GDBS Validation Matrix

Independent verification reference. Each engine, the benchmark it is checked against, and the external source anyone can use to confirm it.

Document: public, no NDA required Version: 1.0 Compiled: 2026-05-25 Scope: deterministic physics and numerical engines

GDBS is a deterministic scientific-computing platform: the same inputs produce the same outputs on every machine, with no training data, no fitting, and no stochastic sampling. This document lists each engine alongside a benchmark with a known answer and the published or analytic reference for that answer. Every entry marked Verified can be reproduced and checked against the cited external source. Nothing in this table is calibrated, tuned, or fitted to its reference.

How to read this table

Verified
The engine computes the quantity from more fundamental inputs (physical constants, governing equations, or first principles) and the result falls within the stated tolerance of an external published value or an exact analytic result. No calibration to the reference is applied.
Self-check
A numerical-consistency test that is standard in the field: convergence order (the error shrinks at the theoretical rate as the grid refines) or constraint preservation (a quantity that must stay zero does). It validates the method's internal correctness rather than a comparison to external data.
Referenced
An established published value shown for context. It is not independently reproduced by the engine, and it is never counted as a passed computation. It is included so coverage is complete and honest about where an independent solver does not yet exist.

Honesty statement. No value in the Verified column is fitted to the answer it is compared against. Where the platform has no independent solver for a quantity, the published number is shown as Referenced and is plainly labelled as such. Self-checks are labelled as self-checks, not as agreement with measured data. "Last validated" is the date the benchmark was last confirmed in the platform's automated test suite; live-engine benchmarks reproduce on demand.

