GDBS (Geometric Database System) is a browser-native physics computing platform. It runs real, validated physics across multiple domains and reports a trust verdict - how many digits survived the arithmetic - on every result. It is where you prototype and validate a method before taking it to HPC.

How is GDBS different from running code on an HPC cluster?

It is not a replacement for the cluster, it is the step before it. HPC codes run production-scale problems that need a mesh, an allocation, and a job queue. GDBS lets you develop and validate the same method in a browser tab, with no queue and no install, then hand off to HPC.

Is GDBS machine learning, or a surrogate model?

No. GDBS is deterministic analytic computation. There is no training data, no loss function, no gradient descent, and no stochastic sampling. The same inputs always produce the same outputs on every machine.

What is GeoNum and why does it matter?

GeoNum (Geometric Number Scale) is the precision arithmetic system underlying GDBS, citable at DOI 10.5281/zenodo.19199836. Standard IEEE 754 floating point hides precision loss; GeoNum tracks it and reports a trust verdict on every result.

Is GDBS validated against published results?

Yes. The engine ships with re-runnable test suites that gate every release, and results are compared against a published reference where one exists - for example GW150914, the Blasius wall shear 0.4696, and the Hawking temperature to 0.27 percent. See the validation pages at https://gdbs.getvaultsync.com/validation.html .

Can I cite GDBS results in published research?

Yes. Results are deterministic and reproducible. Academic and research licensees are required to cite GDBS in published work; the GeoNum precision system is separately citable at DOI 10.5281/zenodo.19199836.

GDBS PRO - Validate Your Physics in the Browser, Then Take It to HPC

	GDBS (browser)	HPC cluster
Best for	Prototyping, validation, teaching, parameter scans	Production-scale runs (AMR, matter coupling, multi-node)
To start	Open a browser tab	Request an allocation, wait in the queue
Iteration speed	Seconds, on your own device	Hours to days per scheduled job
Setup	No install, no scheduler, no infrastructure	Mesh, modules, job scripts, scheduler
Trust per result	A trust verdict reported on every value	Assumed; checked separately
Scale ceiling	Single-GPU / browser	Effectively unbounded
Cost model	License, no metered compute fees	Allocation plus core-hours

Area	Implementation
Client-side compute	Engines run in-browser via WebAssembly; per the DUA, inputs and results stay local and are never sent to or stored on our servers.
Data at rest (account data)	AES-256-GCM per write (random nonce + auth tag); every server-side collection encrypted; fail-loud decryption.
Data in transit	TLS 1.2+ at the edge; HSTS; no cleartext fallback.
Password storage	BCrypt hashed; constant-time verify with a dummy hash on unknown users to prevent enumeration.
Session auth	JWT (HS256), short-lived access + refresh tokens; refresh re-checks disabled accounts; reset tokens are single-use.
Authorization	RBAC on all admin and investor endpoints; API keys capped to non-admin scope.
Path / injection	Charset-validated identifiers; paths confined to the data root; GQL identifiers and literals escaped; arXiv ids regex-validated.
Plugin / extension execution	Third-party plugins run only in an isolated Web Worker under a worker-scoped CSP: no external module loading, no network egress, no DOM/GPU access, watchdog compute budget. Uploads are screened and sandbox dry-run, entering at unverified trust; violations auto-reject. First-party plugins are code-reviewed.
CORS	Explicit allowlist (no `AllowAnyOrigin`); bearer tokens, no credentialed cookies.
Rate limiting	Per-IP throttling on auth and anonymous endpoints against credential stuffing and abuse.
Request size limits	Bounded request bodies on compute/substrate endpoints; usage-log fields capped.
Secrets management	No secrets in tracked config; live values loaded at startup from an overlay outside version control.
License keys	128-bit entropy; constant-time comparison.
Payment data	Stripe Checkout redirect; cardholder data never touches GDBS (SAQ-A, PCI-DSS).
Audit logging	All API calls logged with session id, action, and timing; admin activity has its own review surface.
Hosting	US-based; TLS at the edge.

Tier	Support commitment
Enterprise	Contractual SLA per the EULA. Initial substantive response within 1 business day; dedicated success contact; custom SLA available on request.
Pro	Contractual SLA per the EULA. Initial substantive response within 1 business day; priority handling.
Standard / Plus	Best-effort priority handling, same 1-business-day response target on a commercially reasonable basis.
Academic / Free	Standard best-effort handling.

DSO Framework role-gated

Distinction-Shade Ontology - novel theory, access restricted to the DSO / admin role. Kept separate from the published-physics domains; never used as a validation reference for any other module.

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Plasma Stability - Ideal-MHD δW Solver

Relational Depth: 0 (13D)

Configuration Type

Constants B0 q0 qa Grid

Geometry A κ δ

Simulation Settings β steps Radial pts Max β factor Coherence target

Optimizer - Auto-Tuning

Grid search across the full parameter space to find optimal plasma configurations. Evaluates thousands of candidates and ranks them by your target metric.

PRO

Upgrade to unlock auto-tuning and advanced features.

Configuration Type

Aspect Ratio Range Min Max

Optimization Target Grid Top N

Constants B0 q0 qa Grid

Predictor - Trajectory Planner

Given a target outcome (Q > 1, ITER-class β_N), the Predictor chains optimizer waypoints into a step-by-step adjustment roadmap with go/no-go coherence gates at each stage.

