WEBVTT

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Welcome to G H U Lab. This revised
walkthrough covers every menu section,

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the three Simulator modes and the embedded
research experiments.

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It now demonstrates the S U seven
certificates, approximation errors,
uncertainty

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budget, thermal solver comparison, named
collider references and the first

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Kaluza Klein gluon against L H C data.

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Choose a chapter to revisit a topic.

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Start with a named model or reference.

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Change one assumption at a time, and read
the result with its units and scope.

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Theorem, verified, measured and unknown
describe different kinds of evidence.

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A computed scenario value is not
automatically an experimental measurement.

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Open Hierarchy. For a bulk content of the S
U seven model, inspect the

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compactification scale and Higgs mass under
the displayed conventions.

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The ceiling belongs to the stated small-
angle moment approximation.

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Change the diagnostic gauge coupling to
zero point seven.

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The response plots separate a change of
model convention from propagation

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of the measured W input and from winding
convergence.

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Read the axes and the central values
together.

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The calculated phase does not reproduce the
printed phase.

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The mismatch varies between rows, and an
overall multiplication of the potential

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cannot move its stationary points.

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Absolute scales remain conditional on
resolving this discrepancy.

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The arithmetic identities are separate
statements.

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Load the first certified benchmark.

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The table encloses two different stationary
points: the quartic logarithmic

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approximation and the full Fourier minimum.

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Phase, Higgs mass and compactification
scale have separate absolute and relative

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error intervals. They apply to the
displayed matter content, gauge choice

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and fixed mass inputs.

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What limits the precision?

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Read approximation bias, root-location
bounds and the Fourier remainder separately

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from the propagated W-mass uncertainty.

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The ten percent coupling variation is a
chosen scenario, without an assigned

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probability. Physical theory uncertainty is
explicitly not quantified;

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there is no combined physical error bar.

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Save the error certificate.

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The download keeps the rational enclosures,
numerical budget, W input and

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attribution. The full mass enclosure
already includes root and Fourier errors;

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do not add its half-width again.

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A different matter content or mass
convention needs a matching certificate

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of its own.

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The ATLAS and C M S rows are separate
published Higgs-mass references.

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Compare the certified curvature mass with
each stated channel and error band.

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The listed difference is not an exclusion
significance.

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Connecting a one-loop curvature mass to a
measured pole mass still requires

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matching and higher-order uncertainties.

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The dataset links explain the route to a
fuller comparison.

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Channels have not been combined into a
likelihood.

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C E R N hosts the experiments and is not a
third independent measurement.

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Archive the inputs and sources beside the
result; a certified numerical calculation

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alone does not establish agreement with
nature.

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Open Design a scale. The map run backwards:
name a compactification scale

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and a Higgs-mass window, and get a bulk
content that lands there — or a named

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certificate that none exists.

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Enter a target compactification scale of
two teraelectronvolts and run the

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design. Inspect the returned content or the
named certificate.

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A search budget is a stopping condition,
not evidence that no solution exists.

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budget means the search stopped, not that
the rung is empty; the page keeps

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the two apart on purpose. The reachable-set
panel resolves each cluster into

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the finite set of points it really is.

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Open Count a rung. How many bulk contents
sit on a rung — counted, not built.

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The counting graph is generated when the
section opens.

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Click a different horizontal position to
move the moment probe and compare

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counts across the rungs. These are counts
of contents, not a list of experimentally

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viable models.

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The four published-seed totals reproduce an
independent enumeration of 69

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022 464 contents. The candidate uses even

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rungs and half-integral A₄; its counts are
computed separately, without transferring

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the published measured-mass fibre.

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Open Atlas. Every bulk content of at most
five multiplets — 1

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286 of them — with its potential drawn as
one tile.

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Draw the lattice of one thousand two
hundred and eighty-six contents.

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Each tile is a different potential.

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Inspect its colour and shape; a flat or
blank potential is itself a result.

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Clicking a tile transfers that content to
the model.

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One tile is green in the Higgs window, and
it is the published row (2).

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A blank tile is a content whose potential
is flat, and the harness predicts

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which tiles blank before they are drawn.

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Open Same potential?. Whether two bulk
contents are the same one-loop potential,

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by Part VII's Theorem 3.

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Copy the first content and construct its
canonical representative.

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Compare the potential curves and the five
coordinates.

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Different lists of matter can produce
exactly the same one-loop potential

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under the stated theorem.

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Same five coordinates ⟺ identically the
same potential.

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The dashed curve riding exactly on the
solid one is the theorem, not a
coincidence.

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Load the equal-moment example and inspect
the local range.

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These two contents have exactly the same D,
A four and G through their integer

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coordinates, while their endpoint
coordinate differs.

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Matching the small-angle expansion is a
weaker condition than matching the

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complete potential.

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Switch to the full phase interval.

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The plotted full potentials separate even
though the local expansions match.

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These curves illustrate finite Fourier
sums; the exact coordinate statement

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and the interval proof are recorded
separately.

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Use the full potential when judging a
global vacuum.

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For content B, the endpoint at alpha equal
to one has certified energy below

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its local minimum. This rules out that
local minimum as global.

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It does not prove that the endpoint itself
is global.

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Save the comparison to retain the exact
inputs and the scope of this mathematical

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example.

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Open Anomalies & proton. What each
multiplet contributes to the anomaly bill,

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in eighths, and what the proton-decay
escape costs.

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Read the signed contributions to the
anomaly bill and the rung ladder.

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A nonzero bulk bill does not, by itself,
make the theory inconsistent:

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possible brane matter must be considered
separately.

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The research card later in this section
studies a different warped model.

