Frontier Ledger: UHM vs the Field

Why this page

A mature theory must compete where others already predict. UHM's structural prohibitions (T-296 no second doublet, T-297 no gauge $Z'$, $N_{gen}=3$, FE-uniqueness without leptoquarks) are not silence — at every live frontier they force a definite prediction, usually the boldest one on the table: exact Standard-Model emptiness where competitors expect signals, and definite positive signals elsewhere (O-sector relic, axion, proton decay, Majorana $0\nu\beta\beta$). Each row is falsifiable; several have already been graded by experiment.

#	Frontier	Competitors predict	UHM predicts	Status
1	Muon $g{-}2$	SUSY/2HDM/$Z'$/leptoquark contributions explain the (g−2) anomaly	Zero BSM contribution [T ← T-296,297]: experiment must converge to the full lattice SM value	Lattice HVP (BMW-class) already drifts toward SM ✓ open
2	LFV: $\mu\to e\gamma$, $\mu\to 3e$, $\mu N\to eN$	Many BSM: rates near current bounds	Neutrino-loop floor only ($\sim10^{-54}$): MEG-II, Mu3e, Mu2e see nothing [T ← no new bosons/scalars]	open (any signal falsifies)
3	Lepton universality $R_K, R_{K^*}$	Leptoquark/$Z'$ models predicted deviations	Exact universality [T ← FE without X,Y; T-297]	LHCb 2022 returned to SM ✓ post-factum pass
4	Electron EDM	SUSY/2HDM: $10^{-29}$–$10^{-30}\,e\cdot$cm	EDM desert: no new CP phases without a second doublet ⇒ $d_e\sim$ SM $10^{-38}$ [T-consequence + [C] phase-completeness]	ACME/JILA bound $10^{-30}$ — desert holds ✓ open
5	$0\nu\beta\beta$	Ranges from forbidden (Dirac) to large $m_{\beta\beta}$	Allowed, Majorana (see-saw, derived $M_R\approx2.9\times10^{14}$ GeV) with normal hierarchy ⇒ $m_{\beta\beta}$ in the meV band: null for LEGEND/nEXO, signal for the generation after [C]	open; exact $m_{\beta\beta}$ = ready-input computation (task)
6	Proton decay	Minimal SU(5): $10^{34-36}$ yr (partly dead)	$\tau_p\sim10^{37-38}$ yr [C]: Hyper-K sees nothing; megaton class needed	open ✓ consistent with SK bound
7	WIMP direct detection	WIMPs at XENON/LZ sensitivity	Permanent null: DM = O-sector Wimpzilla $10^{13}$ GeV + $\sim1\%$ axion $m_a\sim3$ neV (candidates)	nulls keep arriving ✓ open
8	Higgs self-coupling	SM exact; BSM: various	$\delta\lambda/\lambda \sim 10^{-2}$–$10^{-3}$ [C] — invisible to HL-LHC, resolvable at FCC	open
9	Neutrino hierarchy	Both orderings on the market	Normal (from $m_2/m_3$ spectral ratio)	JUNO will grade this within years
10	Light sterile neutrinos	LSND/MiniBooNE-class hints	None exist [T ← $N_{gen}=3$]: anomalies must dissolve	MicroBooNE already deflating ✓ open
11	Dilepton resonances ($Z'$,$W'$)	GUT/string spectra	Permanent null at any energy [T-297]	LHC nulls ✓ open
12	Charged Higgs $H^\pm$	2HDM/MSSM: within HL-LHC reach	Does not exist [T-296]	open (discovery falsifies UHM at $\kappa_0$)

Reading the ledger. Rows 1–4 and 10–12 are prohibition-driven: they follow from the same three structural theorems, so one confirmed BSM discovery in any of them breaks the whole block — UHM is maximally exposed, which is what falsifiability means. Rows 5–9 are positive UHM numbers with named experiments. Post-factum passes (row 3; the deflation trends in 1 and 10) are graded honestly: predictions written after the data count only as consistency, never as discovery.