Research

Discovery Catalog

Formulas and physical laws discovered from raw data, validated against published measurements and authoritative datasets.

Astrophysics & Cosmology

#	Discovery	Accuracy	Domain
56	ΛCDM comoving distance	0.096%	Cosmology
57	ΛCDM lookback time	0.010%	Cosmology
48	Distance modulus formula	R² = 0.999983	Cosmology
45	ΛCDM distance family (D, t, μ)	R² > 0.99997	Cosmology
43	Proca dark photon halo ρ(r)	0.009 dex	Dark matter field theory
21	Dark matter from baryonic distribution	R² = 0.918	Dark matter
28	Hubble tension transition model	R² = 0.884	Cosmology
33	White dwarf mass-radius-temperature	R² = 0.973	Stellar physics
59	Pulsar spin-down ISM dependence	R² = 0.76	Pulsars
11	Hot Jupiter inflation mechanism	R² = 0.864	Exoplanets
1	Exoplanet stellar age-radius relation	R² = 0.538	Exoplanets

General Relativity & Gravitational Waves

#	Discovery	Accuracy	Domain
48	Kerr radiative efficiency η(a*)	0.0007%	GR / astrophysics
49	Kerr GW energy fraction F_GW(a*)	0.0017%	LIGO
50	Kerr angular momentum L(a*)	0.00004%	GR / accretion
51	Reissner-Nordström r_ISCO(Q/M)	0.0007%	Charged black holes
53	Kerr prograde photon sphere	0.0003%	EHT shadows
60	Kerr retrograde photon sphere + shadow	~0%	EHT
58	Schwarzschild orbital precession	0.28%	Orbital mechanics
59	Hyperbolic Kepler equation	0.036%	Astrodynamics
38	EMRI-safe SXS radiated energy	R² = 0.940	Gravitational waves
34	Exponential merger amplification	R² = 0.982	Gravitational waves
15	Black hole T×R = ℏc/4π	Exact	Quantum gravity

Nuclear & Particle Physics

#	Discovery	Accuracy	Domain
54	Nuclear charge radii (952 isotopes)	R² = 0.9976, MAE = 0.023 fm	Nuclear physics
35	Nuclear binding energy cross-term	R² = 0.995, MAE = 0.025 MeV	Nuclear physics
57	Nuclear binding isospin correction	R² = 0.962	Nuclear physics
13	Ionization energy formula	R² = 0.943	Atomic physics
58	Ionization energies (extended)	R² = 0.963	Atomic physics
62	Helium atom ground state	230× improvement	Quantum mechanics
14	Atomic radius formula	R² = 0.719	Atomic physics

Quantum & Condensed Matter

#	Discovery	Accuracy	Domain
66	BEC condensate fraction (exact recovery)	R² = 1.0000	Quantum physics
66	Quantum tunneling sech² identity	R² = 1.0000	Quantum physics
61	BCS superconducting gap	R² = 1.000	Superconductivity
60	Anderson localization calibration	R² = 0.999	Solid state physics
51	Debye heat capacity	R² = 0.999957	Solid state physics
55	Tokamak energy confinement	R² = 0.957	Plasma physics / fusion
56	Quantum defect calibration	R² = 0.926	Atomic physics
22	Superconductor electron affinity	R² = 0.65	Materials science

Fluid Dynamics & Heat Transfer

#	Discovery	Accuracy	Domain
49	C¹ continuous Law of the Wall	R² = 0.999981	Turbulence
45	Cylinder eigenvalues β₁, β₂, β₃	0.0005%	Heat transfer
54	Slab eigenvalues	<0.1%	Heat transfer
55	Sphere eigenvalues	<0.5%	Heat transfer
40	Planck radiation fraction	R² = 0.999999	Thermal radiation
9	Airfoil noise interaction term	R² = 0.453	Aeroacoustics

Radiative Processes & Plasma

#	Discovery	Accuracy	Domain
50	Synchrotron kernel F(x)	R² > 0.99999999	Astrophysical radiation
52	Free-free Gaunt factor	R² = 0.999987	Plasma physics
53	Chandrasekhar H-function	0.066%	Radiative transfer
74	Paschen's curve (breakdown voltage)	R² = 0.982	Plasma physics

Mathematics & Special Functions

#	Discovery	Accuracy	Domain
46	Inverse elliptic K⁻¹(K)	0.007%	Mathematics
47	Inverse Bessel I₁/I₀	1.08%	Superparamagnetism
61	Inverse x·I₀/I₁	0.0009%	Electromagnetics
42	Inverse Langevin function	R² = 0.999998	Polymer physics
44	Complementary error function (erfc)	R² = 1.000000	Special functions
46	Gamma function approximation	R² = 0.999995	Special functions
47	Riemann zeta approximation	R² = 0.999528	Number theory
85	Bessel function identity (exact)	15 decimal places	Mathematics
86	Inverse Brillouin function	0.16%	Quantum magnetism

Classical Mechanics

#	Discovery	Accuracy	Domain
52	Pendulum period T(θ₀)	0.013%	Classical mechanics
39	Exact pendulum period formula	R² = 0.999954	Classical mechanics
10	Kepler's law correction	R² = 0.838	Orbital mechanics

Multi-Domain & Universal Laws

#	Discovery	Accuracy	Domain
72	Universal friction equation (10 systems)	R² = 0.801 - 0.9997	Multi-domain engineering
82	Two topologies, 32 systems	Varies	Multi-domain physics
63	MOND acceleration from M-sigma	Dimensional proof	Gravity / dark matter
103	Maxwell, Einstein, Yang-Mills from symmetry	Exact derivation	Field theory

Engineering & Applied Science

#	Discovery	Accuracy	Domain
26	Battery degradation single-number predictor	R² = 0.842	Energy storage
27	Battery equivalent circuit identity	CV = 0.000 (exact)	Electrochemistry
3	Concrete compressive strength	R² = 0.550	Civil engineering
5	Building energy sqrt(height)	R² = 0.920	Architecture / energy
6	Power plant temperature formula	R² = 0.934	Energy / thermodynamics
36	Guldberg ratio rediscovery	R² = 0.885	Physical chemistry

Biology & Medicine

#	Discovery	Accuracy	Domain
4	Metabolic scaling beyond Kleiber	R² = 0.941	Physiology
80	Enzyme kinetics formula	R² = 0.984	Biochemistry
79	Viral load dynamics	R² = 0.896	Epidemiology
81	Epidemic curve formula	R² = 0.830	Epidemiology
76	Species-area relationship	z(A) varying	Ecology
7	Abalone age from shell weight	R² = 0.541	Marine biology