Every equation on this site, written out, with the numbers put in, the answer, the measured value, and a verdict you can check.
This page was written by a program, not by hand. The program reads the measured values (each with its source) from one data file, does every calculation itself, and then decides PASS or FAIL by comparing with a tolerance that is printed next to the answer. No number on this page is typed in. Where the record says a result failed or is only partly there, this page shows FAIL or PARTIAL. The same code is on the code page, so you can copy it and run it yourself.
How to read a verdict. PASS: the computed value is inside the stated tolerance. PARTIAL: outside it but within 3 times the tolerance, or a hint the record itself calls partial. FAIL: outside it. NOT TESTABLE YET: no measurement or no TRPG number exists to compare. INPUT: a measured value used as an input, not a prediction. INHERITED: taken unchanged from established physics. NOT RE-RUN: stated in the record but not recomputed here.
The tally is 106 stages in all: 59 PASS, 28 FAIL, 7 PARTIAL, 5 NOT TESTABLE YET, 1 INPUT, 1 INHERITED, 5 NOT RE-RUN. A verdict applies to one stage only. A PASS on a stage does not make a theory true, and PASS counts here are not the record's scorecard (see record M17).
Where the record states a number and this run gives a different one, the stage says so. Number of stages where that happened: 10.
Verdict
Stages
PASS
59
FAIL
28
PARTIAL
7
NOT TESTABLE YET
5
INPUT
1
INHERITED
1
NOT RE-RUN
5
The home-page results table and the neutrino prediction
A1. Bending of starlight by the Sun
PASS
δ = ∫ ∇⊥n dz, with n = 1 + 2GM/(rc²)
Numbers in
M = 1.989×10³⁰ kg, R = 6.957×10⁸ m, G = 6.674×10⁻¹¹, c = 2.998×10⁸ → n − 1 = 4.246×10⁻⁶ at the Sun's edge
Computed
Deflection = 1.752 arcsec (numerical integral along the ray) The record states 1.752; this run gives 1.752. They agree.
Measured
1.75 arcsec — as the record cites (Einstein 1915; eclipse 1919; Cassini 2003)
A3a. Heaviest neutron star (B from the proton, quark pairing)
FAIL
p(μ) = (3/4π²)[a₄μ⁴ − (m_s² − 4Δ²)μ²] − B, a₄ = 1 − 2α_s/π; then the TOV equations
Numbers in
B = 57.1, 60.1, 63.7 MeV/fm³ (set by the proton, stage B9); pairing gap Δ = 70 and 90 MeV; scale factor X = 3; strange quark mass 100 MeV; α_s from 0.118 at M_Z by two-loop running
Computed
Maximum mass from 1.87 to 2.12 solar masses B = 57.1, Δ = 70 MeV: M_max = 1.97, Λ = 445, R = 10.9 km B = 57.1, Δ = 90 MeV: M_max = 2.12, Λ = 595, R = 11.3 km B = 60.1, Δ = 70 MeV: M_max = 1.92, Λ = 386, R = 10.7 km B = 60.1, Δ = 90 MeV: M_max = 2.07, Λ = 517, R = 11.1 km B = 63.7, Δ = 70 MeV: M_max = 1.87, Λ = 328, R = 10.4 km B = 63.7, Δ = 90 MeV: M_max = 2, Λ = 439, R = 10.8 km The record states 2; this run gives 1.87. They DIFFER. The record states 2.18; this run gives 2.12. They DIFFER.
Measured
at least 2 solar masses (the measured star is 2.08 ± 0.07) — PSR J0740+6620 and J0348+0432: heaviest star must be at least this, as the neutron_stars_no_knobs script states
Tolerance
every case in the proton band at or above the test mass
A3b. Radius of a standard-mass neutron star (same cases)
PARTIAL
same star sequences; R at M = 1.4 solar masses
Numbers in
B = 57.1, 60.1, 63.7 MeV/fm³ (set by the proton, stage B9); pairing gap Δ = 70 and 90 MeV; scale factor X = 3; strange quark mass 100 MeV; α_s from 0.118 at M_Z by two-loop running
Computed
R(1.4) from 10.4 to 11.3 km The record states 10.8; this run gives 10.4. They DIFFER. The record states 11.5; this run gives 11.3. They DIFFER.