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A non-zero bill is not an inconsistency:
brane fermions pay into the same

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channels with the opposite sign.

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What the ladder forbids is a rung, not a
model.

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Open Escape from proton decay.

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The escape from proton decay, constructed:
type a brane content and watch

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the six channels, the assignments and the
selection rule recompute.

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Choose the scalar charge associated with
the eighty-four representation.

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The rational anomaly channels and charge
assignments update together.

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Inspect which assignments meet the
displayed proton-protection rule; the

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calculation does not supply a measured
proton lifetime.

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Every assignment that protects the proton
can also cancel all six channels —

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protection never costs an anomaly.

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That is an enumeration, not an argument.

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Open Multiplets & parities.

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The layer under the term tables: every
representation broken into multiplets

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with their three Z₂ parities.

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Select the eighty-four representation and
change its parity assignment.

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The decomposition and parity picture update
from the representation data.

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Use the table to connect a surviving zero
mode with the sign of its potential

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contribution.

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The term tables here are DERIVED and then
checked against the ones the rest

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of the page computes with.

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If the two ever disagreed, this panel is
where it would show.

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Open Screen a table. Arithmetic screens for
a published row, with conditional

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rung certificates and independent full-
potential witness checks.

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Enter a candidate resonance at four
thousand gigaelectronvolts.

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The comb samples nearby teeth for the
displayed rungs.

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Its filters, spacing table and download now
use the same conditional-bound

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check for the chosen inputs.

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A surviving tooth is not proof of an
attainable physical vacuum.

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The moment ceilings remain conditional on
the small-angle approximation.

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The five printed phase rounding intervals
contain no stationary point for

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the implemented potential.

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All eight fermion coefficient tables now
agree with an independent reconstruction.

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The physical gauge determinant and the
origin of the printed numerical mismatch

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remain open.

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Expand Certified S U seven benchmarks.

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Twenty-six Lean theorems verify finite
algebraic identities.

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Separate interval proofs certify ten global
minima on the stated one-phase

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domain: five reference contents under each
of two gauge prescriptions.

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These statements do not certify an
arbitrary edited model.

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Download the certificate bundle.

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It contains rational enclosures, continuum
partitions, checksums and reproduction

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records. The infinite Fourier analysis is
computer-assisted and has not been

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formalized in Lean. A global-minimum
certificate is conditional on its potential

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and assumptions; it is not a certificate of
physical viability.

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The English dossier assigns the model to
Komori and Maru, the expansion antecedents

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to Haba, Takenaga and Yamashita and to
Sakamoto and Takenaga, and the S U

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seven application in Part Seven to Carles
Marín.

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Verification does not establish
originality.

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The dossier keeps the remaining physical
questions explicit.

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Open Collider. Which state a dijet search
bounds, plus a separate Higgs-rate

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scenario checked against pinned
experimental datasets.

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Move the dijet mass probe to five point
two.

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Read the selected state, mass scale and
published comparison under its colour

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hypothesis. The separate Higgs experiment
below uses another explicitly supplied

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scalar scenario.

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The dijet delta chi  squared  values are
quoted from the published record;

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the Higgs experiment computes its own
comparison.

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Its 159 HiggsSignals observables are not
159 independent degrees

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of freedom. Coupling and width assumptions
can compensate in visible rates,

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so this scalar comparison is not a complete
G H U fit.

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The displayed recast table belongs to the
earlier archived calculation.

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Separately, the dossier now records the C M
S angular dataset at one hundred

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thirty-eight inverse femtobarns: seven
distributions and seventy-seven bins.

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Integrity checks validate the imported
tables.

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Importing them has not produced a new G H U
fit.

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The released correlation matrix describes
fitted signal strengths.

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It cannot automatically be used as the
covariance of the normalized unfolded

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distributions. A new reinterpretation
requires the G H U signal, selections

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and nuisance parameters, with a justified
statistical model.

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The dossier distinguishes reviewed
resources from analyses actually executed.

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Open Selection rule. Which alpha -domain a
search may legally use, and which

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S U 4 representations can hold a quark
generation.

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Select the representation with Dynkin
labels one, zero, one.

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The centre-charge and chiral-projection
results determine which search domain

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is permitted and which content can host a
generation.

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The domain is computed from the
representation, not chosen for convenience.

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The centre-charge gate is classical and is
credited as such.

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What is ours is the chiral projection that
gives the closed count.

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Open Model calculator. A matter content in,
the Higgs out — the AHMN

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model recomputed in front of you.

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Load the named A H M N reference model.

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Its terms, potential and derived quantities
are recalculated by the browser.

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Start with this anchored content before
changing multiplicities or boundary

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signs, and retain the stated normalization
caveat for absolute scales.

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The mass ratio carries no normalisation and
no caveat.

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Absolute scales do.

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Open eta-meter. What the boundary sign eta
does to a multiplet's contribution —

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in closed form, from one integer.

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Load the supplied example made from a blind
multiplet, then flip every eta

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sign. In this example the potential is
insensitive to that change.

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The eta-difference view exposes the
cancellation; it is not evidence that

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boundary signs never matter.

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In difference mode every blind multiplet
goes blank.

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That is Part V's theorem seen without
reading a number.

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Open Five dimensions. Haba–Yamashita's own
5D S U 3 model,

00:13:24.905 --> 00:13:27.300
with the vacuum their paper leaves undone.

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Compare the pure-gauge case with the
supplied marginal trio.

00:13:31.917 --> 00:13:34.382
Read the potential and vacuum together.