Validation matrix

EngineModule / BenchmarkStatusResult vs referenceExternal reference sourceLast validated
Gravitational WaveformsGW150914 final remnant massVerified63.02 vs 63.1 M☉ (0.13%)Abbott et al. 2016, Phys. Rev. Lett. 116, 0611022026-05-24
Gravitational WaveformsGW150914 final spinVerified0.6855 vs 0.69 (0.65%)Abbott et al. 2016; Husa et al. 20162026-05-24
Gravitational WaveformsGW150914 chirp massVerified28.72 vs 28.6 M☉ (0.4%)Abbott et al. 2016, Phys. Rev. Lett. 116, 0611022026-05-24
Gravitational WaveformsGW170817 (binary neutron star) chirp massVerified1.185 vs 1.188 M☉ (0.3%)Abbott et al. 2017, Phys. Rev. Lett. 119, 1611012026-05-24
Gravitational WaveformsRingdown quasinormal frequencyVerified~271 Hz, within published bandBerti, Cardoso & Will 2006, Phys. Rev. D 73, 0640302026-05-24
Numerical RelativityFactor-2 self-convergence (metric component)Self-checkorder 3.946 (theoretical 4)Alcubierre et al. 2004 (Apples-with-Apples), Class. Quantum Grav. 21, 5892026-04-26
Numerical RelativityMinkowski fixed point (Hamiltonian constraint)Verified1.2e-28 (flat space exact = 0)Flat-space exact solution2026-05-21
General-Relativistic MHDDivergence-free constraint, magnetized torus (GPU)Self-check|∇·B| = 2.4e-4 (target 0)Tóth 2000; Balsara & Spicer 1999 (constrained transport)2026-05-21
General-Relativistic MHDDivergence-free constraint, Orszag-Tang (CPU)Self-check< 1e-12 (machine zero)Constrained-transport invariant2026-05-21
Black-Hole ThermodynamicsHawking temperature across 60 orders of magnitudeVerified0.27% vs analyticHawking 1975, Nature 248, 302026-05-24
Constants & RelativitySchwarzschild radius (1 solar mass)Verified2953.250 m (0.05%)Schwarzschild 19162026-05-24
Constants & RelativityBekenstein-Hawking entropy (1 solar mass)Verified1.049e77 k₃ (1%)Bekenstein 1973, Phys. Rev. D 7, 23332026-05-24
Constants & RelativityBohr radius, Rydberg energy, Compton wavelengthVerified0.001 to 0.01%CODATA 2022 recommended values2026-05-24
Constants & RelativityPlanck mass, Stefan-Boltzmann constantVerified0.001 to 0.01%CODATA 2022 recommended values2026-05-24
QED PrecisionElectron g-2 coefficients, orders 1 to 3Verifiedreproduce exact closed forms to floating-pointSchwinger 1948; Petermann 1957 / Sommerfield 1958; Laporta & Remiddi 19962026-05-01
QED PrecisionElectron g-2 coefficients, orders 4 to 5Referencedwithin published experimental bounds (reproduction, not independent prediction)Aoyama, Hayakawa, Kinoshita & Nio 2012; Kinoshita 20172026-05-01
Electronic StructureH₂ molecular integrals (overlap, core, two-electron)Verified< 0.1%Szabo & Ostlund, Modern Quantum Chemistry, Table 3.172026-05-24
Electronic StructureH₂ total energy (Hartree-Fock, STO-3G)Verified-1.1175 Ha (< 0.5%)Szabo & Ostlund, Modern Quantum Chemistry2026-05-24
Electronic StructureHF, H₂O, CH₄ (Hartree-Fock, STO-3G / 6-31G*)Verified0.5 to 2%NIST Computational Chemistry Comparison & Benchmark DB; Szabo & Ostlund2026-05-24
Electronic StructureH₂O density-functional (LDA / B3LYP)Referencedcorrelation-functional fix pending redeploymentPublished exchange-correlation functionals2026-05-24
Boundary-Layer FluidsBlasius flat-plate wall shear, f″(0)Verified0.4696 ± 0.002Falkner & Skan 1931; Schlichting, Boundary-Layer Theory2026-05-24
Incompressible FluidsTaylor-Green vortex decay rateVerifiedwithin 5% of analytic 4νTaylor & Green 1937 (analytic decay)2026-05-24
Compressible FluidsSod shock tube, density and pressure positivityVerifiedρ > 0, p > 0 at t = 0.2Sod 1978, J. Comput. Phys. 27, 12026-05-24
Compressible FluidsSod shock tube, L1 error vs exact Riemann solutionVerifiedfinite L1 within toleranceSod 1978 exact Riemann solution2026-05-24
Elliptic SolversMultigrid sine-mode residual reduction (16³, 6 V-cycles)Verifiedreduction > 1000xBriggs, Henson & McCormick, A Multigrid Tutorial2026-05-24
Elliptic SolversMultigrid h² convergence (8³ to 16³)Verifiedratio ~4x (second order)Second-order discretization theory2026-05-24
ElectromagneticsFDTD vacuum quiescence (energy conservation)Verifiedpeak energy < 1e-25Yee 1966; Taflove & Hagness, Computational Electrodynamics2026-05-24
ElectromagneticsFDTD dipole source (energy injection, field oscillation)Verifiedpeak > 1e-6, field sign reversalTaflove & Hagness, Computational Electrodynamics2026-05-24
Phase-FieldCahn-Hilliard mass conservation (400 steps)Verified|drift| < 1e-8Cahn & Hilliard 1958, J. Chem. Phys. 28, 2582026-05-24
Phase-FieldAllen-Cahn energy descent under gradient flowVerifiedmonotone energy decreaseAllen & Cahn 1979, Acta Metall. 27, 10852026-05-24
Lattice / Spin SystemsHeisenberg chain, N = 2 singletVerified-0.75 (exact -3J/4)Exact analytic singlet energy2026-05-24
Lattice / Spin SystemsHeisenberg open chain, N = 4Verified-1.6160254 (< 1e-4)Bethe 1931 (Bethe ansatz)2026-05-24
Lattice / Spin SystemsTransverse-field Ising, N = 4Verifiedenergy below field-only baselineAnalytic field-only baseline2026-05-24
Materials (Ionic)NaCl / CsCl Madelung constants (Ewald sum)Verified1.747565 / 1.762675 (exact)Madelung; Ewald 1921, Ann. Phys. 369, 2532026-05-24
Materials (Ionic)NaCl Born-Landé lattice energyVerified~787 kJ/molBorn & Landé model2026-05-24
Materials (Solids)Argon FCC lattice (Lennard-Jones)Verifiedwithin method accuracyLennard-Jones potential2026-05-24
Materials (Superconductors)Nb / Pb critical temperature (Allen-Dynes)Verifiedwithin ~15% (method accuracy)Allen & Dynes 1975; McMillan 19682026-05-24
Materials (Crystals)Si / Ge / Cu lattice constants, band gapsReferencedpublished values, not independently solvedKittel, Introduction to Solid State Physics; Madelung 20042026-05-24
GeophysicsSurface gravity, Earth and MoonVerifiedfrom GM / R²Standard geodesy2026-05-24
GeophysicsSeismic moment at moment magnitude 7Verified3.98e19 N·mHanks & Kanamori 1979, J. Geophys. Res. 84, 23482026-05-24
GeophysicsPREM seismic velocities, gravity coefficient J₂Referencedpublished reference valuesDziewonski & Anderson 1981 (PREM)2026-05-24
Plasma / MHD EquilibriaTokamak ideal-MHD no-wall beta limitSelf-checklands in Troyon band [2, 6]Troyon et al. 1984; Soloviev 19682026-05-24
CosmologyHubble distance c / H₀Verifiedfrom H₀Standard cosmology2026-05-24
CosmologyAge of universe (Friedmann integral)Verifiedwithin tolerancePlanck 2018, Astron. Astrophys. 641, A62026-05-24
CosmologyCMB temperature, acoustic peak, density parametersReferencedpublished valuesPlanck 2018, Astron. Astrophys. 641, A62026-05-24
Molecular PropertiesMolecular weight (glucose, caffeine)Verifiedfrom atomic massesIUPAC standard atomic weights2026-05-24
Molecular PropertiesGlucose diffusion coefficient (Stokes-Einstein)Verifiedfrom Stokes-Einstein relationEinstein 19052026-05-24
Molecular PropertiesBinding free energy, logP, pKa, half-livesReferencedpublished values, no docking / QSAR / pharmacokinetic solverPrimary literature2026-05-24

Notes