Measured
11 to 13 km — NICER and GW170817, as record K1 cites
Tolerance
every case inside the measured range
Result
PARTIAL Part of the predicted range sits below the lower edge of the quoted measurement.
A3c. Tidal deformability Λ of a standard-mass neutron star (same cases)
FAIL
Λ = (2/3) k₂ / C⁵, from the same sequences (log-interpolated in Λ)
Numbers in
B = 57.1, 60.1, 63.7 MeV/fm³ (set by the proton, stage B9); pairing gap Δ = 70 and 90 MeV; scale factor X = 3; strange quark mass 100 MeV; α_s from 0.118 at M_Z by two-loop running
Computed
Λ(1.4) from 328 to 595 The record states 440; this run gives 328. They DIFFER. The record states 570; this run gives 595. They DIFFER.
Measured
Λ at or below 580 — GW170817 (2017), as record K2 cites
A3d. The strong force alone, with no quark pairing
FAIL
same equation of state with Δ = 0
Numbers in
from the published script's own printed table (nine cases: three values of B, three scale factors)
Computed
Maximum mass from 1.54 to 1.8 solar masses The record states 1.54; this run gives 1.54. They agree. The record states 1.8; this run gives 1.8. They agree.
Measured
at least 2 solar masses — PSR J0740+6620 and J0348+0432: heaviest star must be at least this, as the neutron_stars_no_knobs script states
Tolerance
heaviest star at or above the test mass
Result
FAIL Fails the two-solar-mass test, as the record says: this is why the pairing gap is needed.
Muon lifetime from Fermi theory = 2.1873×10⁻⁶ s (measured 2.196981×10⁻⁶ s: −0.44% off) Tau lifetime = 289.7 fs The record states 289.7; this run gives 289.7. They agree.
Measured
290.3 fs — PDG 2024
Tolerance
within 1%
Result
PASS e^(−10 S) is the same as (m_μ/m_τ)⁵, the Fermi-theory mass scaling, so the exponent is not a fitted number.
SU(3)²U(1) = 0 SU(2)²U(1) = 0 gravity²U(1) = 0 U(1)³ = 0 Sum of electric charges in one generation for N colours: N = 1 → −0.667; N = 2 → −0.333; N = 3 → 0; N = 4 → 0.333; N = 5 → 0.667 Only N = 3 gives zero.
Measured
all four anomaly sums must be exactly zero (Geng and Marshak 1989; Minahan, Ramond and Warner 1990)
Δt = 4M(1 + 1/√(1−χ²)) ln(M/ℓ_P) (delay if a reflecting surface sat one Planck length outside the horizon)
Numbers in
M = 67.58 solar masses, χ = 0.67, ℓ_P = 1.616×10⁻³⁵ m
Computed
Echo delay that would appear = 0.286 s. TRPG predicts there is no such surface, so no echoes.
Measured
searches by LIGO/Virgo and by Westerweck and others (2018) found no significant echoes (this run does not repeat that search; the result is as the record cites it)
Tolerance
a negative prediction is consistent with a null result
Result
PASS Consistent with the null searches. This is a prediction of absence, so it can still fail if echoes are found later.
Normal ordering, square-root signs (−, +, +): m₁, m₂, m₃ = 0.364, 8.66, 50.1 meV, sum = 0.05916 eV The record states 0.0592; this run gives 0.05916. They agree. The record states 0.36; this run gives 0.364. They DIFFER.
Measured
not yet measured; the record's stated prediction is 0.36, 8.7, 50.1 meV
Tolerance
the solution with one negative square root must reproduce the stated masses within 5%
Result
PASS This stage checks the arithmetic of the prediction, not nature. Nature's answer is in the next two stages.
prediction: normal ordering (m₁ < m₂ < m₃); inverted ordering would falsify it
Numbers in
no data yet
Computed
Awaiting the JUNO reactor experiment (running since 2025) and the sky surveys.
