GHU Lab

📖 Laboratory 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.

Where physics meets mathematics

Follow boundary conditions into a spectral problem, profiles into Gram matrices, weights into exact traces and a restricted consistency condition into modular arithmetic. The animated film has 46 chapters with translated whiteboards, visible captions and real laboratory demonstrations: English · 22:07 · Castellano · 22:21.

Shared mathematical notes (English) · 113 reproducible checks · Usage, versions and reproduction. These scoped calculations do not establish a complete physical model. The general laboratory tutorial remains a separate guide to 47 chapters and 178 scenes per language. The new physics and mathematics analysis connects the quantization module, 59 Lean declarations in five files, published ATLAS/CMS upper limits, recalibrated GHU potentials and the measured CMS top-pair spectrum. Each quantity retains its units and scientific scope.

User guides · Guías de uso

Start with the searchable English guide or guía en castellano. Forty-six guides cover 30 menu sections, three Simulator modes, eleven embedded experiments, neutrino decays and getting started. These are overlapping navigation levels, not a new count of independent panels.

Each guide explains inputs, outputs, an example, limitations, troubleshooting and sources. The application’s short help and glossary share the same maintained catalogues. Language changes retain the guide; opening help preserves the working calculation. Download the English manual or manual en castellano. The Spanish PDF is composed with Babel; the translation is maintained in the guide data.

Hypotheses: compare, interpret and reproduce

In Same potential? → Hypotheses, compare nine recalibrated GHU cases and inspect the measured CMS top-pair spectrum in a separate context. Four plots show parameter choices, potential differences, measured bins and experimental correlations. Every selection has a contextual reading. The shared Demo and video follow the same controls, then invite you to repeat the comparison.

English guide · Guía en castellano · Practical video chapter · Data structure and reproduction · Equations and certificate scope.

Export figures as SVG, measured bins as CSV, or selection, results, covariance and provenance as JSON. Reimporting the JSON restores a validated selection. A different dataset needs an audited adapter. Ten rational Lean identities, an exact check of the published covariance and three pointwise derivative bounds support specific claims. A compatible GHU prediction, an observed fit and a rigorous full-integral error bound remain pending.

Boundary research: four separate diagnostics

The new English guide and guía en castellano explain the flat boundary spectrum, linked 2D/3D mass views, profile Gram rank, exact parity-inserted traces and restricted six-dimensional family condition. Change numerical values or select points in the plots. Each diagnostic states its assumptions; full anomaly cancellation remains open.

Certificates and their scope

The English SU(7) certification dossier records formal theorems, interval proofs, formula attribution and unresolved physical assumptions. It includes full-potential and moment comparisons, a separated uncertainty budget and named ATLAS/CMS references, with downloadable evidence and reproduction steps.

The thermal card in Simulator compares pinned CosmoTransitions and PhaseTracer results for the same potential and conventions, with tolerance and Fourier-cutoff studies. The thermal comparison record documents their shared shooting-method ancestry. Numerical agreement does not certify a physical model; the mass-reference comparisons and archived dijet tables do not constitute a combined likelihood or a GHU exclusion.

🎬 Watch the controls and results

Guided demos inside the laboratory. Every menu section, Simulator mode and experiment card has a 🎬 Demo button (in How to use this section or in the card heading): it presses the real controls, explains each step in a banner with Next ▶ and ✕, and ends with how to read the result. Each demo is written for its panel and quotes the numbers the page shows at that moment. Try Same potential? or the first KK gluon; add &lang=es for Spanish.

The English video guide and guía en vídeo en español demonstrate every menu section, all Simulator modes and the research experiments. Search the chapters, turn on subtitles with the visible CC · Subtitles button, read the transcript or download the complete video. The subtitle choice is retained when seeking or switching language. Each example explains what changes and how to interpret the output.

