6.0.0 — Research workbench IV

Application: 6.0.0 · Dataset: 2026.11-workbench.4 · Core schema: 2.0.0

Release algorithm umbrella: groups-workbench-4.0.0

Edition date: 2026-11-08, America/Los_Angeles

Research workbench IV extends the field-aware milestone from one chosen monomial to all supported monomials in a selected canonical-dimension interval. The new operator enumerator reports the exact complex dimension of each nonzero invariant space and organizes the result by dimension.

The operator enumerator

The new tool accepts the same bounded four-dimensional Lorentzian scalar/Weyl field domain as the local-operator workbench. A field declares its color and weak representations, integer U(1) charge, and ungauged flavor multiplicity. Every field must descend to the specified global gauge quotient. An obstructed inventory has no count; its exported totals are null.

Choose minimum and maximum dimensions from one through six. The optional identity is a dimension-zero term considered separately. It contributes only when the selected additional charge targets permit it.

For each occupation vector $\mathbf n$, the engine calculates

$$c_{\mathbf n}= \dim_{\mathbb C}\operatorname{Inv}\!\left[ \bigotimes_{i\,\mathrm{bosonic}}\operatorname{Sym}^{n_i}V_i \otimes \bigotimes_{j\,\mathrm{fermionic}}\Lambda^{n_j}V_j \right],$$

where $V_i$ includes the complete Lorentz, gauge, and flavor component space. The occupation census and the invariant projection are separate steps: several independent invariants may share the same field monomial. The result therefore distinguishes sector count from invariant count.

The mathematical method is explained in the enumeration reference and follows the derivative-free character construction in Marinissen, Rahn, and Waalewijn, §II A. A selected row opens the detailed monomial workbench with its full inventory and field powers.

Selection rules and exact completion

Up to three extra U(1) or cyclic selections can be supplied. Each field has one integer charge under each rule. A U(1) rule fixes the total charge; a cyclic rule fixes its residue modulo $2\leq n\leq12$. Charges and targets are bounded by $-24$ and $24$. Zero targets impose polynomial invariance; nonzero targets isolate charged sectors. These rules do not by themselves establish an anomaly-free quantum symmetry.

The enumerator retains the existing representation and flavor bounds. Its additional limits are 100,000 visited multidegrees, 4,096 candidates for exact projection, 100,000,000 aggregate coefficient multiplication pairs, and 4,096 output rows. Each monomial also retains its own character-space and arithmetic guards. Reaching a bound produces an explicit error, with no partial enumeration presented as complete.

Six worked inventories

Inventory	Nonzero monomial sectors	Independent complex invariants through dimension six
Standard Model, one generation	46	55
Standard Model, three generations	46	2,874
Standard Model, three generations, conserve B and L	36	2,316
One Higgs doublet and its conjugate	3	3
Three sterile Weyl flavors and their conjugates	5	60
One scalar with a zero-charge Z₂ selection	3	3

The identity is excluded in these presets. For the Standard Model examples, distinct Hermitian-conjugate monomials are counted separately. Their counts by dimension are:

Field inventory	$d=2$	$d=4$	$d=5$	$d=6$
One generation	1	7	2	45
Three generations	1	55	12	2,806
Three generations, conserve B and L	1	55	0	2,260

The Standard Model guide derives these decompositions using published flavor counts, including Alonso and collaborators’ baryon-preserving counts and their baryon-violating sector counts. These totals describe derivative-free scalar/Weyl polynomials. Field strengths, derivatives, and EFT equivalences are not included.

Reproducible inventories and calculations

The new groups.qft.org/operator-enumeration/1 format records an inventory and its enumeration options. The separate groups.qft.org/operator-enumeration-calculation/1 envelope adds the result, sources, convention, and algorithm versions. Loading validates the input and recomputes; stored answers are ignored. Changed or missing algorithm versions are reported. Existing physical setups can be imported as field inventories, explicitly discarding their fixed monomial powers.

The new algorithm is operator-enumeration-1.0.0. It reuses local-operators-1.0.0, product-gauge-1.0.0, and convention four-d-local-polynomial-v1. The catalogue schema and prior calculation formats remain distinct.

Scientific pages and edition inventory

Three new pages explain the workflow and its interpretation:

• From fields to interactions.
• Exact operator enumeration.
• Standard Model operator sectors.

KaTeX renders their mathematics and the calculated output. The edition has 266 mathematical records, 2,998 claims, 114 source records, fifteen tools, and ten convention profiles. The six new inventories supplement the eleven fixed-monomial physical setups. They do not create new group records.

Verification and publication policy

The enumeration suite checks the published presets, an independent mixed-radix census without the engine’s pruning rules, closed-form scalar Hilbert-series coefficients, dimension partitions, charge selections, conjugation, global descent, resource errors, strict schemas, and replay of altered cached results. Integration and build checks validate the completed application state; the release report records the actual executed results.

At this historical release, the private GitHub source repository was prepared for GitHub Pages. The subsequent Mac development handoff supersedes that hosting policy: Cloudflare Pages is the selected host, and the site remains in local development until its first-launch scope is finished. See the current roadmap. The formal accessibility assessment remains deferred. Independent human review is recorded separately. Articles use CC BY 4.0; code uses MIT.

The next operator milestone is explicit derivatives and field strengths, followed by equations-of-motion and integration-by-parts reduction before claiming an EFT basis. Normalized contractions, broader groups, additional gauge factors, and specialist research workflows remain in the roadmap.