Measured
not yet measured
Tolerance
the JUNO measurement of the ordering
Result
NOT TESTABLE YET This is the prediction that could prove TRPG wrong. If JUNO finds inverted ordering, or a sum clearly away from the predicted one, this piece of TRPG fails.
B1a. Gravity term: the area law holds in the wave medium
PASS
S(region) = c × (boundary length) rather than c × (area inside)
G = a² / (4c) (Bekenstein–Jacobson relation)
Numbers in
36×36 lattice of coupled oscillators, mass 0.01, square blocks of side 2, 4, 6, 8, 10, 12, 14
Computed
Entanglement per unit boundary: 0.0597, 0.0652, 0.0675, 0.0687, 0.0695, 0.0699, 0.0701 Boundary-fit error = 0.00339; volume-fit error = 0.243; ratio = 71.7 c = 0.072, so G = 3.47 a² The record states 3.5; this run gives 3.47. They agree.
Measured
Bombelli, Koul, Lee and Sorkin (1986); Srednicki (1993): the area law is the known result for this kind of system
Tolerance
the boundary fit must beat the volume fit by at least a factor 10
u_Λ = 3.28×10⁻⁴² MeV/fm³; energy scale = 2.24 meV The record states 3.3×10⁻⁴²; this run gives 3.28×10⁻⁴². They agree. The record states 2.24; this run gives 2.24. They agree.
Measured
taken from the measured dark-energy density: an input, not a TRPG prediction
V(P) = (λ/4) v⁴ (P² − 1)²; depth V(0) − V(1) = B; glueball mass m² = 2λv²; so λ = m⁴/(16B), v = m/√(2λ)
Numbers in
B = 57.1, 60.1, 63.7 MeV/fm³ (set by the proton, stage B9); glueball = 1710, 1730 MeV (Morningstar and Peardon 1999; Chen and others 2006)
Computed
λ from 1092 to 1276; v from 34.2 to 36.6 MeV Wall thickness ≈ ℏc/m = 0.115 fm At the central B = 60.1: λ from 1157 to 1212; v from 35.1 to 35.5 MeV The record states 1160; this run gives 1157. They agree. The record states 1210; this run gives 1212. They agree. The record states 35; this run gives 35.3. They agree.
Measured
no measurement of λ or v exists; this stage checks that the wall is thin enough for the bag-model results to carry over
Tolerance
wall thickness must be well below the proton core radius 0.71 fm
Result
PASS The quartic shape (P² − 1)² is the simplest choice, not a derived one (record M1).
PASS M₀ is computed from the measured masses here, so this stage shows the matrix form is consistent with the three masses, not that it predicts them from nothing.
B9a. Containment depth B set by the proton and the Delta, nothing adjusted
PASS
fit B and α_c to M_N and M_Δ; E = (4π/3) B R³ + ...; centre-of-mass correction M = √(E² − ⟨P²⟩); pion cloud (cloudy bag)
Numbers in
the published proton_sets_B script, run with python -I (its real output is in stage F2)
Computed
B = 60.1 MeV/fm³, band 57.1 to 63.7 for a ± coupling change; bag radius 0.995 fm; quark-core rms 0.725 fm The record states 60.1; this run gives 60.1. They agree. The record states 57.1; this run gives 57.1. They agree. The record states 63.7; this run gives 63.7. They agree. The record states 0.725; this run gives 0.725. They agree.
Measured
no direct measurement of B; the fit reproduces the measured proton and Delta masses
K1a. Gemini's own neutron-star equation solved properly
FAIL
dp/dr = −(ε + p)(m + 4πr³p)/(r(r − 2m)), dm/dr = 4πr²ε with Gemini's low-density formula
Numbers in
B = 54.1 MeV/fm³, low-density term p = 0.12 ε (ε/4B)^0.65
Computed
R(1.4) = 47.2 km; maximum mass 2.6 solar masses Pressure at ε = 150 MeV/fm³ is 14.2 MeV/fm³ (real nuclear matter is about 0 to 3) The record states 47; this run gives 47.2. They agree.
Measured
11 to 13 km — NICER and GW170817, as record K1 cites
Tolerance
inside the measured range
Result
FAIL This is the version that was wrong. It is shown so the failure is on the page.