PRO

Available with Full Suite and Enterprise licenses.

Configuration Type

Aspect Ratio Range Min Max

Kappa (Elongation) Range Min Max

Delta (Triangularity) Range Min Max

Trajectory Target Target Coherence Gate Grid

Constants B0 q0 qa

Custom Constraints

Define your specific machine parameters, engineering limits, and operational constraints. Set bounds on field strength, current, wall loading, and divertor heat flux.

PRO

Available with Full Suite and Enterprise licenses.

Analytic Equilibrium (Soloviev)

Closed-form Grad-Shafranov solution. Benchmark anchor for any equilibrium claim, with 2D poloidal flux-surface rendering.

PRO

Ballooning Stability (s-α diagram)

Infinite-n local ballooning eigenvalue scan across magnetic shear and pressure gradient - the standard publication figure.

PRO

Mercier Interchange Criterion

Local stability across the flux surfaces, decomposed into well, shear, and current contributions. Fast - runs in optimizer loop.

PRO

Multi-mode δW Scan

(m,n) family scan with mode-coupling matrix. Identifies dominant unstable mode and resonant surface location.

PRO

Parameter Sensitivity

Central-difference ∂β_N/∂x · x/β_N elasticity. Ranks which knob dominates your design.

PRO

Convergence Study

Richardson extrapolation across n_radial. Proves your result is grid-converged with observed convergence order.

PRO

EFIT g-eqdsk Import

Load any EFIT / JET / DIII-D / NSTX equilibrium file. We parse it, render the poloidal cross-section, and feed it to downstream solvers.

PRO

Canonical Validation Suite

One-click verify against ITER, DIII-D, JET, NSTX, W7-X, LHD, TAE Norman, and Soloviev analytic. Each row shows the source paper and tolerance band.

PRO

All references auto-run on open. Valid = independently computed and within published tolerance. Referenced = published value shown for context, not independently computed. Error = computed but outside tolerance. Hover any row for the full explanation.

Reference	Category	Expected β_N	Computed	Verdict	Source

Medical Module - Molecular Nanoinformatics

Drug-target binding, protein stability, nanoparticle design, drug interactions, and molecular QSAR. Powered by the same 13D geometric engine.

MODULE

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Medical - Molecular Nanoinformatics

Relational Depth: 0 (13D)

Folding & Coherence vs Temperature

Free Energy (ΔG) vs Temperature

Shrake-Rupley Algorithm: SASA computed using Fibonacci lattice sphere sampling. Van der Waals radii from Bondi (1964). Multiple probe radii reveal cavity accessibility and solvent size effects.

Total SASA vs Probe Radius

Per-Residue SASA (1.4Å probe)

DLVO Engine: GeoNum-instrumented Derjaguin-Landau-Verwey-Overbeek theory. κ (Debye screening length) computed in full log-domain arithmetic - intermediate products span 10⁻³⁸ to 10²⁵ (63 orders). Drift tracked at every step.

DLVO Energy Profile (representative pairs)

Barrier Height Distribution

Pairwise Stability Matrix (barrier height, k_BT)

Cumulative Mutations / Molecule vs Cycle

Error-Free Fraction vs Cycle

Polymerase comparison at current settings:

Grid Docking - Lennard-Jones + Coulomb scoring

Rigid-receptor / rigid-ligand grid search with Halton-sampled poses. Scoring: 4ε[(σ/r)¹² − (σ/r)⁶] + q₁q₂/(4πε₀ε_r·r). Eyring transition-state estimate for k_off at 310 K.

Poses Box ± [Å] ε_r (dielectric)

Molecular Dynamics - Lennard-Jones + Berendsen NVT

Velocity-Verlet on LJ atoms (default Ar: σ=3.405 Å, ε/k=119.8 K), periodic BC with minimum-image cutoff at 2.5σ. Outputs T(t), E(t), pressure, MSD, g(r), and self-diffusion D from the late-time MSD slope. Verlet 1967 benchmark cross-check.

N atoms T [K] ρ* (reduced) steps

T, E vs t

Radial distribution g(r)

Pharmacokinetics - one- and two-compartment ODEs (RK4)

Analytic-grade RK4 integration of standard compartment models. IV bolus and oral 1C, plus 2C IV with k₁₂/k₂₁ exchange. Reports AUC, t_max, C_max, t_1/2, clearance.

Model Dose [mg] k_e [1/h] V_d [L] k_a [1/h] (oral) k12 [1/h] (2C) k21 [1/h] (2C) Duration [h]

Hammett pKa - substituent constants (Hansch-Leo 1979)

log₁₀(K/K_H) = ρ · σ_X. Parent benzoic acid pKa = 4.20; ρ = 1.0 for the standard scaffold. Substituent constants tabulated for OH, OMe, NH₂, Me, CF₃, Cl, F, Br, CN, NO₂, COOH at meta and para positions.

Parent pKa ρ Group Position 2nd group (optional) 2nd position

Medical / Molecular Validation - Canonical References

Each row compares a published value (PDB binding affinities, DrugBank half-lives, Sangster logP, PubChem MW, CRC pKa, Mills 1973 diffusion) against GDBS. Molecular weight (atomic-mass sums) and the Stokes-Einstein diffusion coefficient are computed independently from first principles; the pharmacology endpoints (binding, logP, pKa, half-life) are shown as literature references, not independently computed. Valid = computed and within published tolerance. Referenced = published value shown for context. Error = computed but outside tolerance.