The 17 October revision contains 47 chapters and 178 narrated scenes per language, including hypotheses, measurements and certificates, quantization and certificates, boundary research with linked 2D/3D views and the first KK gluon against ATLAS and CMS data. Go directly to approximation errors, uncertainty and Higgs-mass references, equal local moments and different potentials, formal and interval certificates, the CMS dataset scope, or matched thermal solvers and evidence withdrawal after an input change. Narration and captions are available in English and Spanish. All 47 chapters were captured again from the current laboratory, separately in each language. Follow the explanation, then open the matching tool to repeat the example.

For the release history, see Changes. Editions and video archives distinguishes the current instrument, versioned tutorials and the frozen artifacts linked by published papers.

🧭 Navigation, models and integrated tools

The menu is an entry map. Simulator contains builder predictions, the top-KK Higgs-production reference and the neutrino ring. Dedicated experiment cards add flat/warped SU(6), three flavours, fixed-light-input neutrino paths, thermal potential and history, RS anomalies, HiggsTools and the first KK gluon against ATLAS/CMS data (resonance limits and the m(tt̄) spectrum with interference). Robustness, CMS HNL overlays, decays with optional computed Majoron channels, and conditional rung/vacuum checks extend existing views. The archived batch studies supply further scans through command-line tools.

📋 Complete capability map · 🔎 Source-checked inventory.

🧬 Three-flavour inputs and vacuum oscillations explains the implemented curves, first comparisons and the scope of its unitary-limit curves. The new fixed-light-input guide covers nonunitary vacuum current factors and the archived DeepCore 2018 reference.

🧪 Research experiments: compare, understand, export

Use the experiment shortcuts in Paper models (SU(6)), Brane kinetic terms (RS running), Simulator (neutrino flavour, Majoron decays and thermal GHU), Anomalies & proton (RS anomalies), and Collider (Higgs rates and experimental tests). Each experiment states its question, key indicators and interpretation before the detailed numerical tables.

  1. Load a reference and press Use this point as comparison.
  2. Change one physical parameter. Compare the indicators and the saved-reference curve.
  3. Expand numerical details when you need the matrices, convergence or rate tables.
  4. Save a research summary, the complete JSON, or any figure as SVG.

New PhaseTracer and HiggsTools runs use the optional local scientific engine. Frozen benchmark results work offline and are used only for identical inputs. A changed input clears an unmatched experimental verdict. Setup, equations, versions and limitations.

Screen 3 and the candidate seed: the even-rung arithmetic comb is displayed, with a separate table of interval certificates for the small-angle moment relaxation. They apply only to the displayed seed, coupling and mass window. Independent full-Fourier witness checks can reject a stationary candidate when a deeper vacuum exists. A matching tooth is not a certificate that a viable model exists, and the moment bound is not a universal full-potential ceiling.

🔬 Neutrino identifiability: five linked figures

Choose Simulator → Neutrino ring → Fixed light inputs. Move the sweep position, then compare the common-suppression and unequal-deficit presets. Read heavy centre and splitting separately; the fourth graph magnifies the normalized-factor difference. Captions, units and fixed-input labels explain the response. Change sin² θ₂₃ in Three active flavours to move the cross on the DeepCore map.

DeepCore 2018 supplies the original archived standard-three-neutrino grids and contour. No ring exclusion, ordering odds, extrapolation or addition to NuFIT is performed. The fourth batch study records 738 points, source/data hashes and standalone figures. Save each SVG and the full JSON to keep provenance and shared inputs.

🫧 Integrated transition history and reproducible studies

In Simulator → SU(N) builder, load a thermal paper case and open Integrated nucleation, percolation and conditional gravitational waves. Read nucleation, percolation and completion separately. Vary wall speed, fluid efficiency and the expansion background; inspect convergence, then export JSON or SVG. The acoustic estimate is available only for a completing transition in the supported weak, fast-wall regime. Wall friction, plasma evolution and detector significance are not computed.

The October 7 exploration report archives three separate studies: actual HiggsBounds/HiggsSignals evaluations with coupling and invisible-width assumptions, 160 thermal scenarios, and 80 selected full-potential vacuum checks. It includes commands, machine-readable records, figures and search budgets. These calculations do not form a common-action GHU likelihood. The report also identifies useful next extensions.