00:13:34.382 --> 00:13:38.287
This panel uses the five-dimensional S U
three reference, so its arithmetic

00:13:38.287 --> 00:13:42.532
and assumptions must not be borrowed from
the six-dimensional S U seven benchmark.

00:13:43.868 --> 00:13:47.558
Pure gauge never breaks the symmetry (D =
−9).

00:13:47.558 --> 00:13:51.953
In this whole 5D class 8D is even: the odd
rung the S U 7 ceiling stands

00:13:51.953 --> 00:13:53.898
on needs the sixth dimension.

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Open the S U N builder. Boundary conditions
and supported bulk representations

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define the implemented one-loop Wilson-line
potential in five dimensions.

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The model is the input.

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Load section four point three of the source
paper.

00:14:11.818 --> 00:14:15.053
This pure-gauge example prefers the
endpoint at one.

00:14:15.053 --> 00:14:18.733
Read the surviving group from the joint
commutant: being at an endpoint does

00:14:18.733 --> 00:14:21.608
not prove that the generators at zero
survive.

00:14:21.608 --> 00:14:26.048
The potential plot and the reported minimum
now use the same V over C normalization.

00:14:27.335 --> 00:14:31.155
The four worked examples are checked
against the implemented formulas.

00:14:31.155 --> 00:14:35.765
With one Wilson phase, the cosine terms
admit the same moment construction.

00:14:35.765 --> 00:14:39.520
Its closed stationary branch is a small-
angle approximation.

00:14:39.520 --> 00:14:43.150
The numerical Fourier minimum is a separate
calculation, and a finite grid

00:14:43.150 --> 00:14:45.530
is not a certificate of the global minimum.

00:14:48.668 --> 00:14:53.198
Open Paper models. Four models somebody
else published, taken off their

00:14:53.198 --> 00:14:55.768
pages and run through this instrument's
engine.

00:14:57.068 --> 00:15:01.208
Change the triplet Dirac-fermion count to
five in the supported reference.

00:15:01.208 --> 00:15:05.728
Inspect which outputs are actually computed
and which remain structural statements.

00:15:05.728 --> 00:15:09.388
Where offered, the load button transfers
the supported content into the general

00:15:09.388 --> 00:15:10.333
builder.

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Three of the four are supersymmetric and
this engine's potential is not,

00:15:15.053 --> 00:15:18.813
so their rows are boundary-condition and
zero-mode statements only.

00:15:18.813 --> 00:15:22.918
An amber row disagrees with one printed
equation, not with a paper, and names

00:15:22.918 --> 00:15:25.733
which of that paper's own equations agrees
with which.

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Open 4D spectrum. What the model on the
builder CONTAINS: the four-dimensional

00:15:33.513 --> 00:15:35.878
fields and their Kaluza–Klein towers.

00:15:37.202 --> 00:15:40.742
Load the S U six example and move the
Wilson-line probe.

00:15:40.742 --> 00:15:44.132
Compare the potential families with the
exact low-lying tower.

00:15:44.132 --> 00:15:47.022
The lowest levels can require a different
reading from the families used

00:15:47.022 --> 00:15:48.767
to construct the potential.

00:15:50.068 --> 00:15:54.168
The cosine families reconstruct the
potential, but do not by themselves
determine

00:15:54.168 --> 00:15:56.708
every lowest level of the exact tower.

00:15:56.708 --> 00:16:00.868
The moved probe is a chosen phase, not
necessarily a vacuum.

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Read its surviving group separately; a
boundary coordinate alone does not

00:16:04.518 --> 00:16:06.383
determine symmetry breaking.

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Open Anomalies. What that content owes:
every anomaly channel of the unbroken

00:16:14.043 --> 00:16:16.358
group, in exact rationals.

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Load the S U six example. The ledger
evaluates each anomaly channel of the

00:16:22.013 --> 00:16:25.013
unbroken group in exact rational
arithmetic.

00:16:25.013 --> 00:16:29.323
Distinguish a vanishing bill from a case
with no massless fermions to test.

00:16:29.323 --> 00:16:32.078
Brane cancellation is a separate
calculation.

00:16:33.402 --> 00:16:37.632
A non-zero row is a BILL, not an
inconsistency: the brane fermions such a

00:16:37.632 --> 00:16:41.112
model needs pay into the same channels with
the opposite sign.

00:16:41.112 --> 00:16:44.162
And a model with no massless fermion has
nothing to cancel — that is no

00:16:44.162 --> 00:16:46.382
subject, not cancels.

00:16:49.468 --> 00:16:54.038
Open Brane matter. Who pays that bill, and
what it costs: matter on the

00:16:54.038 --> 00:16:58.238
two fixed points, held at once to the
anomaly ledger and to Part I's boundary-
mass

00:16:58.238 --> 00:16:59.133
gate.

00:17:00.468 --> 00:17:04.193
Load the supplied S U five brane example
and solve its supported linear charge

00:17:04.193 --> 00:17:08.908
channels. Compare the anomaly ledger with
the surviving massless fields.

00:17:08.908 --> 00:17:12.568
Paying an anomaly bill and giving a field a
mass are different requirements.

00:17:13.868 --> 00:17:18.453
Two verdicts, kept apart on purpose: the
bill before and after, and the massless

00:17:18.453 --> 00:17:22.998
count before and after. The same field can
pay one and not the other, because

00:17:22.998 --> 00:17:26.288
the charge that cancels an anomaly is not
in general the charge a mass term

00:17:26.288 --> 00:17:30.418
needs. The surviving count is a lower bound
— the rank test assumes generic

00:17:30.418 --> 00:17:31.593
couplings.