Reference	System	Category	Expected	Computed	Verdict	Source

Cosmos Module

Galaxy rotation curves, CMB power spectrum, black hole jets, fundamental constants from golden ratio, and cosmic energy budget. Powered by the same 13D geometric engine.

MODULE

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Cosmos

Relational Depth: 0 (13D)

Rotation Curves: Newtonian vs DSO

Radial Acceleration Relation

Q-Desic - Quantum-Corrected Geodesics

Implements the q-desic framework of Koch, Riahinia & Rincon (PRD 2025, arXiv:2510.00117). Solves d²xβ/dλ² + ⟨Γ̂βμν⟩_g (dxμ/dλ)(dxν/dλ) = 0 for spherically symmetric static spacetimes with quantum correction parameters ε_i,j. Classical GR (all ε=0) is always overlaid for comparison. When ε→0 the equations reduce exactly to Schwarzschild(-de Sitter) geodesics.

Spacetime Metric Central Mass (M⊙) Λ (cosmological constant, geometrized)

Modified Gravity Framework

None (GR) Scale-Dependent Scalar-Tensor f(R)

Geodesic Initial r (units of M) Angular momentum L/M Integration steps

Quantum Corrections (ε_i,j)

Set to 0 for classical GR. Non-zero values activate q-desic corrections.

ε_1,0 (mass correction) ε_0,2 (metric curvature) ε_1,2 (mass-curvature) ε_2,2 (quadratic)

r_QS = 2GM(1+ε_1,2)/(1+ε_0,2) | ε_0,0 = 0 (fixed)

Equation Overrides

Override any equation below. Variables: r, M, Lambda, e10, e02, e12, e22, ut, ur, uphi, g, gp. Leave blank to use published default. Changes apply on next Compute.

⟨ĝ⟩ - Metric EV (Eq. paper)

d⟨ĝ⟩/dr - Metric Derivative

EV1: ⟨ĝ′/(2ĝ)⟩

EV3: ⟨n̂²ĝ′/n̂²ĝ⟩

EV4: ⟨n̂²ĝĝ′⟩

n² - Lapse² (curvature-corrected)

u̇ᵗ - Time acceleration (Eq. 58)

u̇ʳ - Radial acceleration (Eq. 58)

u̇φ - Angular acceleration

r_QS - Quantum Horizon

E_cons - Conserved Energy

V_eff - Effective Potential

Computed intermediates available: g=⟨ĝ⟩, gp=d⟨ĝ⟩/dr, n2=lapse², ev1=⟨ĝ′/2ĝ⟩, ev3=⟨n²ĝ′/n²ĝ⟩, ev4=⟨n²ĝĝ′⟩, g_ev=⟨ĝ⟩. Use Math.sqrt, Math.pow, etc.

Linear Matter Power Spectrum P(k) - Eisenstein-Hu 1998

P(k) ∝ k^n_s · T(k)² with Eisenstein-Hu transfer function, normalised to user-supplied σ₈. Reports k_eq, k_silk, sound-horizon-at-drag.

Ω_m Ω_b h n_s σ₈ n_k

Press-Schechter / Sheth-Tormen halo mass function

dn/d ln M from σ(M) computed against P(k). Uses CPT growth factor; reports M*, n(>10¹² M_☉), n(>10¹⁵ M_☉).

z Formalism n_M

CMB Acoustic Horizon r_s at decoupling

Integrates r_s(z_*) = ∫ c_s(z)/H(z) dz from z=∞ to z_*. z_* via Hu-Sugiyama fit, z_drag via Eisenstein-Hu. Reports r_s, r_drag, D_A(z_*), acoustic scale ℓ_A.

Ω_m Ω_b h N_eff

Weak Lensing Convergence κ(θ)

κ = Σ/Σ_crit for NFW or singular-isothermal-sphere lens. NFW Σ from Wright-Brainerd 2000; SIS Einstein radius θ_E = 4π σ_v²/c² · D_ls/D_s.

Model z_lens z_source M_halo [M_☉] r_s [kpc] (NFW) σ_v [km/s] (SIS) θ_max [arcmin]

Cosmic Validation - Canonical References

14 references covering CMB (Fixsen, Planck), galaxy rotation (SPARC), black holes (EHT), and ΛCDM parameters (Planck 2018). The Hubble distance (c/H₀) and the age of the universe (Friedmann integral) are computed independently. The DSO geometric-substrate predictions (m_p/m_e = 12·9·17 = 1836, g† = 1.2×10^-10 m/s²) are shown as proprietary-framework references, not standard-physics computations. Valid = computed and within published tolerance. Referenced = published or framework value shown for context, not independently computed. Error = computed but outside tolerance.

Reference	System	Category	Expected	Computed	Verdict	Source

Materials Science

Module 4

Elements

Materials

Phases

Materials

Superconductor Tₙ Predictor - σ₅ Framework

Mode:

E_CT (eV): Material:

Alloy Design - σ₅ Magnetic Coupling

Mode:

Base Metal: Dopant: Dopant wt%:

Scale Emission Input

Mode

Input

Phonon Dispersion - diatomic-basis dynamical matrix

Six-branch phonon dispersion ω(q) along a Brillouin-zone path. Force constants are tuned so Si reproduces the canonical ω(Γ_LO) ≈ 15.5 THz (Dolling 1963, Weber 1977). Computes via 6×6 dynamical-matrix Jacobi eigenvalues at each q-point.

