, generated subgroup order ≤4096.
Workbench III addition	Released domain
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Local operators and field statistics	Four-dimensional Lorentzian scalar and Weyl fields; SU(3) × SU(2) × U(1) with specified diagonal quotient of order 1, 2, 3, or 6. At most 16 species, 3 ungauged flavors per species, 6 field occurrences and canonical dimension 6; color labels p+q≤2, weak label 0–2, integer charges −24…24. No derivatives. At most 120,000 weights per intermediate character and 20,000,000 coefficient-pair multiplications; the engine returns an exact result or an explicit resource error.
Workbench IV addition	Released domain
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Operator enumeration	The same scalar/Weyl representation bounds, minimum and maximum dimensions 1–6, and an optional dimension-zero identity. At most three integer U(1) or cyclic Z_n selections with 2≤n≤12 and field/target charges −24…24. At most 100,000 visited multidegrees, 4,096 projected candidates, 100,000,000 aggregate coefficient-pair operations, and 4,096 output rows. An error or cancellation yields no completed partial count.

The original five workbenches retain their earlier algorithms and limits. The complete capability matrix and method manifest distinguish those tools from the ten Workbench I–IV additions. All calculations in this edition run locally; citations to GAP or SageMath do not mean a remote backend executed the result.

Completeness and exactness

The seven finite character tables contain every ordinary complex irrep of their specified groups, with exact algebraic character values and class power maps. Their decompositions retain multiplicities. The Lie dimension engine evaluates Weyl’s formula exactly over its finite input range; it does not enumerate all irreps, compute general tensor products for every type, or classify noncompact unitary representations. Read the method pages for normalization and validation details.

Four absence states

Not yet curated means data have not been included. Unsupported means the engine does not perform the operation. Inapplicable means the property belongs to a different category or space. Nonexistent is a mathematical assertion requiring evidence. An omitted value must not be interpreted as zero or as a proof of nonexistence.

Remaining boundaries

Arbitrary embeddings, other compact types beyond the stated tensor methods, products with multiple U(1) factors, complete explicit matrices and invariant tensors, derivative operator enumeration with equations of motion and integration by parts, arbitrary cohomology, noncompact unitary duals, and anomaly classification remain outside this release. The physical setup schema implements fixed-monomial invariant counting; operator enumeration extends it to all admitted monomials of a supplied inventory through dimension six, with optional charge rules. Hermiticity, flavor-basis equivalences, generated explicit contraction bases, and a complete EFT inventory remain additional tasks. Research workbench IV implements a defined subset of Phase C; the roadmap records what remains.

Independent human review is a separate status and is pending for the current edition. Inspect the review queue; source checking and automated fixtures do not confer expert approval.