00:17:34.735 --> 00:17:39.005
Open Scan. Walk the displayed finite space
of boundary conditions and matter

00:17:39.005 --> 00:17:41.480
contents through the selected filters.

00:17:41.480 --> 00:17:45.110
The breaking filter tests which generators
at phase zero survive at the numerically

00:17:45.110 --> 00:17:46.475
located minimum.

00:17:47.802 --> 00:17:50.042
Run the displayed finite sweep.

00:17:50.042 --> 00:17:54.012
Read the denominator, each filter in the
funnel, the survivors and the unresolved

00:17:54.012 --> 00:17:59.027
cases. The interface counts boundary
conditions and equivalence classes
separately,

00:17:59.027 --> 00:18:02.372
so surviving rows are not automatically
distinct theories.

00:18:03.668 --> 00:18:07.638
Surviving boundary conditions are not
surviving theories: [p,q,r,s] ~ [p−

00:18:07.638 --> 00:18:13.318
1,q+1,r+1,s−1] is the same theory, so the
headline is a pair of numbers.

00:18:13.318 --> 00:18:16.238
An undecided vacuum is counted apart from a
no.

00:18:19.335 --> 00:18:21.900
Open One model, every verdict.

00:18:21.900 --> 00:18:25.055
Which of the instrument's answers about
this model are about the THEORY,

00:18:25.055 --> 00:18:27.730
and which only about the frame you are
standing in.

00:18:29.068 --> 00:18:32.518
Start the built-in example, then choose its
displayed equivalent boundary

00:18:32.518 --> 00:18:36.863
condition. Compare the tags identifying
properties of the theory and properties

00:18:36.863 --> 00:18:40.953
of the chosen frame. A changed coordinate
description can move a displayed

00:18:40.953 --> 00:18:43.493
quantity without changing the physical
theory.

00:18:44.802 --> 00:18:48.132
The tags compare quantities in the
evaluated frames.

00:18:48.132 --> 00:18:51.762
Read boundary coordinates and the surviving
symmetry separately.

00:18:51.762 --> 00:18:54.892
Reported energies share the potential
normalization.

00:18:54.892 --> 00:18:58.912
Numerical agreement between the located
minima is evidence for these evaluations,

00:18:58.912 --> 00:19:01.492
not an exhaustive global-minimum
certificate.

00:19:04.602 --> 00:19:09.297
Open Simulator. Choose builder predictions,
a top-Kaluza Klein Higgs-rate

00:19:09.297 --> 00:19:13.302
reference or the neutrino ring; compare
calculated responses with their explicitly

00:19:13.302 --> 00:19:15.532
scoped experimental references.

00:19:16.868 --> 00:19:20.518
Load the published builder example and set
the gauge coupling to one.

00:19:20.518 --> 00:19:24.463
Higgs masses now use analytic Fourier
second derivatives, with an explicit

00:19:24.463 --> 00:19:29.133
truncation error bound. The export retains
the actual coupling and phase,

00:19:29.133 --> 00:19:32.718
and distinguishes a chosen probe from a
numerically located minimum.

00:19:34.068 --> 00:19:37.343
The thermal history belongs to a separate S
U three benchmark and the stated

00:19:37.343 --> 00:19:41.323
supported regime. It is not a detector
forecast or the thermal history of

00:19:41.323 --> 00:19:45.763
this builder. At commuting endpoints, the
present mass dictionary does not

00:19:45.763 --> 00:19:49.153
identify a shifted W candidate to set the
scale.

00:19:49.153 --> 00:19:53.218
That limitation does not imply that the
phase-zero gauge group survives.

00:19:56.335 --> 00:20:00.675
Open Boundary conditions. Which boundary
conditions are the same theory,

00:20:00.675 --> 00:20:03.395
walked as orbits rather than quoted as a
theorem.

00:20:04.735 --> 00:20:08.680
Switch from the interval orbifold to the
two-dimensional Z three example.

00:20:08.680 --> 00:20:13.020
The orbit structure and class count change
with the specified boundary problem.

00:20:13.020 --> 00:20:17.555
Equivalence classes identify descriptions
connected by the allowed transformations.

00:20:18.868 --> 00:20:23.548
The counts come out (N+1) squared  at every
N on S¹/

00:20:23.548 --> 00:20:27.743
Z₂, which is Haba–Hosotani–Kawamura's
theorem as a measurement.

00:20:27.743 --> 00:20:30.788
Press T squared /Z₃ and the answer changes.

00:20:33.935 --> 00:20:36.195
Open Classify an orbifold.

00:20:36.195 --> 00:20:39.910
The alphabet of an orbifold, derived from
its rotation matrix and nothing

00:20:39.910 --> 00:20:40.865
else.

00:20:42.202 --> 00:20:45.872
Select the two-dimensional Z four rotation
and classify it.

00:20:45.872 --> 00:20:49.187
The group-theoretic alphabet is derived
from the matrix.

00:20:49.187 --> 00:20:53.242
You can enter another supported matrix, but
an invalid finite-order hypothesis

00:20:53.242 --> 00:20:56.127
must be refused rather than silently
classified.

00:20:57.468 --> 00:20:59.768
Nothing is entered but the matrix.

00:20:59.768 --> 00:21:03.663
A matrix of infinite order, or one whose
characteristic polynomial is not

00:21:03.663 --> 00:21:08.538
a power of the m-th cyclotomic, comes back
REFUSED rather than classified.

00:21:11.668 --> 00:21:15.743
Open Name the relations. Which equivalence
relation on boundary conditions

00:21:15.743 --> 00:21:20.263
the literature already owns, and whether a
proposed move set connects a class.

00:21:21.602 --> 00:21:25.872
Switch to the Z four boundary problem and
judge the displayed proposed move.