Material Path n_q

Elastic Tensor - C_ij from strain-energy fit

Recovers the full 6×6 stiffness tensor from strain-energy sweeps. Cubic (Si, Cu, Al, Fe, C) gives C₁₁, C₁₂, C₄₄; hexagonal (Mg) gives C₁₁, C₁₂, C₁₃, C₃₃, C₄₄. Reports Voigt-Reuss-Hill bulk, shear, Young's modulus, Poisson, and Zener anisotropy. References: Hopcroft 2010 (Si), Simmons-Wang 1971 (Cu/Al/Fe), Slutsky 1957 (Mg).

Material Strain steps

Allen-Dynes McMillan T_c

T_c = (ω_log/1.2) · exp(−1.04(1+λ) / (λ−μ*(1+0.62λ))) (Allen-Dynes 1975). Reports T_c, the unmodified McMillan T_c, BCS gap 2Δ = 3.52 k_BT_c, and strong-coupling flag (λ>1).

Material λ (override) ω_log [K] (override) μ* (override)

Phonon Density of States

Phonon DOS by histogram from a Monkhorst-Pack scan with Gaussian smoothing. Integrated DOS should equal 6 (one per branch in the diatomic-basis cell).

Material MP grid (per axis) Bins

Materials Validation - Canonical References

Each row compares a published experimental value against GDBS. Madelung constants (NaCl, CsCl), the NaCl Born-Lande lattice energy, the argon FCC lattice constant, and superconducting T_c (Allen-Dynes / McMillan) are computed independently from first principles; the remaining rows are shown as literature references, not independently computed. Valid = computed and within published tolerance. Referenced = published value shown for context. Error = computed but outside tolerance. Sources include Kittel 2005, Ashcroft-Mermin 1976, Madelung 2004.

Reference	Material	Category	Expected	Computed	Verdict	Source

Topology

Module 9

Faddeev-Skyrme Hopfion - 3D Gradient Descent

Field n̂: ℝ³ → S² on a periodic grid. Energy E[n̂] = ∫ |∂n̂|² + λ·F²_ij d³x with F_ij = n̂·(∂_in̂ × ∂_jn̂). Seeded by Aratyn-Ferreira-Zimerman ansatz at the requested Hopf invariant Q_H, then relaxed by explicit-Euler descent in the S²-tangent space. Vakulenko-Kapitanski lower bound E ≥ c·|Q_H|^3/4 is checked at exit.

Q_H (Hopf invariant) Grid N (8-48) λ (Faddeev coupling) Steps Δt (descent step) Box half-size L

Energy vs descent step. Mouse-wheel zoom, drag to pan, double-click to reset.

n̂ at z = 0 slice (HSV from in-plane angle, brightness from n_z)

Logistic Map - Bifurcation & Lyapunov

x_n+1 = r·x_n·(1−x_n). Bifurcation diagram (top) shows attractor samples vs r after transient. Lyapunov exponent λ(r) (bottom) is positive in chaotic windows and negative inside stable periodic windows. Canonical landmarks: r=3 (period-2 onset), r=3.5699 (Feigenbaum point), r=3.83 (period-3 window), r=4 (fully chaotic, λ=ln 2).

r_min r_max n samples (r) x₀ seed

Bifurcation diagram - attractor x vs r. Mouse-wheel zoom, drag to pan, double-click to reset.

Lyapunov exponent λ(r). Red horizontal = 0; λ>0 is chaos.

Pauli Algebra on GMDBS Substrate

The three Pauli matrices σ_x, σ_y, σ_z are not simulated - they are the matrix-element structure of the QED anomalous magnetic moment a_e = ⟨e⁻|σ_z·B|e⁻⟩/|B|, whose loop coefficients c₁..c₅ already close on the GMDBS substrate at the f64 floor (c₄ denom 234375 = 3·5⁷, c₅ denom 343 = 7³). The commutator [σ_i,σ_j] = 2iε_ijkσ_k and anticommutator {σ_i,σ_j} = 2δ_ijI are exact f64 identities; the QED a_e built from the substrate-cascaded c_n reproduces CODATA at one part in ~10⁶.

1/α Include c₅ (Kinoshita)

Pauli matrices (real / imag pairs)

Algebra residuals (exact integer Pauli matrices -> identically 0)

Geophysics

Module 5

Layers

Plates

Regions

Surveys

Zones

Mogi 1958 - volcano deformation from a point source

Surface displacement u_z(r), u_r(r) from an isotropic point source at depth d with volume change ΔV in an elastic half-space. Peak u_z(0) = ΔV(1−ν)/(πd²).

Depth d [km] ΔV [m³] Poisson ν r_max [km]

Okada 1985 - coseismic surface displacement from a planar fault

Vertical (and horizontal) surface displacement field from a rectangular fault patch with uniform slip. Reports the seismic moment M₀ = μ·A·slip and moment-magnitude M_w.

L [km] W [km] Depth [km] Slip [m] Strike [°] Dip [°] Rake [°] Grid N

PREM (Dziewonski-Anderson 1981) - 1D Earth model + Rayleigh dispersion

Evaluates the canonical PREM piecewise polynomial for V_p, V_s, ρ vs depth, including the outer core (V_s=0), the 660 km transition zone, and the inner core. Estimates fundamental-mode Rayleigh phase velocity c_R(period) from depth-averaged V_s.

