Conventions

Names

Every entry has a catalog name, modeled on AnyonWiki’s names for fusion rings:

\mathrm{WHA}^{D,\,t,\,p}_{i}

Part	Meaning	Examples
$D$	dimension
$t$	dimension of $A_{t}$ ; 1 exactly for Hopf algebras
$p$	Wedderburn blocks over the base field; ns when not semisimple	`1^4, 2, [2].1, ns`
$i$	position among everything sharing $(D, t, p)$

Each name carries a status, since the index depends on a classification: canonical when the slice is classified (the split commutative slice, where it agrees with GAP’s SmallGroups numbering, and $\mathrm{Mat}_{2}$ ), family when it is canonical within a family, and provisional otherwise. The machine form is WHA_4_2_1^4_1.

An entry

Field	Holds
`uuid`	assigned once, never changed
`code, code_status`	the name above and its status
`base_field, embedding`	$\mathbb{Q}$ , or $\mathbb{Q}[x]/(f)$ with the root chosen as the generator
`mult, comult, unit, counit, antipode, rmatrix`	exact sparse structure constants
`rmatrix_field`	the cyclotomic field $\mathbb{Q}(\zeta_N)$ of the coefficients of the R-matrix, when it is larger than the base field; null otherwise
`invariants`	$\dim A_{t}$ , blocks, Hopf, semisimple, (co)commutative, tags, and for new entries the Hopf invariants
`rep`	fusion or multifusion, and the AnyonWiki ring and categories when identified, with the residual
`relations`	uuids of the dual and the double when in the database
`provenance`	search, builder (with its parameters), groupoid, reconstruction (with the AnyonWiki category), or converted

One entry per algebra up to isomorphism: when a second construction yields an algebra already present, it is recorded under provenance.also of the existing entry instead of being stored again.