00:21:25.872 --> 00:21:29.567
Read the local and global qualifications
and the source attribution.

00:21:29.567 --> 00:21:33.327
A useful move in one boundary problem is
not automatically a complete equivalence

00:21:33.327 --> 00:21:34.772
relation in another.

00:21:36.068 --> 00:21:39.808
The local/global distinction is the one
that gets misquoted, and the page

00:21:39.808 --> 00:21:41.453
carries it explicitly.

00:21:44.602 --> 00:21:47.132
Open Conjugate boundary conditions.

00:21:47.132 --> 00:21:51.522
How many inequivalent CONJUGATE boundary
conditions there are on S¹/Z₂ —

00:21:51.522 --> 00:21:55.702
and, because that count rests on a
hypothesis nobody has settled, what each

00:21:55.702 --> 00:21:57.417
of the two answers would be.

00:21:58.735 --> 00:22:02.900
Increase the group rank and compare the two
hypotheses printed in the table.

00:22:02.900 --> 00:22:05.845
Conjugate twists transform by congruence.

00:22:05.845 --> 00:22:09.240
Independent boundary transformations and
one linked transformation lead to

00:22:09.240 --> 00:22:13.885
different classification questions, so the
hypothesis travels with the count.

00:22:15.202 --> 00:22:18.782
What the panel puts on screen is the
disagreement, not a number, and that

00:22:18.782 --> 00:22:23.157
is the point: the twists move by congruence
rather than similarity, and independence

00:22:23.157 --> 00:22:27.187
decides between four classes flat in N and
no finite count at all.

00:22:27.187 --> 00:22:30.162
What the label leaves unbroken is not a
property of the label — the same

00:22:30.162 --> 00:22:33.127
verdict the ordinary panel reaches by
another route.

00:22:33.127 --> 00:22:37.012
The exported card carries the hypothesis
beside the count, so a number never

00:22:37.012 --> 00:22:39.472
travels without the condition it rests on.

00:22:42.602 --> 00:22:46.737
Open Brane kinetic terms. What happens to
the tower when brane-localised

00:22:46.737 --> 00:22:50.022
kinetic terms make the masses stop being
n/R.

00:22:51.335 --> 00:22:54.310
Increase the brane kinetic coefficient to
twelve.

00:22:54.310 --> 00:22:58.600
The spectrum responds because the roots are
no longer a simple integer tower.

00:22:58.600 --> 00:23:02.740
Compare the root conditions and
normalization, then use the separate
warped-unification

00:23:02.740 --> 00:23:04.960
card for coupling-running questions.

00:23:06.268 --> 00:23:09.493
The special functions are checked against
mpmath at forty digits, and the

00:23:09.493 --> 00:23:13.088
c  to  0 limit is computed in closed form
by code that shares nothing with

00:23:13.088 --> 00:23:16.658
the solver. That limit found three real
defects.

00:23:19.802 --> 00:23:24.367
Open Gravity–gauge · 3D. Which physical
information a complete tower of masses

00:23:24.367 --> 00:23:27.497
leaves undetermined in a controlled
gravity-gauge example.

00:23:28.802 --> 00:23:32.767
Select eta equal to minus zero point nine,
then display the gauge kinetic

00:23:32.767 --> 00:23:37.722
function. The paired masses and the source
response carry different information.

00:23:37.722 --> 00:23:42.452
The Wilson quantity here is a kinetic
normalization, not a Higgs-mass prediction.

00:23:43.802 --> 00:23:47.187
The positive paired tensor NN and vector DD
masses are protected by their

00:23:47.187 --> 00:23:49.277
common canonical operator.

00:23:49.277 --> 00:23:52.687
The gauge NN control has different
boundaries and moves.

00:23:52.687 --> 00:23:56.762
The source position is in the extra
dimension, not a laboratory location;

00:23:56.762 --> 00:23:59.732
the Wilson kinetic scale is not a Higgs
mass.

00:23:59.732 --> 00:24:04.302
For p=1.1 a canonical bulk scalar realizes
the family, with stability

00:24:04.302 --> 00:24:05.962
and cutoff still open.

00:24:09.068 --> 00:24:13.273
Open The literature. The reading list
behind the series: what each paper

00:24:13.273 --> 00:24:16.663
publishes, and which ones a person has
actually read.

00:24:18.002 --> 00:24:21.132
Filter the reading list to the complete-
triple selection.

00:24:21.132 --> 00:24:25.042
Inspect the recorded sources and what each
paper actually supplies.

00:24:25.042 --> 00:24:29.022
Keyword signals help navigate this corpus;
they are not proofs, and this

00:24:29.022 --> 00:24:31.817
reading list is not an exhaustive map of
the field.

00:24:33.135 --> 00:24:38.005
A signal is a keyword, and a keyword sweep
misses whatever is phrased differently.

00:24:38.005 --> 00:24:41.475
Nothing is asserted from a signal alone,
and the corpus is our reading list

00:24:41.475 --> 00:24:42.865
rather than the field.

00:24:46.002 --> 00:24:50.427
The second Simulator mode is the top Kaluza
Klein Higgs-production reference.

00:24:50.427 --> 00:24:54.332
Its leading rate, finite tower and resummed
comparison answer one specified

00:24:54.332 --> 00:24:55.697
model question.

00:24:57.002 --> 00:25:01.157
Move the Kaluza Klein scale to fifteen
hundred gigaelectronvolts.

00:25:01.157 --> 00:25:04.372
Inspect the rate curve and the separate
convergence display.

