WEBVTT 00:00:02.335 --> 00:00:07.120 Welcome to G H U Lab. This revised walkthrough covers every menu section, 00:00:07.120 --> 00:00:10.720 the three Simulator modes and the embedded research experiments. 00:00:10.720 --> 00:00:15.575 It now demonstrates the S U seven certificates, approximation errors, uncertainty 00:00:15.575 --> 00:00:19.600 budget, thermal solver comparison, named collider references and the first 00:00:19.600 --> 00:00:22.730 Kaluza Klein gluon against L H C data. 00:00:22.730 --> 00:00:26.975 Every section and card also has a Demo button that runs a guided simulation. 00:00:26.975 --> 00:00:29.465 Choose a chapter to revisit a topic. 00:00:29.465 --> 00:00:32.715 The boundary research chapter now adds linked two and three-dimensional mass 00:00:32.715 --> 00:00:36.910 views, independent profiles and scoped anomaly diagnostics. 00:00:38.202 --> 00:00:40.747 Start with a named model or reference. 00:00:40.747 --> 00:00:45.167 Change one assumption at a time, and read the result with its units and scope. 00:00:45.167 --> 00:00:50.157 Theorem, verified, measured and unknown describe different kinds of evidence. 00:00:50.157 --> 00:00:54.327 A computed scenario value is not automatically an experimental measurement. 00:00:57.468 --> 00:01:02.043 Open Hierarchy. For a bulk content of the S U seven model, inspect the 00:01:02.043 --> 00:01:06.068 compactification scale and Higgs mass under the displayed conventions. 00:01:06.068 --> 00:01:09.713 The ceiling belongs to the stated small- angle moment approximation. 00:01:11.002 --> 00:01:14.522 Change the diagnostic gauge coupling to zero point seven. 00:01:14.522 --> 00:01:17.947 The response plots separate a change of model convention from propagation 00:01:17.947 --> 00:01:21.257 of the measured W input and from winding convergence. 00:01:21.257 --> 00:01:23.922 Read the axes and the central values together. 00:01:25.268 --> 00:01:28.753 The calculated phase does not reproduce the printed phase. 00:01:28.753 --> 00:01:32.573 The mismatch varies between rows, and an overall multiplication of the potential 00:01:32.573 --> 00:01:35.043 cannot move its stationary points. 00:01:35.043 --> 00:01:38.903 Absolute scales remain conditional on resolving this discrepancy. 00:01:38.903 --> 00:01:41.703 The arithmetic identities are separate statements. 00:01:43.002 --> 00:01:45.427 Load the first certified benchmark. 00:01:45.427 --> 00:01:49.272 The table encloses two different stationary points: the quartic logarithmic 00:01:49.272 --> 00:01:51.962 approximation and the full Fourier minimum. 00:01:51.962 --> 00:01:56.042 Phase, Higgs mass and compactification scale have separate absolute and relative 00:01:56.042 --> 00:02:00.292 error intervals. They apply to the displayed matter content, gauge choice 00:02:00.292 --> 00:02:02.052 and fixed mass inputs. 00:02:03.402 --> 00:02:05.282 What limits the precision? 00:02:05.282 --> 00:02:09.322 Read approximation bias, root-location bounds and the Fourier remainder separately 00:02:09.322 --> 00:02:12.192 from the propagated W-mass uncertainty. 00:02:12.192 --> 00:02:15.952 The ten percent coupling variation is a chosen scenario, without an assigned 00:02:15.952 --> 00:02:20.592 probability. Physical theory uncertainty is explicitly not quantified; 00:02:20.592 --> 00:02:23.017 there is no combined physical error bar. 00:02:24.335 --> 00:02:26.355 Save the error certificate. 00:02:26.355 --> 00:02:30.415 The download keeps the rational enclosures, numerical budget, W input and 00:02:30.415 --> 00:02:35.250 attribution. The full mass enclosure already includes root and Fourier errors; 00:02:35.250 --> 00:02:37.420 do not add its half-width again. 00:02:37.420 --> 00:02:40.560 A different matter content or mass convention needs a matching certificate 00:02:40.560 --> 00:02:41.620 of its own. 00:02:42.935 --> 00:02:47.170 The ATLAS and C M S rows are separate published Higgs-mass references. 00:02:47.170 --> 00:02:51.295 Compare the certified curvature mass with each stated channel and error band. 00:02:51.295 --> 00:02:54.480 The listed difference is not an exclusion significance. 00:02:54.480 --> 00:02:57.750 Connecting a one-loop curvature mass to a measured pole mass still requires 00:02:57.750 --> 00:03:00.170 matching and higher-order uncertainties. 00:03:01.468 --> 00:03:04.928 The dataset links explain the route to a fuller comparison. 00:03:04.928 --> 00:03:07.753 Channels have not been combined into a likelihood. 00:03:07.753 --> 00:03:11.998 C E R N hosts the experiments and is not a third independent measurement. 00:03:11.998 --> 00:03:16.353 Archive the inputs and sources beside the result; a certified numerical calculation 00:03:16.353 --> 00:03:19.058 alone does not establish agreement with nature. 00:03:22.202 --> 00:03:26.927 Open Design a scale. The map run backwards: name a compactification scale 00:03:26.927 --> 00:03:30.457 and a Higgs-mass window, and get a bulk content that lands there — or a named 00:03:30.457 --> 00:03:32.447 certificate that none exists. 00:03:33.735 --> 00:03:37.345 Enter a target compactification scale of two teraelectronvolts and run the 00:03:37.345 --> 00:03:41.640 design. Inspect the returned content or the named certificate. 00:03:41.640 --> 00:03:46.200 A search budget is a stopping condition, not evidence that no solution exists. 00:03:47.535 --> 00:03:51.450 budget means the search stopped, not that the rung is empty; the page keeps 00:03:51.450 --> 00:03:55.660 the two apart on purpose. The reachable-set panel resolves each cluster into 00:03:55.660 --> 00:03:58.080 the finite set of points it really is. 00:04:01.202 --> 00:04:06.457 Open Count a rung. How many bulk contents sit on a rung — counted, not built. 00:04:07.802 --> 00:04:10.982 The counting graph is generated when the section opens. 00:04:10.982 --> 00:04:14.027 Click a different horizontal position to move the moment probe and compare 00:04:14.027 --> 00:04:18.917 counts across the rungs. These are counts of contents, not a list of experimentally 00:04:18.917 --> 00:04:20.332 viable models. 00:04:21.668 --> 00:04:25.418 The four published-seed totals reproduce an independent enumeration of 69 00:04:25.418 --> 00:04:30.038 022 464 contents. The candidate uses even 00:04:30.038 --> 00:04:34.308 rungs and half-integral A₄; its counts are computed separately, without transferring 00:04:34.308 --> 00:04:36.318 the published measured-mass fibre. 00:04:39.468 --> 00:04:44.073 Open Atlas. Every bulk content of at most five multiplets — 1 00:04:44.073 --> 00:04:47.073 286 of them — with its potential drawn as one tile. 00:04:48.402 --> 00:04:52.232 Draw the lattice of one thousand two hundred and eighty-six contents. 00:04:52.232 --> 00:04:54.562 Each tile is a different potential. 00:04:54.562 --> 00:04:59.257 Inspect its colour and shape; a flat or blank potential is itself a result. 00:04:59.257 --> 00:05:02.102 Clicking a tile transfers that content to the model. 00:05:03.402 --> 00:05:07.887 One tile is green in the Higgs window, and it is the published row (2). 00:05:07.887 --> 00:05:11.582 A blank tile is a content whose potential is flat, and the harness predicts 00:05:11.582 --> 00:05:13.947 which tiles blank before they are drawn. 00:05:17.068 --> 00:05:21.873 Open Same potential?. Whether two bulk contents are the same one-loop potential, 00:05:21.873 --> 00:05:23.993 by Part VII's Theorem 3. 