Essay · Plain · 5 min

The 28 PT predictions in 5 minutes

A quick read of the Tier-1 register: 4 fundamental predictions, 6 numerical, 5 negative, 13 advanced. Each prediction has an explicit refutation criterion and an experiment that will test it within ten years.

Go deeper: T5 , BA5

Not a retrodiction

A theory reproducing 43 observables to 0.30 % is interesting. A theory that on top predicts 28 falsifiable quantities, with no way to fit them after the fact, is a different category. This is PT.

Predictive ratio: R_PT = 43:1 (43 observables reproduced from 1 input $s = 1/2$ ). Compare with the standard Standard Model, R_SM ≈ 2:1.

The 4 fundamental predictions

#	Prediction	Test	Deadline
P1	Neutrinos are Dirac, not Majorana	Detection of neutrinoless double beta $0\nu\beta\beta$ → falsifies PT	LEGEND, nEXO (~2035)
P2	Normal hierarchy: $m_1 < m_2 < m_3$	Inverted hierarchy at $> 5\sigma$ → falsifies PT	JUNO (~2027)
P3	$\theta_{\rm QCD} = 0$ exactly	No QCD axion needed	ADMX, IAXO
P4	$\delta_{\rm CP}({\rm PMNS}) = 197.358°$	Outside $[170°, 224°]$ at $5\sigma$ → falsifies PT	DUNE (~2032)

The 6 fine numerical predictions

#	Prediction	PT value	Error	Experiment
P5	$m_{\nu_3}$	0.0505 eV	0.44 %	KATRIN, JUNO
P6	$\sin^2\theta_{23}$	0.5733	0.04 %	DUNE
P7	$\sin^2\theta_{13}$	0.02222	0.07 %	JUNO
P8	$\lambda_H$ (Higgs self-coupling)	0.125 = $s^2/2$	1 %	HL-LHC
P9	$H_0$	67.41 km/s/Mpc	0.02 %	Euclid, JWST
P15	No Lorentz violation	SO(3,1) derived	—	Lorentz tests

The 5 negative predictions (PT forbids)

No parameter to adjust, hence no escape if experiment finds:

#	Negative prediction	Why PT forbids
P10	No QCD axion	$\theta_{\rm QCD} = 0$ exact, T0 forces $T$ real
P11	No SUSY < 100 TeV	Standard Model complete from $\{s, \mu^*\}$
P12	Exactly 3 generations	Fixed-point combinatorics + Catalan ( $3^2 - 2^3 = 1$ )
P13	Proton stable	Structural baryon conservation
P14	No WIMPs	Dark matter = geometric effect, not particle

Radiative-precision sector

#	Prediction	PT formula	2025 experiment	Status
P25	$a_\mu$ via R_HVP ratio	$1 + \beta_{\rm ghost} (1 - \gamma_7) = 1.04203$	Fermilab final 2025	Compatible
P25b	$a_e$ echo VP	$1.15965218105 \times 10^{-3}$	Hanneke/Cheng	$+0.28$ ppb

Historical muon $g - 2$ anomaly: dissolved by the SM White Paper 2025 (Theory Initiative). PT compatible $-0.85\sigma$ to $-0.24\sigma$ .

The 2032 Grand Crossroads

DUNE will have to measure simultaneously three PMNS predictions:

\delta_{\rm CP} = 197.358° \quad \text{(P4)}

\sin^2\theta_{23} = 0.5733 \quad \text{(P6)}

\sin^2\theta_{13} = 0.0222 \quad \text{(P7)}

If all three are confirmed within 1 %, the probability of coincidence is roughly $(0.01)^3 = 10^{-6}$ . A rare test in physics: three falsifiable predictions descending from zero fitted parameters.

A transparent exception: P20

One prediction (P20, dark-energy equation of state $w_0, w_a$ ) was downgraded in 2026-04 from [PRED-cand] to [EXPL] (exploratory), because the late-time equation of state lacked a canonical derivation.

That late-time dynamics has since been characterised: it is the standard Friedmann evolution of the sieve’s “size” mode at the fixed point. It pins a robust, map-independent prediction — quasi- $\Lambda$ ( $|w_a| \sim 10^{-3}$ , no observable phantom crossing). The present value $w_0$ depends on the sieve-to-scale map: the counting map gives $-1.003$ (a $3.8\sigma$ tension with DESI DR2), the geometric (apparent-horizon) map gives $-0.816$ (only $\sim 1\sigma$ ). PT’s falsifiable stake is the absence of a large evolving signal, not the precise value of $w_0$ .

PT publishes both the downgrade and the refinement. No theory would do this if it were fitting. The status will be reassessed after DESI DR3 (2027), Euclid (2028), CMB-S4 (2030).

In one sentence

The 28 PT predictions are not counter-fits. They are the logical consequences of a single input $s = 1/2$ and the fixed point $\mu^* = 15$ . The theory has no internal way to adjust them; it can only be falsified — or confirmed.