00:25:04.372 --> 00:25:08.452
The chosen comparison window is
conditional, and a custom window is a user-
supplied

00:25:08.452 --> 00:25:09.562
scenario.

00:25:12.668 --> 00:25:15.293
Select the four-dimensional neutrino ring.

00:25:15.293 --> 00:25:18.618
Calibration can hold the light mass and
active-current deficit fixed while

00:25:18.618 --> 00:25:21.193
the required couplings are reconstructed.

00:25:21.193 --> 00:25:23.768
Six heavy pairs belong to this base model.

00:25:25.068 --> 00:25:29.333
Compare mu B equal to zero with five
thousand kilo electron volts.

00:25:29.333 --> 00:25:33.328
The leading light mass and the heavy pair
splittings carry different information.

00:25:33.328 --> 00:25:36.663
Read the approximation indicators alongside
the spectrum.

00:25:39.802 --> 00:25:43.212
The C M S comparison uses published
observed and expected curves with their

00:25:43.212 --> 00:25:47.972
bands. The overlay keeps the selected
flavour and Dirac or Majorana hypothesis

00:25:47.972 --> 00:25:48.972
visible.

00:25:50.268 --> 00:25:53.308
Choose muon flavour and the Majorana
reference.

00:25:53.308 --> 00:25:57.713
Inspect the per-component convention, mass
domain and reference ratios.

00:25:57.713 --> 00:26:01.408
The ring overlay is not a likelihood that
includes its complete flavour structure,

00:26:01.408 --> 00:26:04.388
decay acceptance and multi-state
interference.

00:26:07.535 --> 00:26:10.590
The decay card starts from the weak-channel
scenario.

00:26:10.590 --> 00:26:14.110
Select a heavy pair and inspect where its
width goes, its lifetime and the

00:26:14.110 --> 00:26:16.015
fixed-boost flight estimate.

00:26:17.335 --> 00:26:20.110
Include the calculated Majoron channels.

00:26:20.110 --> 00:26:23.090
The width and the derived lifetime respond
together.

00:26:23.090 --> 00:26:26.135
An extra width is a separate user
hypothesis.

00:26:26.135 --> 00:26:30.035
Read the isolated-pair and overlap
diagnostics before interpreting the same-
sign

00:26:30.035 --> 00:26:31.910
over opposite-sign ratio.

00:26:33.202 --> 00:26:36.482
Change the fixed boost to ten and inspect
the flight curve.

00:26:36.482 --> 00:26:39.962
This illustrates the supplied kinematic
scenario; it does not integrate a

00:26:39.962 --> 00:26:42.707
detector acceptance or a production
spectrum.

00:26:45.802 --> 00:26:50.432
Three sterile copies reconstruct the chosen
light masses and mixing orientation.

00:26:50.432 --> 00:26:54.352
The mass ordering, phases and active
deficits are inputs.

00:26:54.352 --> 00:26:57.597
The card also displays eighteen heavy-pair
flavour weights.

00:26:58.935 --> 00:27:01.745
Change the Dirac phase to ninety degrees.

00:27:01.745 --> 00:27:05.455
Compare neutrino and antineutrino
appearance in the unitary vacuum limit,

00:27:05.455 --> 00:27:07.795
then inspect the flavour fractions.

00:27:07.795 --> 00:27:11.480
Majorana phases cancel from these
oscillation curves but can affect the
displayed

00:27:11.480 --> 00:27:13.570
light-sector double-beta quantity.

00:27:16.668 --> 00:27:20.233
This experiment holds the chosen light
masses and mixing orientation fixed

00:27:20.233 --> 00:27:22.803
while reconstructing a parameter path.

00:27:22.803 --> 00:27:25.293
The green strip tells you what is fixed.

00:27:25.293 --> 00:27:29.793
The five figures separate heavy masses,
splitting, current factors, small

00:27:29.793 --> 00:27:31.788
differences and reference data.

00:27:33.135 --> 00:27:36.300
Move the selected position from one tenth
to eight tenths along the mu B

00:27:36.300 --> 00:27:40.585
path. The mass stays fixed while the pair
splitting changes.

00:27:40.585 --> 00:27:43.325
The open circle tracks the selected point.

00:27:43.325 --> 00:27:47.390
Equal light inputs therefore do not
determine every heavy-sector response.

00:27:48.735 --> 00:27:52.165
Now choose the common active deficit and
its upper endpoint.

00:27:52.165 --> 00:27:56.335
The raw vacuum current factor is
suppressed, but the specified near
normalization

00:27:56.335 --> 00:27:58.395
cancels the common factor.

00:27:58.395 --> 00:28:01.625
The difference figure labels numerical
coincidence rather than amplifying

00:28:01.625 --> 00:28:02.720
roundoff.

00:28:04.068 --> 00:28:06.298
Choose deficit direction three.

00:28:06.298 --> 00:28:09.213
Unequal deficits can leave a shape
response.

00:28:09.213 --> 00:28:12.373
The fourth graph magnifies an absolute
difference that is difficult to see

00:28:12.373 --> 00:28:14.363
in the overlapping curves.

00:28:14.363 --> 00:28:18.863
Its scale is explicit, and the exported
samples retain their original precision.

00:28:20.202 --> 00:28:23.607
The DeepCore map uses the archived twenty-
eighteen standard-three-neutrino

00:28:23.607 --> 00:28:28.032
tables. The cross stays fixed along the
ring path because these light inputs

00:28:28.032 --> 00:28:32.147
stay fixed. The map is not a nonunitary
ring likelihood and is not added

00:28:32.147 --> 00:28:33.532
to NuFIT.

