🧪 A research laboratory for gauge‑Higgs unification

Pick a model of extra‑dimensional matter and this page computes what it predicts: which Wilson‑line domain is legal, where the vacuum sits, the Higgs mass, the anomaly bill, and how high the compactification scale can go. Its interactive calculations and reference examples run offline in your browser. Optional PhaseTracer and HiggsTools calculations use a local scientific engine — and every result states its assumptions.

I read the paper and want to try it → The instrument. Thirty menu sections, three Simulator model modes and ten embedded experiment cards, with integrated diagnostics and experimental comparisons. I found the tool and want to know what it is → The series. Nine parts on gauge‑Higgs unification in ten records, each with its record, its status, and what has moved since.

Read this before quoting a number from here. Our α does not reproduce the published α of N. Haba, T. Yamashita, JHEP 02 (2004) 059 (hep-ph/0401185), eq. (3.20), and the disagreement is not a constant — so it is not a convention that could be absorbed. Every absolute scale on this site (TeV, GeV) inherits that open question and is not citable until it closes. What escapes it entirely, because no normalisation enters them: the mass ratio, the bill in eighths, and the two arithmetic laws. The instrument states this in its own header and carries a permanent “what this cannot tell you” panel; the reasoning is in the log.

Learn each tool · Aprende a utilizar cada opción

Find a task in the English user guide or guía en castellano. Start with an example, understand the controls and read the limits of each result. The searchable index includes the menu, Simulator modes and embedded experiments, with a glossary and downloadable manuals.

🎬 Learn the laboratory on screen · Aprende con el vídeo

Watch actual controls and results in a chaptered Full HD walkthrough, with narrated versions, subtitles and transcripts in English and español. Find a module, watch its example and open that section of the instrument. The guide covers the full menu, all Simulator modes and the embedded research experiments: 47 chapters and 178 scenes per language, recaptured on 17 October. The 46-chapter mathematical companion explains formulas, data and the scope of certificates.

For a complete worked task, open Hypothesis comparison: choose recalibrated cases, expand the potential, read a measured CMS spectrum and its correlations, inspect the evidence and save your selection. Guía en castellano · Data files, units and reproduction.

🧭 The laboratory at a glance

The menu count describes navigation. Model modes, experiment cards and diagnostic tools live inside those sections; the laboratory also supplies reproducible command-line studies.

Area	Available work
🏗️ Models and structure	SU(7), SU(4), general 5D SU(N), spectra, anomalies, brane matter, inverse design, census and boundary-condition classification.
🔮 Simulator	Builder predictions, top-KK Higgs production and the neutrino ring, including CMS HNL comparisons, lifetime, flight and coherence.
🧪 Experiments	Flat and warped SU(6), three active flavours, fixed-light-input neutrino paths, RS anomaly flow, thermal SU(3), integrated transition history and HiggsTools.
📊 Diagnostics	Robustness, computed Majoron channels, conditional rung bounds, full-potential witnesses and gravity–gauge 3D responses.
🔬 Batch research	Higgs coupling/width scans, thermal assumptions, candidate vacuum screening and 738 neutrino scan points, with archived JSON, commands and figures.

📋 Complete inventory, first experiments and sources of the counts →

🔬 Choose a research question

Change a parameter, compare with a saved reference, read the key indicators and export the figures together with a research summary. New experiments sit inside the existing sections.

Quick start, interpretation and local scientific engine →

The October 7 update adds integrated nucleation, percolation and completion to the thermal benchmark, with a conditional acoustic spectrum and explicit wall assumptions. Reproducible studies compare Higgs coupling/width degeneracy, 160 thermal scenarios and 80 selected full-potential vacua. Results, figures and limits of the searches →

Certification and video update · 8 October 2026. The English certification dossier separates formal algebra, interval proofs, numerical cross-checks and unresolved physical assumptions. The updated bilingual guide demonstrates these diagnostics in 139 scenes, including uncertainty, named ATLAS/CMS references and matched thermal solvers. See Changes and Editions for the current release and preserved tutorials.