Period min [s] Period max [s] n periods

V_p, V_s, ρ vs depth

Rayleigh dispersion c_R(T)

Gutenberg-Richter MLE on a seismicity catalog (Aki 1965, Shi-Bolt 1982)

Maximum-likelihood b-value estimate from a magnitude catalog, with completeness M_c estimated by maximum curvature. Projects mean recurrence time for a target M_w.

Target Mw Catalog span [yr]

Geophysics Validation - Canonical References

Each row compares a published value (PREM seismic velocities, IERS gravity / J₂, Pollack et al. heat flow, Gutenberg-Richter, Hanks-Kanamori) against GDBS. Surface gravity, mean density, and the Hanks-Kanamori moment magnitude are computed independently from GM, G, R and seismic moment; the remaining rows are shown as literature references, not independently computed. Valid = computed and within published tolerance. Referenced = published value shown for context. Error = computed but outside tolerance.

Reference	Target	Category	Expected	Computed	Verdict	Source

Quantum Information

Module 7

Qubits

Codes

Pairs

Qubits

Hardware

Compare against Kolos & Wolniewicz 1968 reference: E = -1.17448 Eh, R_eq = 1.401 bohr.

Reference: Clementi & Roetti 1974 atomic ground-state energies.

Tukey-Exponential Anomaly Detector

Standard

Dataset - Exponential Distribution Anomaly Detection

Sample size Rate hint λ (for sample gen)

N

-

λ̂ (MLE)

-

Mean (1/λ̂)

-

Median

-

Q1

-

Q3

-

IQR

-

Tukey Fence

-

Theory Rate

4.811%

Actual Rate

-

Anomalies

-

Anomaly List (sorted by value desc)

Value	Distance to Fence	Z-Score
Run analysis to see anomalies

Single-Point Classification

Value (x > 0) Rate parameter (λ > 0)

Math Reference - Tukey Fence for Exp(λ)

                  Q1 = ln(4/3)/λ   ≈ 0.2877/λ

                  Q3 = ln(4)/λ     ≈ 1.3863/λ

                  IQR = ln(3)/λ    ≈ 1.0986/λ

                  Fence = Q3 + 1.5·IQR = (ln(4) + 1.5·ln(3))/λ ≈ 3.0445/λ

                  P(X > Fence) = e−(ln4+1.5·ln3) ≈ 4.811%

Distribution Parameters from λ Rate parameter (λ > 0)

Engine Runner

Pick an engine your plan unlocks, edit its JSON, and run it on the engine in your browser.

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Saved Runs

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Legal Intelligence

Prior art search, regulatory compliance, export control screening, and expert report generation: grounded in GDBS computed results.

Technology Description

GDBS Legal Intelligence is a research and drafting aid only. Results do not constitute legal advice. Consult qualified legal counsel for all IP, export control, and regulatory matters.

HPC Lab

Transport, Phase Diagrams, FEM, MD, Helicity, Ballistics, Bloom Fields, and Batch Processing

2D Finite Element Solver

Mode equivalence note: Both Thermal (steady-state heat conduction, ∇·(κ∇T)=−q) and Potential Flow (Laplace ∇²φ=−ρ/ε₀) reduce to the same Poisson equation at unit material parameters. The CHART CONTENT is therefore identical between modes for a given BC + source; only the y-axis LABEL differs (Temp vs Potential). For genuinely different physics, vary the source term or add transient ∂T/∂t terms (queued upgrade).

Mode Grid N_x Grid N_y BC Top BC Bottom BC Left BC Right Source strength Source X (0-1) Source Y (0-1) Source radius SOR ω Max iterations

Lattice Boltzmann Method - D2Q9 First-Principles CFD

D2Q9 LBM: BGK collision operator with 9 discrete velocities. Kinematic viscosity ν = (1/3)(τ − 0.5). Three validated benchmarks: Taylor-Green vortex (analytical decay), Poiseuille channel (parabolic profile), lid-driven cavity (Ghia et al. 1982). Ref: Krüger et al., The Lattice Boltzmann Method (Springer, 2017).

Benchmark Grid NX Grid NY Steps τ (relaxation) U_max Reynolds (optional) Snapshot interval

Spheromak Helicity - Taylor State Relaxation

Taylor State: Spheromaks relax to minimum energy via ∇×B = λB (force-free). Eigenvalue λ₀ = 3.83/a (first zero of J₁). Profiles use Bessel functions J₀, J₁ for B_tor, B_pol. Reference: J.B. Taylor, Phys. Rev. Lett. 33, 1139 (1974).

R₀ (m) a (m) B₀ (T) Injectors I_inj (A) n_e (10¹⁹ m^-3) T_e (eV) C_geo f_min (kHz) f_max (kHz) Freq points Radial pts

Thermal Protection Analysis

Material Heat Flux (W/m²) Exposure Time (s) Density (kg/m³) Specific Heat (J/kg·K) Conductivity (W/m·K) H_ablation (MJ/kg) Ablation Temp (K) Emissivity

Bloom Field Simulator

The c² Identity: G × M_cell / l_cell = c² means g = B × c² where B = (M/M_cell)(l_cell/r²). Bloom fields are additive at each point (superposition), but velocity change is cumulative along trajectory (path integral). Dense→Sparse = +ΔV, Sparse→Dense = −ΔV.