00:28:34.868 --> 00:28:38.363
To move the cross, change sine squared
theta twenty-three in the flavour

00:28:38.363 --> 00:28:41.923
card. Here it is set to zero point six.

00:28:41.923 --> 00:28:44.578
The reference updates for the new light
input.

00:28:44.578 --> 00:28:48.953
Outside its published grid the laboratory
withholds a value instead of extrapolating.

00:28:52.068 --> 00:28:56.603
This paper-model experiment reconstructs
the stated flat S U six potential.

00:28:56.603 --> 00:29:00.228
Matter content and the winding cutoff are
explicit controls.

00:29:00.228 --> 00:29:03.468
A small Wilson minimum must be read with
its convergence check.

00:29:04.802 --> 00:29:08.897
Set the winding cutoff to ten and inspect
the shifted minimum and comparison.

00:29:08.897 --> 00:29:12.157
A finite truncation can change the apparent
result.

00:29:12.157 --> 00:29:15.517
The supported potential can be transferred
to the builder; this does not

00:29:15.517 --> 00:29:17.762
certify a complete flavour model.

00:29:20.868 --> 00:29:23.913
The warped-unification card compares
differential gauge running under the

00:29:23.913 --> 00:29:25.933
selected matter assignment.

00:29:25.933 --> 00:29:29.373
Required ultraviolet boundary terms and
their residuals are outputs of that

00:29:29.373 --> 00:29:31.073
stated approximation.

00:29:32.402 --> 00:29:34.937
Switch the matter assignment to C two.

00:29:34.937 --> 00:29:38.487
The running differences and required
boundary terms respond.

00:29:38.487 --> 00:29:41.837
The naive-dimensional-analysis reference is
a scale estimate.

00:29:41.837 --> 00:29:46.152
The separate localization probe is not a
complete fermion-spectrum calculation.

00:29:49.268 --> 00:29:52.213
The thermal card is its own S U three
benchmark.

00:29:52.213 --> 00:29:56.023
It uses named paper cases and compares
potential cutoffs.

00:29:56.023 --> 00:29:59.408
A stored matching PhaseTracer result is
available offline for the recorded

00:29:59.408 --> 00:30:00.508
inputs.

00:30:01.802 --> 00:30:05.332
Load paper case two and compare the
potential and phase flow.

00:30:05.332 --> 00:30:08.997
Coexistence and a nucleation proxy are
different questions.

00:30:08.997 --> 00:30:12.632
A new point needs a matching bounce
calculation; changing the builder model

00:30:12.632 --> 00:30:15.642
does not turn this benchmark into its
thermal history.

00:30:16.935 --> 00:30:20.625
The new comparison runs PhaseTracer and
CosmoTransitions on the same S U

00:30:20.625 --> 00:30:23.020
three potential and canonical field.

00:30:23.020 --> 00:30:26.055
Nine matched temperatures compare the
bounce action.

00:30:26.055 --> 00:30:29.730
The programs share shooting-method
ancestry, so agreement is a numerical

00:30:29.730 --> 00:30:34.270
cross-check, not an independent interval
proof or an experimental validation.

00:30:35.602 --> 00:30:39.372
The table changes the spatial and thermal
Fourier cutoffs together.

00:30:39.372 --> 00:30:43.312
T one-forty solves S three over T equal to
one hundred forty.

00:30:43.312 --> 00:30:48.232
It is a proxy, separate from the integrated
nucleation and percolation results.

00:30:48.232 --> 00:30:51.852
The older displayed proxy used a looser
shooting tolerance; compare like

00:30:51.852 --> 00:30:54.242
settings before interpreting a difference.

00:30:55.535 --> 00:30:57.900
Open the numerical diagnostics.

00:30:57.900 --> 00:31:01.565
Tolerance shifts, profile sampling and the
virial residual test different

00:31:01.565 --> 00:31:03.700
aspects of the calculation.

00:31:03.700 --> 00:31:07.730
The targets are numerical criteria, not
confidence levels.

00:31:07.730 --> 00:31:12.600
Higher loops, thermal resummation and
plasma dynamics remain unquantified.

00:31:12.600 --> 00:31:16.850
These S U three examples are separate from
the S U seven mass certificates.

00:31:18.135 --> 00:31:20.770
Change the coupling away from the
reference.

00:31:20.770 --> 00:31:24.270
The archived solver comparison disappears
because all thermal inputs must

00:31:24.270 --> 00:31:28.620
match. A stale certificate must not follow
an edited point.

00:31:28.620 --> 00:31:32.185
Load a named paper case again to recover
its evidence; a new point needs

00:31:32.185 --> 00:31:33.720
a new calculation.

00:31:35.068 --> 00:31:38.383
Reload case two and save the experiment
JSON.

00:31:38.383 --> 00:31:42.913
It retains both solver versions,
tolerances, cutoffs and sources.

00:31:42.913 --> 00:31:46.818
The thermal potential is credited to Hirose
and Shibuya, CosmoTransitions

00:31:46.818 --> 00:31:51.008
to Carroll Wainwright, and PhaseTracer to
Athron and collaborators.

00:31:51.008 --> 00:31:53.713
Keep this provenance with every exported
result.

00:31:56.802 --> 00:32:00.422
Integrated transition history uses refined
action tables.

00:32:00.422 --> 00:32:04.052
Read nucleation, percolation and completion
separately.

00:32:04.052 --> 00:32:07.587
The false-vacuum fraction and physical-
volume condition make those distinctions

00:32:07.587 --> 00:32:08.582
visible.

00:32:09.868 --> 00:32:13.133
Set the assumed wall speed to zero point
eight and the fluid efficiency to

00:32:13.133 --> 00:32:17.923
zero point one. Compare the history and
conditional acoustic spectrum.