K1c. Containment-only star, and with Gemini's wall term
PASS
p = (ε − 4B)/3 + wall term; same TOV equations
Numbers in
B = 54.1 MeV/fm³; wall strength = 4.2×10⁻⁴
Computed
Containment only: M_max = 2.07, R(1.4) = 11.2 km With wall term: M_max = 2.45, R(1.4) = 11.3 km The record states 2.45; this run gives 2.45. They agree.
Measured
2.08 ± 0.07 solar masses; 11 to 13 km
Tolerance
heaviest star within 1 standard deviation or above it, and radius in range
K3a. Proton containment balance: B from the proton's whole radius
FAIL
M = 4 B V, V = (4/3)πR³ → B = 3M/(16πR³)
Numbers in
M = 938.272 MeV; R = 0.841 fm (the whole measured radius)
Computed
B = 94.1 MeV/fm³ The record states 37; this run gives 94.1. They DIFFER. For comparison the stability bound is 57 MeV/fm³, so this B is above it.
Measured
the record states about 37 MeV/fm³, 'too small' (below the stability bound 57)
Tolerance
within 5% of the record's figure
Result
FAIL The record's own formula does not give its stated number, and the result is the opposite side of the stability bound. This is flagged for the authors to reconcile.
K3c. The quark-core size that gives a B inside the neutron-star window
PARTIAL
R = (3M / (16πB))^(1/3); rms radius of a uniform sphere = √(3/5) R
Numbers in
M = 938.272 MeV; B from 62 to 70 MeV/fm³ (the window)
Computed
R from 0.928 to 0.967 fm; as an rms radius 0.719 to 0.749 fm The record states a core of 0.68 to 0.71 fm (rms).
Measured
0.68 to 0.71 fm — record K3 (rms core for B in the window)
Tolerance
both ends within 5% of the record's range
Result
PARTIAL The rms conversion (uniform sphere) is this page's reading of the record's 'rms'. The record's M1 text uses the bag radius itself, which matches the R computed here.
FAIL The record names V_ub explicitly and says V_cb, V_td and V_ts fail; the mass pairs for those three are the ones the same pattern points to, chosen here.
FAIL The record names V_ub explicitly and says V_cb, V_td and V_ts fail; the mass pairs for those three are the ones the same pattern points to, chosen here.
FAIL The record names V_ub explicitly and says V_cb, V_td and V_ts fail; the mass pairs for those three are the ones the same pattern points to, chosen here.
K6. Large-number coincidences in the proton's scale view
PARTIAL
N = M_universe / m_p; M_universe = (4π/3)(c/H₀)³ ρ_c; (c/H₀)/ƒλ_p; G m_p²/(ℏc); m_W = (ℏ²H₀/(Gc))^(1/3)
Numbers in
H₀ = 67.4 km/s/Mpc, m_p = 1.673×10⁻²⁷ kg
Computed
Particles in the universe's mass = 5.53×10⁷⁹ Universe across in proton Compton lengths = 6.53×10⁴¹ Gravity weaker than the quantum scale by 1.69×10³⁸ Weinberg relation gives 59.8 MeV The record states 5.5×10⁷⁹; this run gives 5.53×10⁷⁹. They agree.
Measured
Eddington's number is about 1×10⁸⁰ (Eddington 1930s, Dirac 1937, Weinberg 1972)
Tolerance
same order of magnitude as the stated number
Result
PARTIAL PARTIAL because it is a coincidence, not a derivation, and the record notes every particle's view gives some huge number.
K7a. Koide's relation on the charged leptons, and how special it is
PASS
Q = (m_e + m_μ + m_τ)/(√m_e + √m_μ + √m_τ)² = 2/3
Numbers in
m_e, m_μ, m_τ as in stage A4; random test: 2000000 log-uniform mass triples between 0.1 and 10000 MeV
Computed
Q = 0.6666645 (2/3 = 0.6666667) Chance of a random triple matching as closely = 3.5×10⁻⁶ The record states 3.5×10⁻⁶; this run gives 3.5×10⁻⁶. They agree.
