GHU Lab

Documentation

Everything a stranger needs to read a number off this site and know exactly what it means: the conventions, the vocabulary, how to reproduce it without the tool, and how to cite it.

Conventions

Every default the instrument fills in for you, with the source that fixes it. This table is generated from src/kernel/model.mjs, which is the only place in the code where a default may be declared — an unsourced default is a hidden hypothesis, so the record refuses to hold one. Whatever the tool fills in is also echoed into the exported result card, under applied, so a reader of the card can see which numbers you chose and which the tool did.

keydefaultunitswhat fixes it
conventions.m_W80.4GeVPDG, as used by arXiv:2503.04090
conventions.g40.63—the Standard-Model su(2)_L value
conventions.mh_window[125.0, 127.0]GeVarXiv:2503.04090, Table 1
conventions.windings600—truncation of the Li_5 sum; see /docs

Two conventions are not defaults but structure, and they matter more than any of the above.

The models the instrument holds

A group is data, not code. The kernel knows about weight lattices, parities and winding sums; it does not know what SU(7) is. Adding a group means adding a JSON document.

idgrouporbifoldfromopens on
su4_ahmnSU(4)T2/Z2Parts III-V of the series; the model is AHMN, arXiv:2312.08608AHMN 2312.08608
su7_km25SU(7)S1/Z2 x S1/Z2Y. Komori, N. Maru, arXiv:2503.04090published row (2)

Each group opens on a named anchor in its own data file, because an instrument must not open empty — and because a default is a claim about typicality, each anchor carries, in the data file itself, a sentence saying what kind of case it is.

Glossary

α
The Wilson-line phase: the vacuum expectation value of the extra-dimensional gauge field, in units where a period is 1. It is the electroweak hierarchy, because 1/R₅ = 2m_W/α.
α_min
Where the one-loop potential is minimised. In this class of models it is an algebraic function of two moments of the bulk content, so it is computed rather than searched for.
bulk content
The list of representations living in the extra dimensions, each with its orbifold parities and a multiplicity. It is the input to everything on this site.
D, A₄
The second and fourth moments of the content, weighted by Wilson-line charge. 8D is always an odd integer, so the curvature at the symmetric point can never vanish and the electroweak verdict is always well defined.
parities
The signs a multiplet picks up at the orbifold fixed points, written (+,+), (+,−) and so on. They decide which components survive with a massless mode.
η (eta)
The boundary-condition sign η = η₀η₁. Part V shows it rides on an index alone, so it is invisible to the Higgs potential exactly on Part IV's vanishing class.
the anchor
A published computation the instrument recomputes at load and shows as a chip, so the tool declares whether it currently reproduces an outside number before it shows you any of its own.
the bill in eighths
The cost of an escape from the proton-decay obstruction, measured in the quantum of D. It is a ratio of integers, so no normalisation enters it.
the ceiling
An upper bound on 1/R₅ that holds for arbitrary bulk content, obtained as an integer program whose relaxation has a two-variable dual, enumerated exactly in rationals.

How to reproduce any of it without this tool

Nothing here needs the page. Each section's mathematics exists twice: once in the kernel the browser runs, and once in a Python or Sage script shipped with the paper it comes from, written independently. Where the two are compared, that is what the verified chip means.

  1. The papers' own scripts. Every released paper carries an ancillary archive on Zenodo with the scripts that produce its numbers, and they run without this repository.
  2. The instrument, offline. Save the app to disk and open it. It is one file with no external request in it; the build refuses to ship one that has any — no fetch, no dynamic import, no new Worker, no <script src>, no http(s) asset.
  3. The harnesses. python build/build_app.py rebuilds the page and then re-runs every check outside it, in node, against numbers produced elsewhere. A red build is not publishable, and the build says so rather than warning.

How to cite

Cite the paper, not the page. The papers have DOIs and are immutable; this site is living and says so on every paper page. If you need to cite the state of the tool as you used it, cite the frozen edition archived with the paper, which is byte-identical to the copy on Zenodo.