00:05:25.335 --> 00:05:29.115 Copy the first content and construct its canonical representative. 00:05:29.115 --> 00:05:32.255 Compare the potential curves and the five coordinates. 00:05:32.255 --> 00:05:35.485 Different lists of matter can produce exactly the same one-loop potential 00:05:35.485 --> 00:05:37.140 under the stated theorem. 00:05:38.468 --> 00:05:41.853 Same five coordinates ⟺ identically the same potential. 00:05:41.853 --> 00:05:46.638 The dashed curve riding exactly on the solid one is the theorem, not a coincidence. 00:05:47.935 --> 00:05:51.435 Load the equal-moment example and inspect the local range. 00:05:51.435 --> 00:05:55.285 These two contents have exactly the same D, A four and G through their integer 00:05:55.285 --> 00:05:59.055 coordinates, while their endpoint coordinate differs. 00:05:59.055 --> 00:06:02.015 Matching the small-angle expansion is a weaker condition than matching the 00:06:02.015 --> 00:06:03.530 complete potential. 00:06:04.868 --> 00:06:07.098 Switch to the full phase interval. 00:06:07.098 --> 00:06:11.048 The plotted full potentials separate even though the local expansions match. 00:06:11.048 --> 00:06:15.013 These curves illustrate finite Fourier sums; the exact coordinate statement 00:06:15.013 --> 00:06:17.688 and the interval proof are recorded separately. 00:06:17.688 --> 00:06:20.663 Use the full potential when judging a global vacuum. 00:06:22.002 --> 00:06:26.112 For content B, the endpoint at alpha equal to one has certified energy below 00:06:26.112 --> 00:06:30.357 its local minimum. This rules out that local minimum as global. 00:06:30.357 --> 00:06:33.492 It does not prove that the endpoint itself is global. 00:06:33.492 --> 00:06:37.092 Save the comparison to retain the exact inputs and the scope of this mathematical 00:06:37.092 --> 00:06:38.157 example. 00:06:41.268 --> 00:06:45.858 Open Anomalies & proton. What each multiplet contributes to the anomaly bill, 00:06:45.858 --> 00:06:49.033 in eighths, and what the proton-decay escape costs. 00:06:50.335 --> 00:06:54.030 Read the signed contributions to the anomaly bill and the rung ladder. 00:06:54.030 --> 00:06:58.620 A nonzero bulk bill does not, by itself, make the theory inconsistent: 00:06:58.620 --> 00:07:01.635 possible brane matter must be considered separately. 00:07:01.635 --> 00:07:05.245 The research card later in this section studies a different warped model. 00:07:06.535 --> 00:07:10.470 A non-zero bill is not an inconsistency: brane fermions pay into the same 00:07:10.470 --> 00:07:12.590 channels with the opposite sign. 00:07:12.590 --> 00:07:15.505 What the ladder forbids is a rung, not a model. 00:07:18.602 --> 00:07:20.897 Open Escape from proton decay. 00:07:20.897 --> 00:07:25.067 The escape from proton decay, constructed: type a brane content and watch 00:07:25.067 --> 00:07:28.917 the six channels, the assignments and the selection rule recompute. 00:07:30.202 --> 00:07:34.092 Choose the scalar charge associated with the eighty-four representation. 00:07:34.092 --> 00:07:37.887 The rational anomaly channels and charge assignments update together. 00:07:37.887 --> 00:07:41.297 Inspect which assignments meet the displayed proton-protection rule; the 00:07:41.297 --> 00:07:44.697 calculation does not supply a measured proton lifetime. 00:07:46.002 --> 00:07:49.502 Every assignment that protects the proton can also cancel all six channels — 00:07:49.502 --> 00:07:51.937 protection never costs an anomaly. 00:07:51.937 --> 00:07:54.657 That is an enumeration, not an argument. 00:07:57.802 --> 00:08:00.157 Open Multiplets & parities. 00:08:00.157 --> 00:08:04.102 The layer under the term tables: every representation broken into multiplets 00:08:04.102 --> 00:08:05.897 with their three Z₂ parities. 00:08:07.202 --> 00:08:11.142 Select the eighty-four representation and change its parity assignment. 00:08:11.142 --> 00:08:15.372 The decomposition and parity picture update from the representation data. 00:08:15.372 --> 00:08:18.667 Use the table to connect a surviving zero mode with the sign of its potential 00:08:18.667 --> 00:08:19.992 contribution. 00:08:21.335 --> 00:08:24.425 The term tables here are DERIVED and then checked against the ones the rest 00:08:24.425 --> 00:08:26.350 of the page computes with. 00:08:26.350 --> 00:08:29.880 If the two ever disagreed, this panel is where it would show. 00:08:33.002 --> 00:08:37.527 Open Screen a table. Arithmetic screens for a published row, with conditional 00:08:37.527 --> 00:08:40.982 rung certificates and independent full- potential witness checks. 00:08:42.268 --> 00:08:46.143 Enter a candidate resonance at four thousand gigaelectronvolts. 00:08:46.143 --> 00:08:49.368 The comb samples nearby teeth for the displayed rungs. 00:08:49.368 --> 00:08:53.308 Its filters, spacing table and download now use the same conditional-bound 00:08:53.308 --> 00:08:55.423 check for the chosen inputs. 00:08:55.423 --> 00:08:58.968 A surviving tooth is not proof of an attainable physical vacuum. 00:09:00.268 --> 00:09:04.278 The moment ceilings remain conditional on the small-angle approximation. 00:09:04.278 --> 00:09:07.633 The five printed phase rounding intervals contain no stationary point for 00:09:07.633 --> 00:09:09.603 the implemented potential. 00:09:09.603 --> 00:09:14.023 All eight fermion coefficient tables now agree with an independent reconstruction. 00:09:14.023 --> 00:09:17.353 The physical gauge determinant and the origin of the printed numerical mismatch 00:09:17.353 --> 00:09:18.563 remain open. 00:09:19.868 --> 00:09:22.923 Expand Certified S U seven benchmarks. 00:09:22.923 --> 00:09:27.068 Twenty-six Lean theorems verify finite algebraic identities. 00:09:27.068 --> 00:09:30.468 Separate interval proofs certify ten global minima on the stated one-phase 00:09:30.468 --> 00:09:34.883 domain: five reference contents under each of two gauge prescriptions. 00:09:34.883 --> 00:09:38.238 These statements do not certify an arbitrary edited model. 00:09:39.535 --> 00:09:41.740 Download the certificate bundle. 00:09:41.740 --> 00:09:46.445 It contains rational enclosures, continuum partitions, checksums and reproduction 00:09:46.445 --> 00:09:50.660 records. The infinite Fourier analysis is computer-assisted and has not been 00:09:50.660 --> 00:09:55.060 formalized in Lean. A global-minimum certificate is conditional on its potential 00:09:55.060 --> 00:09:58.785 and assumptions; it is not a certificate of physical viability. 00:10:00.135 --> 00:10:04.500 The English dossier assigns the model to Komori and Maru, the expansion antecedents 00:10:04.500 --> 00:10:09.100 to Haba, Takenaga and Yamashita and to Sakamoto and Takenaga, and the S U 00:10:09.100 --> 00:10:12.315 seven application in Part Seven to Carles Marín. 00:10:12.315 --> 00:10:15.385 Verification does not establish originality. 00:10:15.385 --> 00:10:18.775 The dossier keeps the remaining physical questions explicit. 00:10:21.868 --> 00:10:26.428 Open Collider. Which state a dijet search bounds, plus a separate Higgs-rate 00:10:26.428 --> 00:10:29.568 scenario checked against pinned experimental datasets. 00:10:30.868 --> 00:10:33.818 Move the dijet mass probe to five point two. 00:10:33.818 --> 00:10:37.478 Read the selected state, mass scale and published comparison under its colour 00:10:37.478 --> 00:10:42.043 hypothesis. The separate Higgs experiment below uses another explicitly supplied 00:10:42.043 --> 00:10:43.528 scalar scenario. 