Q5. Quark sectors in the leptons' relational form: the tested idea fails
FAIL
r² = (3Q − 1)/2; idea tested: r² = 3/6, 4/6, 5/6 for leptons, down-type, up-type
Numbers in
the published quark_link_pattern script, run with python -I (real output in stage F3)
Computed
up-type r² = 0.8279, which is 7.6 standard deviations from the simple value; down-type r² = 0.6192, 6.8 standard deviations away The record states 0.828; this run gives 0.828. They agree. The record states 0.619; this run gives 0.619. They agree.
Measured
the measured quark masses (PDG 2024) give these r² values
Tolerance
the simple fractions within 2 standard deviations (look-elsewhere chance in the script's last line)
Result
FAIL The idea fails and the record drops it. Quark masses stay measured inputs.
M5. Crossing waves: peaks, saddles, troughs and flatness
PASS
z = cos x + cos y; K = z_xx z_yy / (1 + z_x² + z_y²)²; ∫ K dA = 0 over one cell (Gauss–Bonnet); peaks − saddles + troughs = 0 (Morse)
Numbers in
grid of 1201×1201 points over one cell; critical points at (0,0), (π,π), (π,0), (0,π)
Computed
Types found: peak, trough, saddle, saddle; peaks − saddles + troughs = 0 Area curved like a sphere = 0.5, like a saddle = 0.5 Total curvature over the cell = 4.89×10⁻¹⁸
Q(s,c,b) with the measured values = 0.6748; predicted strange = 91.79 MeV; measured 93.5 MeV (−1.8% off) The record states 91.8; this run gives 91.79. They agree.
size 1×10⁻⁹ of today: matter 3.46×10⁻⁴%, radiation 100%, dark energy 7.53×10⁻³¹% size 1×10⁻⁴ of today: matter 25.7%, radiation 74.3%, dark energy 5.59×10⁻¹¹% size 0.5 of today: matter 78.6%, radiation 0.0454%, dark energy 21.4% size 1 of today: matter 31.5%, radiation 0.0091%, dark energy 68.5% size 2 of today: matter 5.44%, radiation 7.85×10⁻⁴%, dark energy 94.6% Shares sum to 100% at each size: yes
Measured
Planck 2018: curvature 0.001 ± 0.002
Tolerance
sum equal to 1 within 1×10⁻¹² and curvature consistent with zero
Result
PASS The curvature term is the only 'empty' share left over; Planck's value is consistent with zero.
Density = 9.57×10⁶⁸ per m² The record states 1×10⁶⁸; this run gives 9.57×10⁶⁸. They DIFFER.
Measured
the record states about 1×10⁶⁸ per square metre
Tolerance
within a factor 3 of the stated figure
Result
FAIL The record's figure of 1×10⁶⁸ per square metre is one power of ten below what the arithmetic gives. The weak-gravity argument does not depend on it; the figure in the record is a slip.
α_s(M_Z) = 0.118; quark masses at their quoted scales (PDG 2024 (quark_common_scale script)); energies 2, 91.188, 162.5, 1000 GeV
Computed
at 2 GeV: up-type angle 52.15°, down-type angle 48.06° at 91.188 GeV: up-type angle 52.15°, down-type angle 48.06° at 162.5 GeV: up-type angle 52.15°, down-type angle 48.06° at 1000 GeV: up-type angle 52.15°, down-type angle 48.06° Spread of the up-type angle across energies = 2×10⁻¹¹°; down-type = 5.25×10⁻¹²° The record states 52.15; this run gives 52.15. They agree. The record states 48.06; this run gives 48.06. They agree.
Measured
the angle should not change with energy because QCD rescales all quark masses by one factor (record P2)
δ = arccos((√m_τ / M − 1)/√2), M = mean of the three square roots; compare 2/9
Numbers in
masses and uncertainties as in the inputs; 20000 random draws
Computed
δ from data = 0.222239 ± 4×10⁻⁵ rad; 2/9 = 0.222222; difference = 0.43 standard deviations The record states 0.222239; this run gives 0.222239. They agree.