Formula consistency correction · 8 October 2026. SU(N) vacuum depths now use the same V/C normalization as the potential. The surviving symmetry is computed at the located vacuum, including boundary points. Conditional comb bounds share one applicability check across the plot, table and download. Simulator exports record the actual coupling, probe status and analytic Fourier Hessian. The SU(7) literature anchor remains open: interval checks bound the disagreement for the implemented potential. Evidence and source links. The revised bilingual video includes these corrections and links the original 7 October guide as a historical version.

🧬 Same light inputs, different neutrino responses

In Simulator → Neutrino ring, open Fixed light inputs. Five descriptive figures compare heavy centres, pair splitting, raw and normalized vacuum current factors, a magnified difference and the archived IceCube DeepCore 2018 map. Compare the common and unequal deficit presets; save the complete inputs and SVG figures.

Method, first experiments and data provenance →. The light inputs are reconstructed. The standard-three-neutrino map is not a ring likelihood and is not combined with NuFIT.

🌌 Explore gravity and gauge fields in 3D

Open Gravity–gauge · 3D → Change the kinetic deformation and the source position while two interactive plots and a table update together. The paired mass tower stays fixed; the source response and Wilson-line kinetic scale change. Rotate either plot, or select a point on the response surface to change the inputs.

This research diagnostic compares a specified family of actions and boundary conditions. It does not predict a detected graviton, a Higgs mass or a collider rate. Controls, interpretation and limitations →

🧾 Every number carries what is known about it

Four words, and they are fields in the exported result card rather than decoration. This is the whole difference between an instrument and a demonstration.

word	what it promises
theorem	Proved, in a paper of the series, and the page names which one.
verified	Checked against an independent computation — usually brute force over the same object — but not proved.
measured	Computed here, and inheriting whatever open questions its inputs carry. Every absolute scale on this site is of this kind.
unknown	Said out loud, with the reason, instead of a plausible number. The tool refuses to fill a gap it cannot compute.

The fourth is the one that costs something, so it is worth saying why it is there. This project has retracted one of its own novelty claims before — a closed‑form identity published in May 2026 and withdrawn in July on finding it was a corollary of Helset–Martin–Trott 2020. The algebra was right; the claim about its standing was not. A tool that could not label its own output unknown would have no way to do that to itself.

📚 The series

part	paper	record
I	Anomaly- and Tadpole-Compatible Fermion Completion of Six-Dimensional SU(4) Gauge-Higgs Unification 10.5281/zenodo.21432625	published 0 changes
II	Three Gates to a Quark Generation: An Exact Criterion for Which SU(4) Representations Contain the Standard Model 10.5281/zenodo.21432627	published 0 changes
III	A Centre-Charge Selection Rule for the Wilson-Line Potential: The Fundamental Domain of Gauge-Higgs Unification Is Representation-Dependent 10.5281/zenodo.21438226	published 2 changes
IV	Schur Functions at (1,-1,t,t^{-1}): A Closed Form on the Non-Identity Component of O(4) 10.5281/zenodo.21463000	published 1 change
V	What the Higgs Potential Cannot See: Bulk Matter That Cannot Help Select a Boundary Condition 10.5281/zenodo.21727094	published 1 change
VI	Proton Decay in SU(7) Grand Gauge-Higgs Unification: An Obstruction, Its Minimal Escapes, and the One Row of Their Table 1 That Can Pay for Them 10.5281/zenodo.22033302	published 2 changes
VII	An Upper Bound on the Compactification Scale of SU(7) Grand Gauge-Higgs Unification, and the Dijet Angular Distribution That Tests It 10.5281/zenodo.22087251	published 3 changes
VIII	A Certified 2.68 TeV Gap in the Closed-Form Map of the Compactification Scale in SU(7) Grand Gauge-Higgs Unification, and the Invariant Its Two Observables Cannot See 10.5281/zenodo.22159036	published 1 change
IX-A	The Alphabet of Orbifold Boundary Conditions: a boundary condition is a representation, and the alphabet is forced by the fixed-point counts (Part IX-A) 10.5281/zenodo.22254861	published 0 changes
IX-B	An Affine Semigroup from Orbifold Boundary Conditions: cut, phylogenetic and hierarchical models in the unit-weight sector, and weighted configurations beyond them (Part IX-B) 10.5281/zenodo.22254863	published 0 changes

📝 What has moved

The papers are frozen; this site is not. Every change is logged with what moved, why, and whether it affects the version of record.