00:10:44.868 --> 00:10:48.433 The dijet delta chi squared values are quoted from the published record; 00:10:48.433 --> 00:10:51.333 the Higgs experiment computes its own comparison. 00:10:51.333 --> 00:10:56.153 Its 159 HiggsSignals observables are not 159 independent degrees 00:10:56.153 --> 00:11:00.578 of freedom. Coupling and width assumptions can compensate in visible rates, 00:11:00.578 --> 00:11:04.068 so this scalar comparison is not a complete G H U fit. 00:11:05.402 --> 00:11:09.582 The displayed recast table belongs to the earlier archived calculation. 00:11:09.582 --> 00:11:13.977 Separately, the dossier now records the C M S angular dataset at one hundred 00:11:13.977 --> 00:11:18.947 thirty-eight inverse femtobarns: seven distributions and seventy-seven bins. 00:11:18.947 --> 00:11:21.947 Integrity checks validate the imported tables. 00:11:21.947 --> 00:11:24.997 Importing them has not produced a new G H U fit. 00:11:26.335 --> 00:11:30.175 The released correlation matrix describes fitted signal strengths. 00:11:30.175 --> 00:11:33.605 It cannot automatically be used as the covariance of the normalized unfolded 00:11:33.605 --> 00:11:38.790 distributions. A new reinterpretation requires the G H U signal, selections 00:11:38.790 --> 00:11:42.700 and nuisance parameters, with a justified statistical model. 00:11:42.700 --> 00:11:47.150 The dossier distinguishes reviewed resources from analyses actually executed. 00:11:50.268 --> 00:11:54.663 Open Selection rule. Which alpha -domain a search may legally use, and which 00:11:54.663 --> 00:11:58.088 S U 4 representations can hold a quark generation. 00:11:59.402 --> 00:12:03.897 Select the representation with Dynkin labels one, zero, one. 00:12:03.897 --> 00:12:07.122 The centre-charge and chiral-projection results determine which search domain 00:12:07.122 --> 00:12:10.127 is permitted and which content can host a generation. 00:12:10.127 --> 00:12:14.447 The domain is computed from the representation, not chosen for convenience. 00:12:15.735 --> 00:12:19.195 The centre-charge gate is classical and is credited as such. 00:12:19.195 --> 00:12:22.575 What is ours is the chiral projection that gives the closed count. 00:12:25.668 --> 00:12:30.323 Open Model calculator. A matter content in, the Higgs out — the AHMN 00:12:30.323 --> 00:12:32.523 model recomputed in front of you. 00:12:33.868 --> 00:12:36.608 Load the named A H M N reference model. 00:12:36.608 --> 00:12:41.458 Its terms, potential and derived quantities are recalculated by the browser. 00:12:41.458 --> 00:12:44.878 Start with this anchored content before changing multiplicities or boundary 00:12:44.878 --> 00:12:49.473 signs, and retain the stated normalization caveat for absolute scales. 00:12:50.802 --> 00:12:54.402 The mass ratio carries no normalisation and no caveat. 00:12:54.402 --> 00:12:56.052 Absolute scales do. 00:12:59.202 --> 00:13:03.482 Open eta-meter. What the boundary sign eta does to a multiplet's contribution — 00:13:03.482 --> 00:13:06.132 in closed form, from one integer. 00:13:07.468 --> 00:13:11.153 Load the supplied example made from a blind multiplet, then flip every eta 00:13:11.153 --> 00:13:15.773 sign. In this example the potential is insensitive to that change. 00:13:15.773 --> 00:13:19.313 The eta-difference view exposes the cancellation; it is not evidence that 00:13:19.313 --> 00:13:21.273 boundary signs never matter. 00:13:22.602 --> 00:13:25.812 In difference mode every blind multiplet goes blank. 00:13:25.812 --> 00:13:28.887 That is Part V's theorem seen without reading a number. 00:13:32.002 --> 00:13:36.772 Open Five dimensions. Haba–Yamashita's own 5D S U 3 model, 00:13:36.772 --> 00:13:39.167 with the vacuum their paper leaves undone. 00:13:40.468 --> 00:13:43.783 Compare the pure-gauge case with the supplied marginal trio. 00:13:43.783 --> 00:13:46.248 Read the potential and vacuum together. 00:13:46.248 --> 00:13:50.153 This panel uses the five-dimensional S U three reference, so its arithmetic 00:13:50.153 --> 00:13:54.398 and assumptions must not be borrowed from the six-dimensional S U seven benchmark. 00:13:55.735 --> 00:13:59.425 Pure gauge never breaks the symmetry (D = −9). 00:13:59.425 --> 00:14:03.820 In this whole 5D class 8D is even: the odd rung the S U 7 ceiling stands 00:14:03.820 --> 00:14:05.765 on needs the sixth dimension. 00:14:08.868 --> 00:14:13.448 Open the S U N builder. Boundary conditions and supported bulk representations 00:14:13.448 --> 00:14:17.723 define the implemented one-loop Wilson-line potential in five dimensions. 00:14:17.723 --> 00:14:19.393 The model is the input. 00:14:20.735 --> 00:14:23.685 Load section four point three of the source paper. 00:14:23.685 --> 00:14:26.920 This pure-gauge example prefers the endpoint at one. 00:14:26.920 --> 00:14:30.600 Read the surviving group from the joint commutant: being at an endpoint does 00:14:30.600 --> 00:14:33.475 not prove that the generators at zero survive. 00:14:33.475 --> 00:14:37.915 The potential plot and the reported minimum now use the same V over C normalization. 00:14:39.202 --> 00:14:43.022 The four worked examples are checked against the implemented formulas. 00:14:43.022 --> 00:14:47.632 With one Wilson phase, the cosine terms admit the same moment construction. 00:14:47.632 --> 00:14:51.387 Its closed stationary branch is a small- angle approximation. 00:14:51.387 --> 00:14:55.017 The numerical Fourier minimum is a separate calculation, and a finite grid 00:14:55.017 --> 00:14:57.397 is not a certificate of the global minimum. 00:15:00.535 --> 00:15:05.065 Open Paper models. Four models somebody else published, taken off their 00:15:05.065 --> 00:15:07.635 pages and run through this instrument's engine. 00:15:08.935 --> 00:15:13.075 Change the triplet Dirac-fermion count to five in the supported reference. 00:15:13.075 --> 00:15:17.595 Inspect which outputs are actually computed and which remain structural statements. 00:15:17.595 --> 00:15:21.255 Where offered, the load button transfers the supported content into the general 00:15:21.255 --> 00:15:22.200 builder. 00:15:23.535 --> 00:15:26.920 Three of the four are supersymmetric and this engine's potential is not, 00:15:26.920 --> 00:15:30.680 so their rows are boundary-condition and zero-mode statements only. 00:15:30.680 --> 00:15:34.785 An amber row disagrees with one printed equation, not with a paper, and names 00:15:34.785 --> 00:15:37.600 which of that paper's own equations agrees with which. 00:15:40.735 --> 00:15:45.380 Open 4D spectrum. What the model on the builder CONTAINS: the four-dimensional 00:15:45.380 --> 00:15:47.745 fields and their Kaluza–Klein towers. 00:15:49.068 --> 00:15:52.608 Load the S U six example and move the Wilson-line probe. 00:15:52.608 --> 00:15:55.998 Compare the potential families with the exact low-lying tower. 00:15:55.998 --> 00:15:58.888 The lowest levels can require a different reading from the families used 00:15:58.888 --> 00:16:00.633 to construct the potential. 00:16:01.935 --> 00:16:06.035 The cosine families reconstruct the potential, but do not by themselves determine 00:16:06.035 --> 00:16:08.575 every lowest level of the exact tower. 00:16:08.575 --> 00:16:12.735 The moved probe is a chosen phase, not necessarily a vacuum. 00:16:12.735 --> 00:16:16.385 Read its surviving group separately; a boundary coordinate alone does not 00:16:16.385 --> 00:16:18.250 determine symmetry breaking. 