New Physics Predictions
What GTE forbids (SUSY, axion, dark photon, extra dimensions) and what it predicts (mirror dark sector, GTE-P7 at 211.9 MeV, proton topological stability, ΛGTE = 2.03 GeV). Every item is derived, not assumed.
Why the LHC Has Found Nothing Beyond the Higgs
Since the Higgs boson was confirmed in 2012, the Large Hadron Collider has found no evidence of physics beyond the Standard Model — no supersymmetric particles, no extra dimensions, no new forces. Many BSM theories predicted particles that should already have appeared at TeV energies. They have not.
What GTE Forbids: Structural Absences
The following are not merely unpredicted — they are structurally impossible within the GTE certificate structure. Every null experimental result is a confirmed GTE prediction.
What GTE Predicts: The Mirror Dark Sector
The Z₇ arithmetic that generates the SM winding sectors {0,2,3,4,6} does not exhaust Z₇. The complementary sectors {1,5} are equally consistent with Z₇ arithmetic — they form the mirror branch, a dark sector forced by the same arithmetic as the SM itself.
Mirror particles carry SU(3)dark color and no SM gauge charges: no electric charge, no SM weak charge, no SM color. The winding algebra forbids SM-gauge coupling at dimension-4. They are dark by construction.
These masses are CatAD: derived from the same cascade formula that gives SM lepton masses at 0.295% RMS precision, applied to mirror-branch winding inputs. The mass ratios are predicted: mχ₂/mχ₁ = 45.4. If any one mass is confirmed, the theory predicts where to find the other two.
GTE-P7: The Highest-Priority New Physics Signal
Dark lepton resonance at 211.9 MeV
GTE-P7 is a resonance appearing in the Elegant Kernel computation for the mirror branch — derived from the same UCL pipeline that generates SM lepton masses, applied to a specific mirror-branch cascade triple. Its mass arises from the mirror-branch winding sector with zero free parameters.
The 211.9 MeV mass lies in the range accessible to Belle II, currently taking data. Observable channels: e⁺e⁻ → χ + invisible (single charged track + missing energy), and displaced-vertex signatures with centimeter-scale decay length.
Other Key Predictions
Proton topological stability (dimension-4)
Baryon number is a topological charge of the Z₇ winding field: B = (1/3)Σj χq(wj). Topological charges cannot change under any local field operator of dimension ≤ 4. Dimension-4 proton decay is structurally impossible — not merely suppressed.
Important: Dimension-6 operators (GUT-scale suppressed, ~MGUT⁻²) are not forbidden. The standard GUT channel p → e⁺π⁰ may exist at dimension-6.
The ΛGTE = 2.03 GeV scale
The kink dissolution threshold ΛGTE = 7 × Mkink = (8/7)mτ ≈ 2.03 GeV is where individual kinks dissolve into the ΦMDL substrate. This is derived, not tunable — it is fixed by mτ and |Z₇| = 7, both of which are themselves derived.
Observable signatures near √s ≈ 2 GeV: a change in the effective number of hadronic degrees of freedom, anomalous energy deposition patterns, and a transition in the kink structure function observable in lattice QCD calculations.
Gravitational wave background from Z₇ phase transition
The Z₇ domain-wall annihilation at TG ≈ 0.70 GeV produces a stochastic gravitational wave background peaked in the frequency band of the Einstein Telescope and LISA. The signal is generated by the collapse of the Kibble foam within ~10−24 s of formation.
Neutrino mass sum Σmν = 59.4 meV
The total neutrino mass sum (Normal Ordering) is derived from the GTE neutrino cascade, giving Σmν = 59.4 meV. Current cosmological constraint: Σmν < 120 meV (Planck 2018). The GTE prediction is comfortably inside the current bound and will be testable by CMB-S4 and Euclid at the ~10 meV level.
The Complete New-Physics Picture
| Item | GTE Position | Key Experiment |
|---|---|---|
| Supersymmetric particles | Absent (no winding sector) | LHC (confirmed null) |
| Axion | Absent (θQCD=0 from F₂₁) | ADMX, CASPEr (confirmed null) |
| Dark photon | Absent (no U(1) in dark sector) | NA64, Belle II (confirmed null) |
| Large extra dimensions | Absent (3+1D forced) | LHC (confirmed null) |
| GTE-P7 at 211.9 MeV | Predicted (CatAD) | Belle II — 50 ab⁻¹ by 2031 |
| χ₁ dark matter at 0.54 MeV | Predicted (CatAD) | Sub-MeV direct detection (future) |
| χ₃ at 3.60 GeV | Predicted (CatAD) | LHC mono-jet, Higgs invisible |
| Proton dim-4 decay: none | Forbidden (CatAL) | Hyper-K, DUNE |
| r = 0 primordial tensors | Predicted (CatA) | CMB-S4, LiteBIRD ~2028 |
| Z₇ phase transition GW background | Predicted (CatAD) | Einstein Telescope, LISA ~2030s |
| Σmν = 59.4 meV | Predicted (CatAD) | CMB-S4, Euclid ~2030 |
| ΛGTE ≈ 2.03 GeV threshold | Predicted (CatAD) | Lattice QCD, BES-III |
Key Points
- The absence of BSM physics at the LHC is a confirmed GTE prediction — the complete SM particle spectrum is exhausted by Z₇ winding sectors {0,2,3,4,6}, with no room for superpartners.
- GTE forbids structurally: SUSY particles, axions, dark photons, extra dimensions. The reasons are Lean-certified theorems, not assumptions.
- GTE predicts structurally: a mirror dark sector with masses 0.54 MeV / 24.5 MeV / 3.60 GeV; the GTE-P7 resonance at 211.9 MeV (highest-priority Belle II target); proton topological stability against dimension-4 decay; and a GW background from the Z₇ phase transition.
- All predictions are derived from the GTE polynomial with zero free parameters — the same arithmetic that gives ns, ηB, and the Higgs mass. They are genuine predictions, not post-hoc fits.
See Also
gte_baryon_number_topological_charge— BaryonNumber.lean ↗