2026-10-28extensionthe instrument · affects the record: no

Continuous neutral isolation with proof, bilingual Demo and narrated supplement

what

Boundary research now includes section 6b: positivity and isolation of the light vector in a declared five-component GHU block. Three exact Wilson-angle queries (1/10, 1/5, 1/4) share fixed unit-square geometry and wall coefficients, with no added boundary kinetic term. A separate selector prevents accidental mixing with the fermion landscape or finite scalar stratum.

Results include rational mass enclosures, a lower bound on the next active eigenvalue and a positive separation. A self-contained written proof connects the exact matrices and trial to the continuous operator through min-max and Temple's existing inequality. The downloadable ZIP contains this proof, data, verifier and receipt. The engine is maintained externally; the lab presents certified queries. No mathematical novelty or new Lean formalization claimed.

why

The continuous proof justifies spectral bounds including natural boundary conditions; finite-matrix residuals alone would not suffice. The separate selector protects the certified scope from unrelated parameters.

so

The certificate does not bound SZ or RZW, select a vacuum, establish currents or identify the physical Higgs. No mass in GeV or experimental exclusion follows. Three decoupled zero directions are retained separately from the active ordering.

English/Spanish help, PDF manuals and live-demo steps describe the new instrument. A bilingual narrated supplement adds six chapters with real captures, captions, transcripts and proof links. The main films retain their previous dates and scope. This change does not add a menu section, card or simulator mode. Publication is a separate operation.

check

Run python _test_z_isolation.py, node _test_z_isolation.mjs, node build/boundary_research.mjs and the app/site builds. Replay python proof/z-isolation/verify.py proof/z-isolation/certificate.json --self-test.

2026-10-26extensionthe instrument · affects the record: no

Exact finite neutral quotient, corrected bilingual Demo and current manuals

what: Boundary research gains a sixth instrument for the finite complex C^5 → C^7 → C^2. The exact generic/restored stratum selects quotient dimension 0 or 1 independently of the numerical Wilson slider. Its downloadable package contains the matrices, rank and kernel witnesses, written proof and exact SymPy verifier. The live bilingual Demo now visits all six instruments; guides, both PDF manuals and the certificate catalogue are synchronized.
why: The finite algebraic question has an explicit checkable answer, while its continuous and physical interpretation remains open. The older four-instrument Demo was overriding the shared storyboard, hiding later additions; removing that duplicate restores the complete route in both languages.
so: This certificate establishes the stated finite quotient and distinguishes it from the gauge stabilizer. It does not certify the continuous-domain reduction, a Wilson–Higgs direction, a physical mass or mathematical novelty. No new Lean formalization is claimed. Both films retain their 17 October recordings and do not cover section 6; the players link to the updated live Demo. The current 181-scene storyboard is preparation for a future recording. Existing frozen papers and media retain their scopes.
check: Run python _test_neutral_certificate.py, node _test_boundary_research.mjs, node build/boundary_research.mjs and the app/site builds. Replay python proof/neutral-complex/verify.py proof/neutral-complex/certificate.json.

The whole log →

🔧 The code

The instrument is one self-contained HTML file with no automatic external requests, built from a Python and JavaScript source tree by build/build_app.py, which re-runs every harness and refuses to publish a red build. It is a living instrument and it is rewritten often; what travels with a paper is not this tool but its evidence — the gate scripts and their archived receipts, from which every number in that paper regenerates without this site. What we do keep alive is every URL a published record points at — see editions — and the log of what has moved since.