00:16:21.335 --> 00:16:25.910 Open Anomalies. What that content owes: every anomaly channel of the unbroken 00:16:25.910 --> 00:16:28.225 group, in exact rationals. 00:16:29.535 --> 00:16:33.880 Load the S U six example. The ledger evaluates each anomaly channel of the 00:16:33.880 --> 00:16:36.880 unbroken group in exact rational arithmetic. 00:16:36.880 --> 00:16:41.190 Distinguish a vanishing bill from a case with no massless fermions to test. 00:16:41.190 --> 00:16:43.945 Brane cancellation is a separate calculation. 00:16:45.268 --> 00:16:49.498 A non-zero row is a BILL, not an inconsistency: the brane fermions such a 00:16:49.498 --> 00:16:52.978 model needs pay into the same channels with the opposite sign. 00:16:52.978 --> 00:16:56.028 And a model with no massless fermion has nothing to cancel — that is no 00:16:56.028 --> 00:16:58.248 subject, not cancels. 00:17:01.335 --> 00:17:05.905 Open Brane matter. Who pays that bill, and what it costs: matter on the 00:17:05.905 --> 00:17:10.105 two fixed points, held at once to the anomaly ledger and to Part I's boundary- mass 00:17:10.105 --> 00:17:11.000 gate. 00:17:12.335 --> 00:17:16.060 Load the supplied S U five brane example and solve its supported linear charge 00:17:16.060 --> 00:17:20.775 channels. Compare the anomaly ledger with the surviving massless fields. 00:17:20.775 --> 00:17:24.435 Paying an anomaly bill and giving a field a mass are different requirements. 00:17:25.735 --> 00:17:30.320 Two verdicts, kept apart on purpose: the bill before and after, and the massless 00:17:30.320 --> 00:17:34.865 count before and after. The same field can pay one and not the other, because 00:17:34.865 --> 00:17:38.155 the charge that cancels an anomaly is not in general the charge a mass term 00:17:38.155 --> 00:17:42.285 needs. The surviving count is a lower bound — the rank test assumes generic 00:17:42.285 --> 00:17:43.460 couplings. 00:17:46.602 --> 00:17:50.872 Open Scan. Walk the displayed finite space of boundary conditions and matter 00:17:50.872 --> 00:17:53.347 contents through the selected filters. 00:17:53.347 --> 00:17:56.977 The breaking filter tests which generators at phase zero survive at the numerically 00:17:56.977 --> 00:17:58.342 located minimum. 00:17:59.668 --> 00:18:01.908 Run the displayed finite sweep. 00:18:01.908 --> 00:18:05.878 Read the denominator, each filter in the funnel, the survivors and the unresolved 00:18:05.878 --> 00:18:10.893 cases. The interface counts boundary conditions and equivalence classes separately, 00:18:10.893 --> 00:18:14.238 so surviving rows are not automatically distinct theories. 00:18:15.535 --> 00:18:19.505 Surviving boundary conditions are not surviving theories: [p,q,r,s] ~ [p− 00:18:19.505 --> 00:18:25.185 1,q+1,r+1,s−1] is the same theory, so the headline is a pair of numbers. 00:18:25.185 --> 00:18:28.105 An undecided vacuum is counted apart from a no. 00:18:31.202 --> 00:18:33.767 Open One model, every verdict. 00:18:33.767 --> 00:18:36.922 Which of the instrument's answers about this model are about the THEORY, 00:18:36.922 --> 00:18:39.597 and which only about the frame you are standing in. 00:18:40.935 --> 00:18:44.385 Start the built-in example, then choose its displayed equivalent boundary 00:18:44.385 --> 00:18:48.730 condition. Compare the tags identifying properties of the theory and properties 00:18:48.730 --> 00:18:52.820 of the chosen frame. A changed coordinate description can move a displayed 00:18:52.820 --> 00:18:55.360 quantity without changing the physical theory. 00:18:56.668 --> 00:18:59.998 The tags compare quantities in the evaluated frames. 00:18:59.998 --> 00:19:03.628 Read boundary coordinates and the surviving symmetry separately. 00:19:03.628 --> 00:19:06.758 Reported energies share the potential normalization. 00:19:06.758 --> 00:19:10.778 Numerical agreement between the located minima is evidence for these evaluations, 00:19:10.778 --> 00:19:13.358 not an exhaustive global-minimum certificate. 00:19:16.468 --> 00:19:21.163 Open Simulator. Choose builder predictions, a top-Kaluza Klein Higgs-rate 00:19:21.163 --> 00:19:25.168 reference or the neutrino ring; compare calculated responses with their explicitly 00:19:25.168 --> 00:19:27.398 scoped experimental references. 00:19:28.735 --> 00:19:32.385 Load the published builder example and set the gauge coupling to one. 00:19:32.385 --> 00:19:36.330 Higgs masses now use analytic Fourier second derivatives, with an explicit 00:19:36.330 --> 00:19:41.000 truncation error bound. The export retains the actual coupling and phase, 00:19:41.000 --> 00:19:44.585 and distinguishes a chosen probe from a numerically located minimum. 00:19:45.935 --> 00:19:49.210 The thermal history belongs to a separate S U three benchmark and the stated 00:19:49.210 --> 00:19:53.190 supported regime. It is not a detector forecast or the thermal history of 00:19:53.190 --> 00:19:57.630 this builder. At commuting endpoints, the present mass dictionary does not 00:19:57.630 --> 00:20:01.020 identify a shifted W candidate to set the scale. 00:20:01.020 --> 00:20:05.085 That limitation does not imply that the phase-zero gauge group survives. 00:20:08.202 --> 00:20:12.542 Open Boundary conditions. Which boundary conditions are the same theory, 00:20:12.542 --> 00:20:15.262 walked as orbits rather than quoted as a theorem. 00:20:16.602 --> 00:20:20.547 Switch from the interval orbifold to the two-dimensional Z three example. 00:20:20.547 --> 00:20:24.887 The orbit structure and class count change with the specified boundary problem. 00:20:24.887 --> 00:20:29.422 Equivalence classes identify descriptions connected by the allowed transformations. 00:20:30.735 --> 00:20:35.415 The counts come out (N+1) squared at every N on S¹/ 00:20:35.415 --> 00:20:39.610 Z₂, which is Haba–Hosotani–Kawamura's theorem as a measurement. 00:20:39.610 --> 00:20:42.655 Press T squared /Z₃ and the answer changes. 00:20:45.802 --> 00:20:48.062 Open Classify an orbifold. 00:20:48.062 --> 00:20:51.777 The alphabet of an orbifold, derived from its rotation matrix and nothing 00:20:51.777 --> 00:20:52.732 else. 00:20:54.068 --> 00:20:57.738 Select the two-dimensional Z four rotation and classify it. 00:20:57.738 --> 00:21:01.053 The group-theoretic alphabet is derived from the matrix. 00:21:01.053 --> 00:21:05.108 You can enter another supported matrix, but an invalid finite-order hypothesis 00:21:05.108 --> 00:21:07.993 must be refused rather than silently classified. 00:21:09.335 --> 00:21:11.635 Nothing is entered but the matrix. 00:21:11.635 --> 00:21:15.530 A matrix of infinite order, or one whose characteristic polynomial is not 00:21:15.530 --> 00:21:20.405 a power of the m-th cyclotomic, comes back REFUSED rather than classified. 00:21:23.535 --> 00:21:27.610 Open Name the relations. Which equivalence relation on boundary conditions 00:21:27.610 --> 00:21:32.130 the literature already owns, and whether a proposed move set connects a class. 00:21:33.468 --> 00:21:37.738 Switch to the Z four boundary problem and judge the displayed proposed move. 00:21:37.738 --> 00:21:41.433 Read the local and global qualifications and the source attribution. 00:21:41.433 --> 00:21:45.193 A useful move in one boundary problem is not automatically a complete equivalence 00:21:45.193 --> 00:21:46.638 relation in another. 00:21:47.935 --> 00:21:51.675 The local/global distinction is the one that gets misquoted, and the page 00:21:51.675 --> 00:21:53.320 carries it explicitly. 