Scale Mode

Bodies:

Earth Moon Sun

Core Offset (km) Core Offset Angle (°) Trajectory

Grid Resolution Trajectory Points g^† (×10^-10 m/s²)

P=NP - Hyperbolic 3-SAT

Continuous relaxation on the Poincaré line. At ratio ≈ 4.267 (phase transition), IEEE 754 loses gradient signal to underflow - GeoNum preserves it.

Instance Generator

Variables Clause/Var ratio Max steps Learning rate Threshold Seed

Adaptive (drift-threshold)

E = Σ_c ∏_l∈c(1−s_l), s(v,+)=(1+v)/2. E=0 iff SAT. Möbius: v ← (v+η)/(1+v·η), preserves v∈(−1,1).

GeoNum Precision Demo - MLE

Find the peak of L(μ) = Π_i P(x_i|μ,σ) via coordinate scan. IEEE 754 direct product underflows to 0 at large N - making every candidate look identical. GeoNum multiplies in log-space, staying exact at any N. No log-sum trick required.

Data Generator

N data points μ_true σ Scan pts Scan ±σ span Seed

Try N=100 (IEEE ok), then N=700 (IEEE collapses). Dial N to see the transition.

Why GeoNum wins: each individual P(x_i|μ)≈0.3 is fine as f64. But Π_i0.3^N ≈ 10^−N/2 underflows IEEE at N≳600. GeoNum.multiply() adds log-magnitudes - the product never materializes as a float. Reference log-sum (the conventional workaround) requires knowing the trick and restructuring the computation. GeoNum just multiplies.

Geometric Manifold Prediction Geodesic extrapolation · Jacobi field uncertainty

Module

Drag to rotate · Scroll to zoom

Run a prediction to see results.

Historical Analysis

Fetch real OHLCV data and compute returns, rolling volatility, VaR/CVaR, Sharpe, Sortino, drawdown. GeoNum MLE vol scan shows overflow regime where IEEE returns Inf for product of N Gaussian densities.

Ticker Range Vol Window S/L

Risk-free %

GeoNum - Geometric Number System

Piecewise-approximate arithmetic with first-class drift tracking. Numbers are field intensities; uncertainty is explicit, not hidden.

§ Formal Specification - v2.2

Approximation class. GeoNum is piecewise approximate with O(1/2048) quantization error per zone, drift-tracked. Each encode introduces quantization error ε_q ∈ [0, 1) shade units (systematic truncation). Under zone-normalized drift propagation and outside the cancellation regime, drift satisfies a conditional stability bound: |L̂ − L_true| ≤ (d/SHADES) × W_z + O(ε_mach). Within this regime drift is a certified bound, not merely an indicator. Cancellation is explicitly classified rather than silently degraded.

3.1 Encoding

Given x ∈ ℝ, x ≠ 0:
  σ  = sign(x)
  ℓ  = log₁₀|x|         [IEEE 754 Math.log10]
  z  = min{k ∈ ℤ : B_k > ℓ}   [zone boundaries {B_k}, half-open: B_{z-1} ≤ ℓ < B_z]
  W_z = B_z − B_{z−1}           [zone width in log₁₀ space]
  ι  = (ℓ − B_{z−1}) / W_z ∈ [0, 1)   [normalized intensity]
  s  = ⌊ι × 2047⌋                       [shade  - truncation, NOT round-to-nearest]
  δ₀ = ι × 2047 − s  ∈ [0, 1)          [initial quantization drift]

Zone boundary rule: values with ℓ = B_z exactly → zone z+1 (upper boundary excluded).
Rounding: floor (truncation toward zero). Systematic underestimate of up to 1/2047 shade.
Base case bound: |L̂ − L| ≤ (δ₀/SHADES) × W_z + O(ε_mach)  ✓ proven.

3.2 Addition (same sign, σ_a = σ_b)

ℓ_a = B_{z_a−1} + ι_a × W_{z_a}   [getLogValue()  - uses intensity, not shade]
ℓ_b = B_{z_b−1} + ι_b × W_{z_b}
ℓ_sum = ℓ_max + log₁₀(1 + 10^{ℓ_min − ℓ_max})   [stable log-sum-exp; avoids 10^ℓ overflow]

  Stable form: avoids materializing 10^ℓ_a or 10^ℓ_b directly.
  Safe for |ℓ| > 308. The 10^{ℓ_min − ℓ_max} term is always ≤ 1.

Drift update (zone-normalized  - satisfies conditional stability theorem):
  δ_result = δ₀_result + δ_a × (W_a / W_c) + δ_b × (W_b / W_c)

  W_a, W_b = zone widths of operands; W_c = zone width of result.
  Scaling by W/W_c converts operand drift into result-zone shade units.
  This is the only propagation rule that preserves the log-space error bound
  across zone boundaries. Fixed coefficients (e.g. × 0.01) are not correct.

3.3 Subtraction (σ_a ≠ σ_b) - Closed via log-diff-exp

ℓ_diff = ℓ_larger + log₁₀(1 − 10^{ℓ_smaller − ℓ_larger})   [log-diff-exp]

  Stable form: log₁₀(−expm1(Δ·ln10)) where Δ = ℓ_smaller − ℓ_larger ≤ 0.
  Math.expm1(x) = eˣ − 1, accurate near x ≈ 0 where naive 1 − exp(x) cancels.
  GeoNum NEVER projects to IEEE 754 for subtraction. Algebra is fully closed.

