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 [H]; T-297 no gauge $Z'$, stratified by T-329 — none in the doublet sector [C at (Cl)], none at any energy [H]; the FE-uniqueness without leptoquarks — [H] in the axis picture, [C at (Cl)] through T-326; $N_{gen}=3$) are not silence — at every live frontier they commit UHM to a definite prediction, usually the boldest one on the table. Where T-297 or the FE-uniqueness carries a row, the prediction is the stake of a hypothesis, not a consequence of a theorem (it was presented as a theorem until 2026-09-25): 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 [H ← T-297, FE-uniqueness; T-296] (read "[T ← T-296,297]" until 2026-09-25): 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 [H ← no new bosons (T-297, FE-uniqueness) or scalars (T-296)]	open (any signal falsifies)
3	Lepton universality $R_K, R_{K^*}$	Leptoquark/$Z'$ models predicted deviations	Exact universality [H ← FE without X,Y; T-297] (read [T] until 2026-09-25)	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 [H] (T-297; a gauged $B-L$ near the seesaw scale would put a $Z'$ beyond any collider, so nulls do not test it). Stratified by T-329: no $Z'$ in the doublet sector [C at (Cl)]; none within collider reach if $B-L$ breaks at the seesaw scale	LHC nulls ✓ open
12	Charged Higgs $H^\pm$	2HDM/MSSM: within HL-LHC reach	Does not exist [H ← T-296] (read [T-296] as a theorem until 2026-09-25)	open (discovery falsifies UHM at $\kappa_0$)

Experimental reach: what any of this can decide, and when

The ledger's content is not exhausted by "falsifiable in principle". Set against the reach of funded and planned experiments, the twelve rows sort into three groups — and only the last is decidable soon.

Prediction	Reach of the relevant experiment	Verdict on timing
$\tau_p \sim 10^{37\text{–}38}$ yr	Hyper-K reaches $\sim 10^{35}$ yr	2–3 orders beyond reach; needs a megaton class not yet planned
$m_{\beta\beta}$ in the meV band (normal ordering)	LEGEND-1000 / nEXO reach $\sim 10$–$20$ meV	below reach: the next generation sees the same "emptiness"
$M_R \approx 2.9\times10^{14}$ GeV; $O$-relic at $\sim10^{13}$ GeV	no direct probe at these scales	not directly testable
$m_a \sim 3$ neV ($f_a \approx 2\times10^{15}$ GeV)	GUT-scale axion searches	plausibly reachable in the 2030s
Normal neutrino mass ordering	JUNO, DUNE	decidable within years — one honest bit
Rows 1–4, 10–12 (prohibitions)	LHC / MEG-II / Mu3e / Mu2e / LZ …	any positive signal falsifies; null results merely keep the block alive

Read together with the prohibition rows, the honest summary is: the theory forbids essentially everything that could be seen in the next fifteen years, predicts positively what cannot be seen in them, and stakes one decidable bit (the neutrino ordering). This is a real, but narrow, exposure — and it is the strongest reason to treat the physics sector as a research programme rather than a confirmed derivation.

Reading the ledger. Rows 1–4 and 10–12 are prohibition-driven: they follow from the same three structural results — of which T-297 and the FE-uniqueness are hypotheses [H] since 2026-09-25 — 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.