00:21:56.468 --> 00:21:58.998 Open Conjugate boundary conditions. 00:21:58.998 --> 00:22:03.388 How many inequivalent CONJUGATE boundary conditions there are on S¹/Z₂ — 00:22:03.388 --> 00:22:07.568 and, because that count rests on a hypothesis nobody has settled, what each 00:22:07.568 --> 00:22:09.283 of the two answers would be. 00:22:10.602 --> 00:22:14.767 Increase the group rank and compare the two hypotheses printed in the table. 00:22:14.767 --> 00:22:17.712 Conjugate twists transform by congruence. 00:22:17.712 --> 00:22:21.107 Independent boundary transformations and one linked transformation lead to 00:22:21.107 --> 00:22:25.752 different classification questions, so the hypothesis travels with the count. 00:22:27.068 --> 00:22:30.648 What the panel puts on screen is the disagreement, not a number, and that 00:22:30.648 --> 00:22:35.023 is the point: the twists move by congruence rather than similarity, and independence 00:22:35.023 --> 00:22:39.053 decides between four classes flat in N and no finite count at all. 00:22:39.053 --> 00:22:42.028 What the label leaves unbroken is not a property of the label — the same 00:22:42.028 --> 00:22:44.993 verdict the ordinary panel reaches by another route. 00:22:44.993 --> 00:22:48.878 The exported card carries the hypothesis beside the count, so a number never 00:22:48.878 --> 00:22:51.338 travels without the condition it rests on. 00:22:54.468 --> 00:22:58.603 Open Brane kinetic terms. What happens to the tower when brane-localised 00:22:58.603 --> 00:23:01.888 kinetic terms make the masses stop being n/R. 00:23:03.202 --> 00:23:06.177 Increase the brane kinetic coefficient to twelve. 00:23:06.177 --> 00:23:10.467 The spectrum responds because the roots are no longer a simple integer tower. 00:23:10.467 --> 00:23:14.607 Compare the root conditions and normalization, then use the separate warped-unification 00:23:14.607 --> 00:23:16.827 card for coupling-running questions. 00:23:18.135 --> 00:23:21.360 The special functions are checked against mpmath at forty digits, and the 00:23:21.360 --> 00:23:24.955 c to 0 limit is computed in closed form by code that shares nothing with 00:23:24.955 --> 00:23:28.525 the solver. That limit found three real defects. 00:23:31.668 --> 00:23:36.233 Open Gravity–gauge · 3D. Which physical information a complete tower of masses 00:23:36.233 --> 00:23:39.363 leaves undetermined in a controlled gravity-gauge example. 00:23:40.668 --> 00:23:44.633 Select eta equal to minus zero point nine, then display the gauge kinetic 00:23:44.633 --> 00:23:49.588 function. The paired masses and the source response carry different information. 00:23:49.588 --> 00:23:54.318 The Wilson quantity here is a kinetic normalization, not a Higgs-mass prediction. 00:23:55.668 --> 00:23:59.053 The positive paired tensor NN and vector DD masses are protected by their 00:23:59.053 --> 00:24:01.143 common canonical operator. 00:24:01.143 --> 00:24:04.553 The gauge NN control has different boundaries and moves. 00:24:04.553 --> 00:24:08.628 The source position is in the extra dimension, not a laboratory location; 00:24:08.628 --> 00:24:11.598 the Wilson kinetic scale is not a Higgs mass. 00:24:11.598 --> 00:24:16.168 For p=1.1 a canonical bulk scalar realizes the family, with stability 00:24:16.168 --> 00:24:17.828 and cutoff still open. 00:24:20.935 --> 00:24:25.140 Open The literature. The reading list behind the series: what each paper 00:24:25.140 --> 00:24:28.530 publishes, and which ones a person has actually read. 00:24:29.868 --> 00:24:32.998 Filter the reading list to the complete- triple selection. 00:24:32.998 --> 00:24:36.908 Inspect the recorded sources and what each paper actually supplies. 00:24:36.908 --> 00:24:40.888 Keyword signals help navigate this corpus; they are not proofs, and this 00:24:40.888 --> 00:24:43.683 reading list is not an exhaustive map of the field. 00:24:45.002 --> 00:24:49.872 A signal is a keyword, and a keyword sweep misses whatever is phrased differently. 00:24:49.872 --> 00:24:53.342 Nothing is asserted from a signal alone, and the corpus is our reading list 00:24:53.342 --> 00:24:54.732 rather than the field. 00:24:57.868 --> 00:25:02.293 The second Simulator mode is the top Kaluza Klein Higgs-production reference. 00:25:02.293 --> 00:25:06.198 Its leading rate, finite tower and resummed comparison answer one specified 00:25:06.198 --> 00:25:07.563 model question. 00:25:08.868 --> 00:25:13.023 Move the Kaluza Klein scale to fifteen hundred gigaelectronvolts. 00:25:13.023 --> 00:25:16.238 Inspect the rate curve and the separate convergence display. 00:25:16.238 --> 00:25:20.318 The chosen comparison window is conditional, and a custom window is a user- supplied 00:25:20.318 --> 00:25:21.428 scenario. 00:25:24.535 --> 00:25:27.160 Select the four-dimensional neutrino ring. 00:25:27.160 --> 00:25:30.485 Calibration can hold the light mass and active-current deficit fixed while 00:25:30.485 --> 00:25:33.060 the required couplings are reconstructed. 00:25:33.060 --> 00:25:35.635 Six heavy pairs belong to this base model. 00:25:36.935 --> 00:25:41.200 Compare mu B equal to zero with five thousand kilo electron volts. 00:25:41.200 --> 00:25:45.195 The leading light mass and the heavy pair splittings carry different information. 00:25:45.195 --> 00:25:48.530 Read the approximation indicators alongside the spectrum. 00:25:51.668 --> 00:25:55.078 The C M S comparison uses published observed and expected curves with their 00:25:55.078 --> 00:25:59.838 bands. The overlay keeps the selected flavour and Dirac or Majorana hypothesis 00:25:59.838 --> 00:26:00.838 visible. 00:26:02.135 --> 00:26:05.175 Choose muon flavour and the Majorana reference. 00:26:05.175 --> 00:26:09.580 Inspect the per-component convention, mass domain and reference ratios. 00:26:09.580 --> 00:26:13.275 The ring overlay is not a likelihood that includes its complete flavour structure, 00:26:13.275 --> 00:26:16.255 decay acceptance and multi-state interference. 00:26:19.402 --> 00:26:22.457 The decay card starts from the weak-channel scenario. 00:26:22.457 --> 00:26:25.977 Select a heavy pair and inspect where its width goes, its lifetime and the 00:26:25.977 --> 00:26:27.882 fixed-boost flight estimate. 00:26:29.202 --> 00:26:31.977 Include the calculated Majoron channels. 00:26:31.977 --> 00:26:34.957 The width and the derived lifetime respond together. 00:26:34.957 --> 00:26:38.002 An extra width is a separate user hypothesis. 00:26:38.002 --> 00:26:41.902 Read the isolated-pair and overlap diagnostics before interpreting the same- sign 00:26:41.902 --> 00:26:43.777 over opposite-sign ratio. 00:26:45.068 --> 00:26:48.348 Change the fixed boost to ten and inspect the flight curve. 00:26:48.348 --> 00:26:51.828 This illustrates the supplied kinematic scenario; it does not integrate a 00:26:51.828 --> 00:26:54.573 detector acceptance or a production spectrum. 00:26:57.668 --> 00:27:02.298 Three sterile copies reconstruct the chosen light masses and mixing orientation. 00:27:02.298 --> 00:27:06.218 The mass ordering, phases and active deficits are inputs. 00:27:06.218 --> 00:27:09.463 The card also displays eighteen heavy-pair flavour weights. 00:27:10.802 --> 00:27:13.612 Change the Dirac phase to ninety degrees. 00:27:13.612 --> 00:27:17.322 Compare neutrino and antineutrino appearance in the unitary vacuum limit, 00:27:17.322 --> 00:27:19.662 then inspect the flavour fractions. 