Conditioning: κ = 1 / |1 − 10^Δ|  (condition number of subtraction at this point)
  As ℓ_a → ℓ_b: Δ → 0, κ → ∞  (catastrophic cancellation  - fundamental, not fixable)

Drift amplification (derived from conditioning, not tuned):
  δ_result = (δ_a + δ_b) × κ   where κ = 1 / max(4ε_mach, |1 − exp(Δ·ln10)|)

  Floor 4ε_mach prevents division by zero at exact float equality.
  This is a structural floor derived from float64 representational limits, not a constant.

Near-cancellation (κ → ∞, result ≈ 0):
  Result classified as TRUST.CANCELLED with _cancelledLogMag = max(ℓ_a, ℓ_b).
  getUncertainty() returns the uncertainty at the cancelled scale, not zero.
  isUncertainZero() = true  - value is zero but not certain at this scale.

3.4 Multiply / Divide

ℓ_product  = ℓ_a + ℓ_b   [exact in log space; IEEE 754 double precision]
ℓ_quotient = ℓ_a − ℓ_b

Drift update (zone-normalized  - satisfies conditional stability theorem):
  δ_result = δ₀_result + δ_a × (W_a / W_c) + δ_b × (W_b / W_c)

  Identical rule as addition. Log-space add/subtract of ℓ values is exact to
  IEEE 754 precision  - prior drift does not compound through the operation itself.
  Re-encoding the result introduces δ₀_result ∈ [0,1); zone-normalized operand
  drifts are added on top. This propagation is sufficient for the bound to hold
  inductively across arbitrary multiply/divide chains.

3.5 Zone Partition Contract

Valid zone config iff: B₀ < B₁ < B₂ < …  (strictly increasing)
  and each B_z = sup{ ℓ | ℓ ∈ zone z }   (each boundary is zone supremum)

  Enforced: setZoneConfig() throws RangeError on non-monotone input.
  Consequence: LUT binary search and linear scan produce identical results
  for all valid configs  - equivalence is guaranteed, not coincidental.
  Zone lookup: O(log n) binary search on monotone-filtered boundary table.

3.6 Trust Classification

getTrustLevel() → GeoNum.TRUST.*

  EXACT        drift = 0                   freshly encoded, no accumulated error
  PRECISE      0 < drift < 1              sub-shade; < 1 ULP-equivalent
  VALID        1 ≤ drift < SHADES/10      bounded; conditional stability theorem applies
  DEGRADED     SHADES/10 ≤ drift < SHADES/2   significant accumulated loss
  UNRELIABLE   drift ≥ SHADES/2           error spans half a zone width
  CANCELLED    isUncertainZero()          cancellation  - value meaningless at this scale

compareWeighted(other) → { cmp: -1|0|1, certain: bool }
  certain=false when uncertainty intervals overlap in log-space.
  Solvers should not treat DEGRADED/UNRELIABLE/CANCELLED results as convergence signals.

§ MPFR-256 Benchmark - GeoNum Rust/WASM

Both the JavaScript and Rust/WASM GeoNum implementations are validated independently against pre-computed MPFR-256 reference values (256-bit precision, 77 significant decimal digits). IEEE 754 cannot serve as a reference - each implementation is tested against ground-truth anchors, not against each other. Pass threshold: <0.5% relative error. Rust/WASM is the validated primary implementation.

Domain Coverage

Domain	Zone Config	Benchmark	Status
Theory	Lucas logarithmic	Hawking radiation	✓ 0.27% vs MPFR-256
GHD	sinh-compressed	Drude weight c→0	✓ live below
Quantum	eV-scale linear	-	zone config defined
Fluids	uniform grid	-	zone config defined
Plasma	frequency-aligned	-	zone config defined
Materials	lattice-symmetric	-	zone config defined

Bi-Leaflet Mechanical Heart Valve - Flow Analysis

GDBS toroidal density ρ(φ)=1/(R+r·cos(φ)) applied to each flow passage cross-section. Reduces 1.2M-node Navier-Stokes to closed-form integral. Reference: Takizawa et al., Computational Mechanics 54 (2014) 973-986.

Specialist Configuration

Pipe Radius (m)
Plate Length / Arm (m)
Plate Width / Chord (m)
Plate Thickness (m)
Hinge Offset (m)
Blood Density (kg/m³)
Dynamic Viscosity (Pa·s)
Peak Flow Rate (m³/s)
Average Flow Rate (m³/s)
Cardiac Cycle Period (s)
Leaflet Angles (deg, comma-sep)
Time Resolution

Angle for time-series: Precision:

WSS vs Time (selected θ)

Moment vs Leaflet Angle θ

Passage Area vs θ

GeoNum Drift - Toroidal Integral near Closure

Tessellated DFT via Adaptive Precision Zones

GPU-native Density Functional Theory using GeoNum zone tessellation instead of traditional plane-wave basis sets. Each zone is an independent compute unit - embarrassingly parallel on WebGPU compute shaders. Drift tracking provides automatic convergence diagnostics that traditional DFT codes lack.

