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Plain · quantitative validation

43 observables, 0 continuous fit parameters

All values are derived from the symmetry s = 1/2 (Theorem T1), at the physical attractor of the reduced sector μ* = 15 (T5). No continuous parameter is fitted.

Across 43 observables compared with the PDG, the mean error is 0.316 %, the median 0.061 %. The conservative aggregate excluding SC self-consistencies and exact integers contains 37 independent real-valued entries.

SCU fixes the dimensional reading unit, like c in SI, without introducing a fit.

Standard

All 43 observables, filterable

Filter by sector, search by name. Click a row to expand the detailed derivation (PT formula, monograph chapter, epistemic status).

Filter by sector:

43 observables · mean error 0.316% · median 0.061% · click a row to see the derivation

# Observable Sector PT PDG Error
1 1/α_EM gauge 137.035 999 083 137.035 999 084 400.0 ppb
2 α_s(m_Z) gauge 0.11806 0.11800 0.048 %
3 sin²θ_W gauge 0.23119 0.23121 0.010 %
4 G_F gauge 1.16638×10⁻⁵ 1.16638×10⁻⁵ ~0% (self-consistent)
5 m_μ leptons 105.658 MeV 105.658 MeV ~0% (self-consistent)
6 m_τ leptons 1776.86 MeV 1776.86 MeV ~0% (self-consistent)
7 m_u quarks 2.156 MeV 2.16 MeV 0.170 %
8 m_d quarks 4.656 MeV 4.67 MeV 0.290 %
9 m_s quarks 93.395 MeV 93.4 MeV 0.0050 %
10 m_c quarks 1272.4 MeV 1270.0 MeV 0.190 %
11 m_b quarks 4164.8 MeV 4180.0 MeV 0.360 %
12 m_t quarks 172 698 MeV 172 760 MeV 0.036 %
13 m_W bosons 80.3635 GeV 80.369 GeV 0.0070 %
14 m_Z bosons 91.1878 GeV 91.188 GeV 0.016 %
15 m_H bosons 125.287 GeV 125.25 GeV 0.030 %
16 |V_ud| CKM 0.974 184 0.97373 0.047 %
17 |V_us| CKM 0.224 214 0.2243 0.038 %
18 |V_ub| CKM 0.003 814 0.00382 0.146 %
19 |V_cd| CKM 0.221 072 0.221 0.033 %
20 |V_cs| CKM 0.974 406 0.975 0.061 %
21 |V_cb| CKM 0.040 746 0.0408 0.132 %
22 |V_td| CKM 0.007 999 0.008 0.017 %
23 |V_ts| CKM 0.038 811 0.0388 0.029 %
24 |V_tb| CKM 0.999 215 0.9991 0.012 %
25 δ_CP^CKM CKM 66.912° 67 ± 4° 0.131 %
26 sin²θ_12 PMNS 0.303 684 0.304 0.104 %
27 sin²θ_23 PMNS 0.573 252 0.573 0.044 %
28 sin²θ_13 PMNS 0.022 216 0.0222 0.073 %
29 δ_CP^PMNS PMNS 197.358° 197 ± 25° 0.182 %
30 J_PMNS PMNS 0.009 889 ~0.0099 0.107 %
31 m_ν3 PMNS 0.050 475 eV ~0.051 eV 0.443 %
32 Δm²_31 PMNS 2.514×10⁻³ eV² 2.51×10⁻³ eV² 0.173 %
33 Δm²_21 PMNS 7.412×10⁻⁵ eV² 7.42×10⁻⁵ eV² 0.113 %
34 σ_QCD QCD 0.1942 GeV² 0.194 GeV² 0.103 %
35 α'_Regge QCD 0.8775 GeV⁻² 0.88 GeV⁻² 0.280 %
36 ⟨G²⟩ QCD 0.0395 GeV⁴ 0.04 GeV⁴ 1.270 %
37 Γ_t QCD 1.3060 GeV 1.42 ± 0.19 GeV 8.000 %
38 R_τ QCD 3.6492 3.636 ± 0.010 0.364 %
39 J_CKM QCD 3.093×10⁻⁵ 3.08×10⁻⁵ 0.436 %
40 N_c combinatorics 3 3 exact
41 N_gen combinatorics 3 3 exact
42 G_PT/α_EM gravity 6.284697838 normalisation interne ~0% (self-consistent)
43 H_0 cosmology 67.41 km/s/Mpc 67.4 ± 0.5 km/s/Mpc 0.080 %

Plain

Six numbers to remember

Mean error

0.316 %

Median error

0.061 %

Observables under 0.5 %

41 / 43

Continuous fit parameters

0

Dimensional convention

SCU

Conservative aggregate

37 obs.

Standard

How are the 43 errors distributed?

Distribution of |PT − PDG| / PDG discrepancies across the 43 observables.

0 4 8 12 16 obs 9 < 0.01 % 15 0.01–0.1 % 17 0.1–0.5 % 0 0.5–1 % 1 1–2 % 1 > 2 % 41 of 43 observables below 0.5 % error

Standard

Which Standard Model sectors are covered?

Gauge

4

Examples

1/α_EM, α_s, sin²θ_W, sin²θ_eff

Leptons

5

Examples

m_e, m_μ, m_τ, Q_Koide, C_Koide

Quarks

6

Examples

m_u, m_d, m_s, m_c, m_b, m_t

Bosons

4

Examples

m_W, m_Z, m_H, λ_H

CKM

4

Examples

V_us, V_cb, V_ub, δ_CP

PMNS

4

Examples

sin²θ_12, sin²θ_13, sin²θ_23, δ_CP

Neutrinos

3

Examples

m_ν₃, Δm²_31, Δm²_21

QCD

3

Examples

σ_QCD, f_π, m_π

Gravity / cosmo

6

Examples

G/α, H₀, Ω_info, Ω_Λ, n_s, F_echo

Combinatorial

4

Examples

N_c, N_gen, C_F, D=2

Standard · epistemic status

An important distinction

4 self-consistencies (SC)

Q_Koide = 2/3, N_c = 3, N_gen = 3, m_e = 1/2 (SCU). These are not strict predictions: they are internal self-consistency constraints of the sieve.

2 exact integers

N_c = 3 (mod-3 combinatorics) and N_gen = 3 (Catalan: 3² − 2³ = 1). No expected nor measurable error.

37 independent entries

Mean error 0.367 %, median 0.103 %. This block excludes SC self-consistencies and exact integers. The entries remain derived without continuously fitted parameters, then compared with measurement.

Technical

How to read the aggregates

Mean error

The mean is computed on absolute relative discrepancies |PT − exp| / exp. It is sensitive to the few observables that are furthest away.

Median

The median gives the typical case: half of the observables are closer, half are farther. It is more robust to outliers.

Conservative aggregate

SC self-consistencies and exact integers are separated from the independent real-valued entries so the global score is not artificially inflated.

Going further

Verify it yourself

Reproducibility

Run the scripts in browser

Pyodide WASM runs the T5, T6, α_EM and lemma E/F/G checks live.

 Manipulation

α_EM, γ_p, sin²θ_p calculators

Three interactive calculators to see the formulas at work.

 Predictions

28 falsifiable Tier-1 predictions

Beyond the 43 reproductions: what PT predicts for DUNE, JUNO, Euclid.

 Canonical source

Appendix A of the monograph

Complete table of the 43 observables with chapter-by-chapter derivation.

 Methodology

Epistemic statuses

THM, ID, BRIDGE, DER, VAL, PRED — what each tag really means.

 Robustness

Why this score is hard to reject

5 criteria: zero free parameters, ablation tests, explicit statuses.