00:27:19.662 --> 00:27:23.347 Majorana phases cancel from these oscillation curves but can affect the displayed 00:27:23.347 --> 00:27:25.437 light-sector double-beta quantity. 00:27:28.535 --> 00:27:32.100 This experiment holds the chosen light masses and mixing orientation fixed 00:27:32.100 --> 00:27:34.670 while reconstructing a parameter path. 00:27:34.670 --> 00:27:37.160 The green strip tells you what is fixed. 00:27:37.160 --> 00:27:41.660 The five figures separate heavy masses, splitting, current factors, small 00:27:41.660 --> 00:27:43.655 differences and reference data. 00:27:45.002 --> 00:27:48.167 Move the selected position from one tenth to eight tenths along the mu B 00:27:48.167 --> 00:27:52.452 path. The mass stays fixed while the pair splitting changes. 00:27:52.452 --> 00:27:55.192 The open circle tracks the selected point. 00:27:55.192 --> 00:27:59.257 Equal light inputs therefore do not determine every heavy-sector response. 00:28:00.602 --> 00:28:04.032 Now choose the common active deficit and its upper endpoint. 00:28:04.032 --> 00:28:08.202 The raw vacuum current factor is suppressed, but the specified near normalization 00:28:08.202 --> 00:28:10.262 cancels the common factor. 00:28:10.262 --> 00:28:13.492 The difference figure labels numerical coincidence rather than amplifying 00:28:13.492 --> 00:28:14.587 roundoff. 00:28:15.935 --> 00:28:18.165 Choose deficit direction three. 00:28:18.165 --> 00:28:21.080 Unequal deficits can leave a shape response. 00:28:21.080 --> 00:28:24.240 The fourth graph magnifies an absolute difference that is difficult to see 00:28:24.240 --> 00:28:26.230 in the overlapping curves. 00:28:26.230 --> 00:28:30.730 Its scale is explicit, and the exported samples retain their original precision. 00:28:32.068 --> 00:28:35.473 The DeepCore map uses the archived twenty- eighteen standard-three-neutrino 00:28:35.473 --> 00:28:39.898 tables. The cross stays fixed along the ring path because these light inputs 00:28:39.898 --> 00:28:44.013 stay fixed. The map is not a nonunitary ring likelihood and is not added 00:28:44.013 --> 00:28:45.398 to NuFIT. 00:28:46.735 --> 00:28:50.230 To move the cross, change sine squared theta twenty-three in the flavour 00:28:50.230 --> 00:28:53.790 card. Here it is set to zero point six. 00:28:53.790 --> 00:28:56.445 The reference updates for the new light input. 00:28:56.445 --> 00:29:00.820 Outside its published grid the laboratory withholds a value instead of extrapolating. 00:29:03.935 --> 00:29:08.470 This paper-model experiment reconstructs the stated flat S U six potential. 00:29:08.470 --> 00:29:12.095 Matter content and the winding cutoff are explicit controls. 00:29:12.095 --> 00:29:15.335 A small Wilson minimum must be read with its convergence check. 00:29:16.668 --> 00:29:20.763 Set the winding cutoff to ten and inspect the shifted minimum and comparison. 00:29:20.763 --> 00:29:24.023 A finite truncation can change the apparent result. 00:29:24.023 --> 00:29:27.383 The supported potential can be transferred to the builder; this does not 00:29:27.383 --> 00:29:29.628 certify a complete flavour model. 00:29:32.735 --> 00:29:35.780 The warped-unification card compares differential gauge running under the 00:29:35.780 --> 00:29:37.800 selected matter assignment. 00:29:37.800 --> 00:29:41.240 Required ultraviolet boundary terms and their residuals are outputs of that 00:29:41.240 --> 00:29:42.940 stated approximation. 00:29:44.268 --> 00:29:46.803 Switch the matter assignment to C two. 00:29:46.803 --> 00:29:50.353 The running differences and required boundary terms respond. 00:29:50.353 --> 00:29:53.703 The naive-dimensional-analysis reference is a scale estimate. 00:29:53.703 --> 00:29:58.018 The separate localization probe is not a complete fermion-spectrum calculation. 00:30:01.135 --> 00:30:04.080 The thermal card is its own S U three benchmark. 00:30:04.080 --> 00:30:07.890 It uses named paper cases and compares potential cutoffs. 00:30:07.890 --> 00:30:11.275 A stored matching PhaseTracer result is available offline for the recorded 00:30:11.275 --> 00:30:12.375 inputs. 00:30:13.668 --> 00:30:17.198 Load paper case two and compare the potential and phase flow. 00:30:17.198 --> 00:30:20.863 Coexistence and a nucleation proxy are different questions. 00:30:20.863 --> 00:30:24.498 A new point needs a matching bounce calculation; changing the builder model 00:30:24.498 --> 00:30:27.508 does not turn this benchmark into its thermal history. 00:30:28.802 --> 00:30:32.492 The new comparison runs PhaseTracer and CosmoTransitions on the same S U 00:30:32.492 --> 00:30:34.887 three potential and canonical field. 00:30:34.887 --> 00:30:37.922 Nine matched temperatures compare the bounce action. 00:30:37.922 --> 00:30:41.597 The programs share shooting-method ancestry, so agreement is a numerical 00:30:41.597 --> 00:30:46.137 cross-check, not an independent interval proof or an experimental validation. 00:30:47.468 --> 00:30:51.238 The table changes the spatial and thermal Fourier cutoffs together. 00:30:51.238 --> 00:30:55.178 T one-forty solves S three over T equal to one hundred forty. 00:30:55.178 --> 00:31:00.098 It is a proxy, separate from the integrated nucleation and percolation results. 00:31:00.098 --> 00:31:03.718 The older displayed proxy used a looser shooting tolerance; compare like 00:31:03.718 --> 00:31:06.108 settings before interpreting a difference. 00:31:07.402 --> 00:31:09.767 Open the numerical diagnostics. 00:31:09.767 --> 00:31:13.432 Tolerance shifts, profile sampling and the virial residual test different 00:31:13.432 --> 00:31:15.567 aspects of the calculation. 00:31:15.567 --> 00:31:19.597 The targets are numerical criteria, not confidence levels. 00:31:19.597 --> 00:31:24.467 Higher loops, thermal resummation and plasma dynamics remain unquantified. 00:31:24.467 --> 00:31:28.717 These S U three examples are separate from the S U seven mass certificates. 00:31:30.002 --> 00:31:32.637 Change the coupling away from the reference. 00:31:32.637 --> 00:31:36.137 The archived solver comparison disappears because all thermal inputs must 00:31:36.137 --> 00:31:40.487 match. A stale certificate must not follow an edited point. 00:31:40.487 --> 00:31:44.052 Load a named paper case again to recover its evidence; a new point needs 00:31:44.052 --> 00:31:45.587 a new calculation. 00:31:46.935 --> 00:31:50.250 Reload case two and save the experiment JSON. 00:31:50.250 --> 00:31:54.780 It retains both solver versions, tolerances, cutoffs and sources. 00:31:54.780 --> 00:31:58.685 The thermal potential is credited to Hirose and Shibuya, CosmoTransitions 00:31:58.685 --> 00:32:02.875 to Carroll Wainwright, and PhaseTracer to Athron and collaborators. 00:32:02.875 --> 00:32:05.580 Keep this provenance with every exported result. 00:32:08.668 --> 00:32:12.288 Integrated transition history uses refined action tables. 00:32:12.288 --> 00:32:15.918 Read nucleation, percolation and completion separately. 00:32:15.918 --> 00:32:19.453 The false-vacuum fraction and physical- volume condition make those distinctions 00:32:19.453 --> 00:32:20.448 visible. 00:32:21.735 --> 00:32:25.000 Set the assumed wall speed to zero point eight and the fluid efficiency to 00:32:25.000 --> 00:32:29.790 zero point one. Compare the history and conditional acoustic spectrum. 00:32:29.790 --> 00:32:33.595 Wall friction, plasma evolution and detector significance are not calculated 00:32:33.595 --> 00:32:35.125 by these controls. 