An instrument for gauge‑Higgs unification, and the papers it comes from
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. It runs entirely in your browser, offline, with nothing
to install — and every number it prints says what is known about it.
Read this before quoting a number from here.
Our α does not reproduce the published α of Y. Komori, N. Maru, arXiv:2503.04090, 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.
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May 2026 and withdrawn in July on finding it was a corollary of Helset–Martin–Trott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
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.
2026-08-11extensionPart IV · affects the record: no The compression to three integers holds at every root of unity, and there it is proved
- what
Part IV's alphabet, (1,−1,t,t⁻¹), is the second member of a family: the full set of
t-th roots of unity together with one free reciprocal pair. arXiv:2608.09619
evaluates s_λ(μ_t, z, z⁻¹) for every t ≥ 2 and every λ, with no hypothesis on the
shape: the value is a signed product of exactly three factors over a fixed denominator, or zero, and
the three arguments are read off the t-quotient of λ. At t = 2 the alphabet is Part
IV's.
- why
Part IV grades its closed form an Observation: checked against the bialternant in exact
arithmetic on 3060 and 4845 partitions with no mismatch, and not proved. The general
statement carries a proof — a Laplace expansion along the t frozen rows of the bialternant
with one cancellation lemma in the symmetric group, which also delivers the sign.
- so
No number in Part IV moves and its record does not need a new version. What moves is a status word:
at t = 2 the closed form stops being an Observation.
- check
- the paper, and
theorem_full.py in its scripts repository: 959 exact values, 476 zeros, 0 sign failures, 0 magnitude failures
2026-08-08extensionPart V · affects the record: no The η closed form, checked on 119 contents instead of five
- what
The closed form for the η-dependence of the Higgs mass matrix — ΔH₁₁ = −2(2π)²L₁·M₂/8,
ΔH₂₂ = −2(2π)²L₂·M₂/8, ΔH₁₂ = 0 — was published against five worked cases. The instrument
runs it against the direct winding sum on all 119 multiplets of the catalogue: worst
disagreement 0.0162 %. On the 16 multiplets the catalogue declares blind, the closed form
predicts exactly zero and the winding sum measures exactly zero.
- why
Five cases cannot distinguish "the formula is right" from "the formula is right on the cases it
was built on". 119 can, and the blind ones are the sharpest of the 119 because a prediction of
exactly zero has nowhere to hide.
- so
The record is unaffected — no number in Parts IV or V moves. What changes is the strength of the
evidence behind one of them.
A trap paid for here, and it is the reason the blind cases are stated separately: 16 multiplets
have no Part IV box, and the first sweep silently printed M₂ = 0 for them and concluded
"invisible to η". That was the right answer for the wrong reason — those 16 happen to be exactly
the 16 the catalogue declares blind. On another group the same code would have lied. A missing
datum is now an explicit unknown, never a zero.
- check
- open the eta-meter; the sweep runs in your browser against the winding sum
The whole log →
The code
The instrument is one self-contained HTML file with no external request in it, 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. Each released paper also gets a frozen copy of the tool as it
stood at publication — see editions — so a link in a
paper keeps working even after the living instrument has been rewritten.