🌌 Gravity–gauge · 3D: a quick start

Open the panel, or choose Gravity & gauge · research → Gravity–gauge · 3D in the app menu. Its inputs belong to this panel and travel with its exported files and link.

  1. Start at p = 1.1. Compare the presets η = −0.9 and η = 0. The paired masses stay fixed, while the response and Wilson kinetic scale change.
  2. Move η (the kinetic deformation) and t (the source position). The table and both plots update immediately. The controls cover −0.99 ≤ η ≤ 4 and 0.12 ≤ t ≤ 0.98. Here η is a continuous parameter, separate from the boundary-condition sign used in the other panels.
  3. Choose the spectral-weight ratio or the kinetic function Z for the response surface. Its height is logarithmic. Drag to rotate; in select point mode, click the surface to set η and t. Shift-drag rotates in either mode.
  4. Focus a plot and use the arrow keys to turn it, the mouse wheel to adjust its relief, or double-click to reset the view. Reset restores the model and both views.
  5. Use the header's card, LaTeX and link buttons to save the current inputs, outputs and scope. Open the panel's how-to for help in place.

Read the comparison carefully. NN means a vanishing normal derivative at both ends; DD means a vanishing field at both ends. The tensor-NN and vector-DD massive towers are paired under the stated action and boundaries. The vector-NN control has different boundaries and its massive levels can move. The tensor zero mode has no vector-DD partner.

The first three paired masses are dimensionless Python/SciPy reference roots checked by an independent differential-equation calculation. The first massive vector-NN root is solved in the browser. The source response holds the four-dimensional gauge coupling fixed. The Wilson scale is a kinetic normalization; it is not a Higgs mass.

Scope. p = 1.1 admits the stated scalar-supported bulk background; p = 1 is a kinematic reference, with η = −0.99 recovering the minimal AdS gauge case. Boundary dynamics, scalar/radion stability, a complete Higgs potential and collider rates remain open. This is not experimental evidence for a graviton or a completed unified model.

Full guide, equations, numerical provenance and literature. The source tree includes 104 numerical checks and a dedicated Chromium check of the panel's controls, exports and mobile layout.

The result card — what the two download buttons give you

Every panel has ⇩ card and ⇩ LaTeX in its header. The card is the only thing that leaves the tool, and it is deliberately more than a number: it carries the input you gave and the defaults the tool applied on your behalf, every value with its status, the certificates a referee needs to re-check a bound without this tool, and a provenance line.

The status column is the part worth learning. theorem is proved and names the statement; verified was checked against an independent implementation; measured is true of what was run and no more; and unknown is not computed, with the reason printed beside it. An unknown is a verdict, not a gap — a tool that returned a plausible number there would be worse than one that refuses, because you would have no way to tell.

The provenance line ends in a kernel fingerprint, a digest of the code that produced the numbers. It is the field to look at when two cards disagree: same input and same fingerprint with different numbers is a bug worth reporting, while a different fingerprint means the engine moved between the two runs and the change log says what moved. Without it those two situations look identical. Since September 2026 the tool refuses to build a card that cannot name its kernel.

Full guide, with a real export read block by block.

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
conventions.gauge_seed"published"—the gauge coefficients as printed in arXiv:2503.04090 eq. (68); Part VII section 13 carries a candidate split, and the page can stand on it instead

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
su3_hySU(3) 5DS1/Z2N. Haba, T. Yamashita, JHEP 02 (2004) 059 (hep-ph/0401185), eq. (3.20)the smallest content of the archived bank
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. The small-angle approximation gives a closed map from moments of the bulk content. Full-Fourier checks instead locate stationary points numerically and compare their potential values; the two procedures have different scopes.
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. On the published SU(7) seed, 8D is an odd integer. The candidate seed has an even lattice and admits zero. Read the selected seed before transferring a curvature or rung statement.
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 under named conventions and the small-angle moment map, obtained from an integer program and a certified relaxation. The new interval certificates exclude the infinite moment tail for each listed rung. They do not prove attainability or a universal ceiling for the full Fourier potential.

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.