00:32:38.268 --> 00:32:42.203 This warped-model experiment separates ultraviolet and infrared anomaly factors, 00:32:42.203 --> 00:32:45.463 gauge cancellation and the baryon-current matrix. 00:32:45.463 --> 00:32:49.503 Its sources and approximation are distinct from the base S U seven ledger. 00:32:50.802 --> 00:32:54.292 Remove the lepton generations in this test configuration. 00:32:54.292 --> 00:32:57.752 The imbalance exposes a gauge anomaly that needs completion. 00:32:57.752 --> 00:33:01.727 A nonzero baryon-current anomaly is a separate statement; it is not a computed 00:33:01.727 --> 00:33:04.497 proton lifetime or baryogenesis yield. 00:33:07.602 --> 00:33:10.992 Begin with the stored Standard Model-like scalar reference. 00:33:10.992 --> 00:33:14.592 Local couplings determine production rates, partial widths and branching 00:33:14.592 --> 00:33:18.812 fractions. Matching HiggsBounds and HiggsSignals calculations use pinned 00:33:18.812 --> 00:33:20.687 experimental datasets. 00:33:22.002 --> 00:33:25.042 Add one mega electron volt of invisible width. 00:33:25.042 --> 00:33:28.702 The local predictions update, and the old experimental result is withdrawn 00:33:28.702 --> 00:33:31.257 because its inputs no longer match. 00:33:31.257 --> 00:33:34.462 Run the optional engine or import a matching result before assigning a new 00:33:34.462 --> 00:33:36.102 experimental verdict. 00:33:39.202 --> 00:33:43.562 Every menu section, Simulator mode and experiment card now has a Demo button, 00:33:43.562 --> 00:33:45.537 marked with a film clapper. 00:33:45.537 --> 00:33:49.577 It presses the real controls, explains each step in a banner, and ends with 00:33:49.577 --> 00:33:54.482 how to read the result. Here the Kaluza Klein gluon card starts its own demo. 00:33:55.802 --> 00:33:59.892 Stop the demo and take over: load the published R S point of Casagrande and 00:33:59.892 --> 00:34:03.622 collaborators, with all nine of its quark bulk masses. 00:34:03.622 --> 00:34:07.042 The card computes the couplings of a warped Kaluza Klein gluon to zero-mode 00:34:07.042 --> 00:34:11.012 quarks, its width and branching fractions, and compares its leading-order 00:34:11.012 --> 00:34:15.232 rates with the ATLAS top-pair limit and the C M S dijet limit as r, prediction 00:34:15.232 --> 00:34:16.377 over limit. 00:34:17.668 --> 00:34:21.748 At three point seven five tera electron volts, r for the top pair is close 00:34:21.748 --> 00:34:25.318 to one: the two thousand eight reference point sits at the edge of the ATLAS 00:34:25.318 --> 00:34:29.938 comparison. That is a comparison with ATLAS's thirty percent width benchmark, 00:34:29.938 --> 00:34:32.438 not a validated exclusion at this width. 00:34:33.735 --> 00:34:37.510 Below the plots, the top-pair mass spectrum is computed with the interference 00:34:37.510 --> 00:34:41.555 between the Kaluza Klein gluon and the Q C D gluon, in the fifteen bins of 00:34:41.555 --> 00:34:44.080 the C M S parton-level measurement. 00:34:44.080 --> 00:34:47.745 For this point the light-quark and top couplings have opposite signs, so 00:34:47.745 --> 00:34:50.360 the interference is constructive below the pole. 00:34:51.668 --> 00:34:56.473 Now load the flat G H U coloron at four point five tera electron volts. 00:34:56.473 --> 00:35:00.653 Every quark couples equally, the couplings share one sign, and the interference 00:35:00.653 --> 00:35:04.113 turns destructive: the low bins go down instead of up. 00:35:05.402 --> 00:35:09.412 The last plot is the expected delta chi squared against the measured covariance, 00:35:09.412 --> 00:35:12.557 with ten percent S M theory uncertainty per bin. 00:35:12.557 --> 00:35:15.737 Set that uncertainty to zero and the reach moves from about three point eight 00:35:15.737 --> 00:35:18.397 to about five tera electron volts. 00:35:18.397 --> 00:35:22.267 With the same ten percent taken as one correlated normalisation, delta chi 00:35:22.267 --> 00:35:25.882 squared would be five point three instead of one point eight: the reach depends 00:35:25.882 --> 00:35:28.902 on that assumption, and the card shows both. 00:35:28.902 --> 00:35:32.937 It is a sensitivity if the data equal the S M, not an exclusion, and the 00:35:32.937 --> 00:35:37.467 open certificates show the independent Dirac-trace and L H A P D F check. 00:35:40.602 --> 00:35:44.742 The boundary research card separates four questions: a fermion mass gap, 00:35:44.742 --> 00:35:48.742 independent profiles, parity-inserted traces and a restricted six-dimensional 00:35:48.742 --> 00:35:52.407 tensor condition. Load the research baseline. 00:35:52.407 --> 00:35:56.187 These are diagnostic tools, not a completed particle model. 00:35:57.535 --> 00:36:00.660 The two-dimensional map shows the lightest paired mass. 00:36:00.660 --> 00:36:04.225 The horizontal axis is boundary coupling and the vertical axis is the imposed 00:36:04.225 --> 00:36:09.295 Wilson angle. Darker means larger mass, on the fixed colour scale. 00:36:09.295 --> 00:36:12.715 The white point is the selected calculation and the red line fixes the coupling 00:36:12.715 --> 00:36:17.285 for the curve below. Select or drag a point, then release to update the input 00:36:17.285 --> 00:36:18.430 values. 00:36:19.735 --> 00:36:22.230 Switch to the three-dimensional surface. 00:36:22.230 --> 00:36:25.985 Height and colour encode exactly the same mass data as the map. 00:36:25.985 --> 00:36:29.590 Change the viewing angle to see the surface clearly; that angle changes the 00:36:29.590 --> 00:36:35.075 camera, not the physics. Selecting the surface uses the nearest sampled node. 00:36:35.075 --> 00:36:37.830 The map remains available for precise selection. 00:36:39.135 --> 00:36:42.370 Return to the map and set the boundary coupling to zero. 00:36:42.370 --> 00:36:46.785 The first normal root vanishes, and the paired and unpaired curves coincide. 00:36:46.785 --> 00:36:50.430 Restoring coupling one opens a normal gap of about zero point two seven four 00:36:50.430 --> 00:36:52.570 in units of inverse radius. 00:36:52.570 --> 00:36:57.205 The Wilson angle is supplied here; this calculation does not find the vacuum. 00:36:58.535 --> 00:37:01.725 Set the separate profile example to zero mass. 00:37:01.725 --> 00:37:06.010 One Gram eigenvalue becomes numerically zero, so these three profiles span 00:37:06.010 --> 00:37:08.375 only two independent directions. 00:37:08.375 --> 00:37:12.090 The bars use a linear scale and the printed values show their size. 00:37:12.090 --> 00:37:14.710 A numerical threshold is displayed above them. 00:37:16.002 --> 00:37:20.542 Restore profile mass one. All three eigenvalues are positive, despite 00:37:20.542 --> 00:37:25.062 nonzero overlaps. Overlap means the profiles are not orthogonal; 00:37:25.062 --> 00:37:27.602 dependence would require a null direction. 00:37:27.602 --> 00:37:31.357 This example tests linear independence, not the origin of three physical 00:37:31.357 --> 00:37:32.512 families. 00:37:33.802 --> 00:37:36.722 Switch from the six-dimensional corner insertion to the four-dimensional 00:37:36.722 --> 00:37:40.932 intersection insertion. The exact trace table changes. 00:37:40.932 --> 00:37:45.172 A nonzero evaluation detects a nonzero polynomial, but a zero at one probe 00:37:45.172 --> 00:37:47.477 cannot establish cancellation. 00:37:47.477 --> 00:37:52.182 Local normalization, mirror contributions and anomaly inflow are still required. 