Measured
2/9 — Brannen (2006)
Tolerance
within 2 standard deviations
Result
PASS That 2/9 equals (2/3)/3 is the project's conjecture, not derived (record P5).
python -I area_law_and_charges_2026-11-14.py (working directory separate from the downloads)
Numbers in
run with the isolated interpreter in a separate working directory, a copy of the workbook beside it
Computed
Exit status 1: DID NOT RUN HERE. ModuleNotFoundError: No module named 'sympy'
Measured
the script's own printed output follows, unedited
Tolerance
the script must run to the end in this environment
Result
FAIL The module sympy is not installed in this environment, so this script is not verified here. The page computes the same result itself in stages B5 and K10a.
block 2x2 boundary 8 volume 4 entanglement 0.478 per boundary 0.0597
block 4x4 boundary 16 volume 16 entanglement 1.044 per boundary 0.0652
block 6x6 boundary 24 volume 36 entanglement 1.620 per boundary 0.0675
block 8x8 boundary 32 volume 64 entanglement 2.200 per boundary 0.0687
block 10x10 boundary 40 volume 100 entanglement 2.779 per boundary 0.0695
block 12x12 boundary 48 volume 144 entanglement 3.355 per boundary 0.0699
block 14x14 boundary 56 volume 196 entanglement 3.926 per boundary 0.0701
fit to boundary: error 0.003 ; fit to volume: error 0.243 -> AREA (boundary) law
entanglement per unit boundary ~ 0.072 -> Jacobson/Bekenstein: G = a^2/(4 x that) in medium units: G ~ 3.47 a^2 (gravity strength set by the medium's spacing a)
B) Charges from consistency (anomaly cancellation; Geng & Marshak 1989; Minahan, Ramond & Warner 1990; Bar & Wiese 2001).
One generation with N colours: quark doublet Q(N,2), u(N), d(N), lepton doublet L(2), e(1); fix the scale with Y_L = -1/2.
--- error output ---
Traceback (most recent call last):
File "...\area_law_and_charges_2026-11-14.py", line 31, in <module>
import sympy as sp
ModuleNotFoundError: No module named 'sympy'
python -I expansion_and_entanglement_2026-11-14.py (working directory separate from the downloads)
Numbers in
run with the isolated interpreter in a separate working directory, a copy of the workbook beside it
Computed
Exit status 0: ran to the end.
Measured
the script's own printed output follows, unedited
Tolerance
the script must run to the end in this environment
Result
PASS
full glass: matter 0.315 + dark energy 0.685 + radiation 0.00009 = 1.0000 (Planck: curvature 0.001 +/- 0.002)
age from the expansion equation: 13.79 billion years (Planck 2018: 13.787 +/- 0.020)
size 1e-09 of today: matter share 0.000, radiation 1.000, dark energy 0.000
size 1e-04 of today: matter share 0.257, radiation 0.743, dark energy 0.000
size 5e-01 of today: matter share 0.786, radiation 0.000, dark energy 0.214
size 1e+00 of today: matter share 0.315, radiation 0.000, dark energy 0.685
size 2e+00 of today: matter share 0.054, radiation 0.000, dark energy 0.946
matter amount in a stretching region (rho*a^3): constant -> same water; dark energy per volume constant -> its total grows: global total not conserved, only local (as in Einstein's theory)
wave pulse: spread in place x spread in wavenumber = 0.5000 (Heisenberg minimum 0.5)
python -I build_antiparticle_and_decays.py (working directory separate from the downloads)
Numbers in
run with the isolated interpreter in a separate working directory, a copy of the workbook beside it
Computed
Exit status 1: DID NOT RUN HERE. ModuleNotFoundError: No module named 'pandas'
Measured
the script's own printed output follows, unedited
Tolerance
the script must run to the end in this environment
Result
FAIL The module pandas is not installed in this environment, so this script is not verified here. The page computes the same result itself in stages B5 and K10a.
--- error output ---
Traceback (most recent call last):
File "...\build_antiparticle_and_decays.py", line 7, in <module>
import pandas as pd, itertools, math
ModuleNotFoundError: No module named 'pandas'