00:32:17.923 --> 00:32:21.728
Wall friction, plasma evolution and
detector significance are not calculated

00:32:21.728 --> 00:32:23.258
by these controls.

00:32:26.402 --> 00:32:30.337
This warped-model experiment separates
ultraviolet and infrared anomaly factors,

00:32:30.337 --> 00:32:33.597
gauge cancellation and the baryon-current
matrix.

00:32:33.597 --> 00:32:37.637
Its sources and approximation are distinct
from the base S U seven ledger.

00:32:38.935 --> 00:32:42.425
Remove the lepton generations in this test
configuration.

00:32:42.425 --> 00:32:45.885
The imbalance exposes a gauge anomaly that
needs completion.

00:32:45.885 --> 00:32:49.860
A nonzero baryon-current anomaly is a
separate statement; it is not a computed

00:32:49.860 --> 00:32:52.630
proton lifetime or baryogenesis yield.

00:32:55.735 --> 00:32:59.125
Begin with the stored Standard Model-like
scalar reference.

00:32:59.125 --> 00:33:02.725
Local couplings determine production rates,
partial widths and branching

00:33:02.725 --> 00:33:06.945
fractions. Matching HiggsBounds and
HiggsSignals calculations use pinned

00:33:06.945 --> 00:33:08.820
experimental datasets.

00:33:10.135 --> 00:33:13.175
Add one mega electron volt of invisible
width.

00:33:13.175 --> 00:33:16.835
The local predictions update, and the old
experimental result is withdrawn

00:33:16.835 --> 00:33:19.390
because its inputs no longer match.

00:33:19.390 --> 00:33:22.595
Run the optional engine or import a
matching result before assigning a new

00:33:22.595 --> 00:33:24.235
experimental verdict.

00:33:27.335 --> 00:33:30.680
Open the first Kaluza Klein gluon card in
Collider and load the published

00:33:30.680 --> 00:33:33.880
R S point of Casagrande and collaborators.

00:33:33.880 --> 00:33:37.300
The card computes the couplings of a warped
Kaluza Klein gluon to zero-mode

00:33:37.300 --> 00:33:41.270
quarks, its width and branching fractions,
and compares its leading-order

00:33:41.270 --> 00:33:45.490
rates with the ATLAS top-pair limit and the
C M S dijet limit as r, prediction

00:33:45.490 --> 00:33:46.635
over limit.

00:33:47.935 --> 00:33:52.015
At three point seven five tera electron
volts, r for the top pair is close

00:33:52.015 --> 00:33:55.585
to one: the two thousand eight reference
point sits at the edge of the ATLAS

00:33:55.585 --> 00:34:00.205
comparison. That is a comparison with
ATLAS's thirty percent width benchmark,

00:34:00.205 --> 00:34:02.705
not a validated exclusion at this width.

00:34:04.002 --> 00:34:07.777
Below the plots, the top-pair mass spectrum
is computed with the interference

00:34:07.777 --> 00:34:11.822
between the Kaluza Klein gluon and the Q C
D gluon, in the fifteen bins of

00:34:11.822 --> 00:34:14.347
the C M S parton-level measurement.

00:34:14.347 --> 00:34:18.012
For this point the light-quark and top
couplings have opposite signs, so

00:34:18.012 --> 00:34:20.627
the interference is constructive below the
pole.

00:34:21.935 --> 00:34:26.740
Now load the flat G H U coloron at four
point five tera electron volts.

00:34:26.740 --> 00:34:30.920
Every quark couples equally, the couplings
share one sign, and the interference

00:34:30.920 --> 00:34:34.380
turns destructive: the low bins go down
instead of up.

00:34:35.668 --> 00:34:39.678
The last plot is the expected delta chi
squared against the measured covariance,

00:34:39.678 --> 00:34:42.823
with ten percent S M theory uncertainty per
bin.

00:34:42.823 --> 00:34:46.003
Set that uncertainty to zero and the reach
moves from about three point eight

00:34:46.003 --> 00:34:48.663
to about five tera electron volts.

00:34:48.663 --> 00:34:52.698
It is a sensitivity if the data equal the S
M, not an exclusion, and the

00:34:52.698 --> 00:34:57.228
open certificates show the independent
Dirac-trace and L H A P D F check.

00:35:00.335 --> 00:35:03.595
Use a comparison snapshot before changing a
point.

00:35:03.595 --> 00:35:08.985
Save the experiment JSON to retain the
inputs, calculated arrays, assumptions,

00:35:08.985 --> 00:35:11.570
provenance and optional saved reference.

00:35:11.570 --> 00:35:15.020
The global result card and LaTeX exports
provide another view of the selected

00:35:15.020 --> 00:35:16.330
calculation.

00:35:17.668 --> 00:35:20.463
Choose a figure and save its vector SVG.

00:35:20.463 --> 00:35:24.643
The new neutrino figures carry sampled data
and provenance in their metadata.

00:35:24.643 --> 00:35:28.333
The link button preserves controls in the
address; archive external results

00:35:28.333 --> 00:35:30.913
and comparisons in JSON as well.

00:35:32.202 --> 00:35:35.897
The browser calculations and stored
references run offline.

00:35:35.897 --> 00:35:39.922
New HiggsTools and PhaseTracer points use
the optional local engine.

00:35:39.922 --> 00:35:43.927
The source repository contains the
reproduction commands, independent checks

00:35:43.927 --> 00:35:48.507
and archived studies. Return to a chapter,
vary one assumption, and

00:35:48.507 --> 00:35:50.762
keep the scope beside every result.