00:37:53.468 --> 00:37:57.073 One identical six-dimensional family with opposite lepton chirality fails 00:37:57.073 --> 00:37:59.243 the restricted doublet condition. 00:37:59.243 --> 00:38:03.748 Three families pass. The condition allows multiples of three; it does not 00:38:03.748 --> 00:38:07.663 select exactly three, and it is not the full anomaly test of the higher-dimensional 00:38:07.663 --> 00:38:08.793 orbifold. 00:38:10.135 --> 00:38:12.390 Keep the assumptions with the result. 00:38:12.390 --> 00:38:16.345 Save the card data to preserve every input, the sampled mass grid, exact 00:38:16.345 --> 00:38:19.595 moments, sources and unresolved requirements. 00:38:19.595 --> 00:38:24.345 The guide explains the equations, examples, controls and failure cases. 00:38:24.345 --> 00:38:28.085 The overall quantum consistency remains an open research question. 00:38:31.202 --> 00:38:34.462 Use a comparison snapshot before changing a point. 00:38:34.462 --> 00:38:39.852 Save the experiment JSON to retain the inputs, calculated arrays, assumptions, 00:38:39.852 --> 00:38:42.437 provenance and optional saved reference. 00:38:42.437 --> 00:38:45.887 The global result card and LaTeX exports provide another view of the selected 00:38:45.887 --> 00:38:47.197 calculation. 00:38:48.535 --> 00:38:51.330 Choose a figure and save its vector SVG. 00:38:51.330 --> 00:38:55.510 The new neutrino figures carry sampled data and provenance in their metadata. 00:38:55.510 --> 00:38:59.200 The link button preserves controls in the address; archive external results 00:38:59.200 --> 00:39:01.780 and comparisons in JSON as well. 00:39:03.068 --> 00:39:06.763 The browser calculations and stored references run offline. 00:39:06.763 --> 00:39:10.788 New HiggsTools and PhaseTracer points use the optional local engine. 00:39:10.788 --> 00:39:14.793 The source repository contains the reproduction commands, independent checks 00:39:14.793 --> 00:39:19.373 and archived studies. Return to a chapter, vary one assumption, and 00:39:19.373 --> 00:39:21.628 keep the scope beside every result. 00:39:22.900 --> 00:39:29.815 Open Quantization and certificates in the new research menu. These are independent diagnostics, with exact 00:39:29.815 --> 00:39:37.225 rational inputs and separate assumptions. The guided demo changes real controls. A passing arithmetic 00:39:37.225 --> 00:39:44.900 criterion is one ingredient of consistency. It does not certify a complete gauge Higgs model. 00:39:45.650 --> 00:39:54.185 Choose C over two. The universal class fails, while periods on closed spin four manifolds pass. This is not 00:39:54.185 --> 00:40:02.555 a contradiction. The tests use different backgrounds. The universal test detects a period of one half. On 00:40:02.555 --> 00:40:09.510 the stated spin backgrounds, the period of Y squared is even. That topological fact is external to the Lean 00:40:09.510 --> 00:40:12.108 arithmetic proof. 00:40:12.858 --> 00:40:19.293 The diamonds are universal integral classes. The rings between them pass only the closed spin four period 00:40:19.293 --> 00:40:27.248 test. The cross marks the current alpha and delta, at fixed beta. Select a lattice point in the application 00:40:27.248 --> 00:40:35.433 and the input gamma changes exactly. These are mathematical criteria, not experimental measurements. Outside 00:40:35.433 --> 00:40:42.733 the displayed window, the interface reports the exact coordinates instead of clipping a point to the border. 00:40:43.483 --> 00:40:51.028 Now choose C over thirty six. The covering direction gives an integer, one. But the displayed quotient 00:40:51.028 --> 00:40:58.483 cocharacter gives one over thirty six. Checking a convenient covering direction can miss a forbidden period. 00:40:58.483 --> 00:41:05.153 Read the witness together with the criterion. The application uses exact fractions, not a floating point 00:41:05.153 --> 00:41:07.358 tolerance. 00:41:08.108 --> 00:41:15.773 Choose A plus B. Alpha and beta are one; gamma is seven twelfths. After changing to the integral basis, 00:41:15.773 --> 00:41:23.458 delta is zero. Both criteria pass. The fractional contributions have to be combined before judging the total 00:41:23.458 --> 00:41:30.900 class. The controls, the witness and the exported result all use the same calculation. 00:41:31.650 --> 00:41:38.390 The axion panel uses the normalization of Choi and collaborators. The integer combination eighteen K two 00:41:38.390 --> 00:41:46.615 plus twenty four K three plus K one must be divisible by thirty six. The default zero, one, twelve satisfies 00:41:46.615 --> 00:41:54.150 it. This reproduces the published q equals six condition. Identifying this axion with the gauge Higgs field 00:41:54.150 --> 00:41:58.650 remains a separate, unresolved physical question. 00:41:59.400 --> 00:42:05.580 The parent map has two columns and a common annihilator. With the inherited spectrum and ordinary integral 00:42:05.580 --> 00:42:13.205 Green Schwarz sources, six times the annihilator is sixteen minus three p minus three q minus six r. For 00:42:13.205 --> 00:42:21.335 integer pairings it is one modulo three, so it cannot vanish. Lean proves that arithmetic for all integers. 00:42:21.335 --> 00:42:27.650 Allowed orbifold backgrounds and extra corner responses are not settled by this result. 00:42:28.400 --> 00:42:35.175 The U two example shows why joint integrality differs from separate factor requirements. With b zero equal 00:42:35.175 --> 00:42:42.665 to one and b one equal to six, the quadratic form is m squared plus m n plus n squared. It is integral for 00:42:42.665 --> 00:42:48.895 every integer pair. The formal criterion also covers rational coefficients with a common nonzero 00:42:48.895 --> 00:42:55.442 denominator. This example is not an anomaly free supergravity spectrum. 00:42:56.192 --> 00:43:04.067 Change b one from six to five. Each cell is a cocharacter labelled by integers m and n. Its printed fraction 00:43:04.067 --> 00:43:11.922 and color are Q modulo one, calculated with exact integer arithmetic. The point one, zero now has period 00:43:11.922 --> 00:43:19.732 seven eighths: a concrete witness of failure. Returning b one to six makes every cell integral. The eighty 00:43:19.732 --> 00:43:26.608 one cells illustrate the criterion; the Lean theorem establishes it for all integer pairs. 00:43:27.358 --> 00:43:33.933 For the Spin twenty audit, the degree eighteen Clifford element squares to minus one. Multiplication by 00:43:33.933 --> 00:43:40.183 minus i makes the representation matrix square to plus one. This distinction matters for an ordinary 00:43:40.183 --> 00:43:48.218 isotropy lift. It does not prove the model inconsistent: a twisted or combined action may be possible. Every 00:43:48.218 --> 00:43:55.108 field and interaction, including bosonic Omega, must share a specified action. 00:43:55.858 --> 00:44:01.998 The catalogue includes four Lean files with forty nine theorem declarations, the exact audit scripts, 00:44:01.998 --> 00:44:09.803 recorded checks and file hashes. All four files replay with Lean four point twenty seven. The older S U 00:44:09.803 --> 00:44:16.688 seven file was adapted from List bind to List flat Map, keeping its theorem statements. Download the 00:44:16.688 --> 00:44:24.123 evidence, verify its integrity and run the listed commands. Full anomaly cancellation and scientific novelty 00:44:24.123 --> 00:44:26.400 remain open.