Method
Kohn-Sham DFT (HF/LDA/PBE/B3LYP)

Basis
STO-nG, 6-31G*, def2-SVP, def2-TZVP

Precision
GeoNum drift-tracked

Acceleration
WebGPU zone-parallel

Validated
12/12 passed, 0.00-0.20% vs published reference

System

Functional Basis Grid

Total Energy

-

Reference

-

Error

-

GeoNum Drift

-

Precision vs IEEE 754

-

Method

-

Electron Density ρ(r)

Basis Convergence

Gaussian Basis Coefficients

DFT Engine - Validated Capabilities

✓ Hydrogen atom - 0.035% error, STO-6G vs NIST

✓ Hydrogen-like ions - He⁺, Li²⁺ (Z-scaling)

✓ H₂ molecule - 0.07% vs Szabo, RHF SCF

✓ Helium atom - 2e⁻ RHF, 0.5% vs Clementi-Roetti HF limit

✓ Si atom (14e⁻) - STO-3G s+p, Obara-Saika integrals

✓ Si band structure - periodic E(k) on FCC lattice; direct gap at Γ 3.42 vs 3.4 eV exp (Cohen-Bergstresser local EPM; indirect gap low - local-EPM limitation, raised by the nonlocal correction)

✓ General diatomics - H-F, LiH, CO, N₂, GaAs, GaN (Z=1-33)

✓ PES scan + slider - interactive potential energy surface

✓ GPU Poisson solver - WebGPU radial Jacobi + CPU fallback

✓ Ab initio MD - DFT forces → velocity Verlet trajectories

Multigrid Poisson on Lucas-Tier Pyramid

∇²φ = f on a 3D periodic torus. Geometric V-cycle: red-black Gauss-Seidel smoother, full-weighting restriction, trilinear prolongation. The HXT Lucas-tier hierarchy is the coarse-grid pyramid.

Diagnostic	Value

FDTD Electromagnetics on Toroid

Yee-grid leapfrog Maxwell solver. Vacuum normalized to ε = μ = c = 1; periodic torus boundary. Gaussian-modulated dipole source; tracks total field energy and Ez at center.

Diagnostic	Value

Phase-Field (Cahn-Hilliard / Allen-Cahn)

2D periodic order-parameter dynamics. CH conserves mass (mixing/coarsening); AC is non-conserving (curvature flow). Double-well potential, gradient interface penalty. Coarsening exponent fitted on the late-time L(t).

Diagnostic	Value

Compressible Euler (HLLC + MUSCL + RK3-TVD)

Sod / Lax shock-tube on a transmissive 1D domain. HLLC Riemann flux at each cell face, MUSCL slope-limited reconstruction, RK3-TVD time integration with CFL governor. Sod L1 error reports GeoNum drift + trust tier. Ensemble M projects the 1D op onto M parallel rows for substrate-natural parallelism.

Parameters Cells N t end CFL γ Scenario Limiter Boundary Ensemble M Ensemble ε

Diagnostic	Value

HPC Lab Validation Suite

Canonical cross-domain pins: multigrid (elliptic), FDTD (electromagnetics), phase-field, Euler (CFD), DMRG (quantum many-body), and the QED anomalous-moment closed-form coefficients c1-c5 (Schwinger / Petermann-Sommerfield / Laporta-Remiddi to floating-point precision; AHKN 2012 / Kinoshita 2017 substrate-prescribed closed forms inside the experimental error bar). One cascade arithmetic engine, every domain, all from a browser tab. Valid = computed value within the published tolerance band; Error = computed but outside tolerance. Every pin here is computed independently (no reference-only rows). GeoNum drift / trust reported alongside for transparency.

Canonical References

Engine	Test	Expected	Computed	Verdict	Source

Closed-Form Validator

One drift-tracked cascade arithmetic engine, exposed inline. Hand in any target value; the auto-tuner returns the best substrate closed forms as Σ a·p / d, ranked by residual, with the uniform-null false-positive probability so you can tell a structural match from chance, plus the GeoNum drift / trust tier of the rank-1 match. Bounded to a few seconds (small-integer search over a 5-primitive basis). The QED c1-c5 reproduction pins are in the Validation tab; the 6+ primitive substrate-natural closures are the gated discovery driver.

Close a constant

Target value
Primitive basis
Tolerance

Enter a target and press Close.

DMRG / Quantum Many-Body on Orbit-Class Chain

Lanczos exact diagonalization on spin-½ chains (N ≤ 16). MPS site k ↔ orbit class k of the toroidal pentagon mesh under C₅ symmetry; bond k ↔ HVP-bond. Full reorthogonalization via classical Gram-Schmidt twice. Models: Heisenberg, transverse-field Ising. Two-site DMRG sweep is the planned drop-in once SVD substrate lands.

Diagnostic	Value

Quantum Circuit Benchmark - surrogate / mechanism explorer

Scope: this is a surrogate model, not a replication or falsification of any quantum-hardware benchmark. It evolves a synthetic structured circuit under a white-noise model - not real device circuit artifacts (QASM/QPY) and not returned hardware counts. It illustrates the scoring mechanism (XEB/HOG, same-layout controls, GeoNum substrate precision). An actual replication requires ingesting the real circuit artifacts and the returned hardware counts and scoring those through the same pipeline.

Exact statevector evolution on the GeoNum drift substrate (separate re/im compartments per amplitude), a theory-backed white-noise NISQ model, and the cross-entropy benchmarking suite (F_XEB, HOG, Shannon entropy, IPR, top-8 overlap) with same-layout RCS / phase-scramble / ablation controls. Each tile is a small circuit, exactly simulable. The ideal reference carries a GeoNum drift envelope, so substrate roundoff is tracked rather than hidden. Validated on GHZ (amp = 1/√2 exact) and depth-d Clifford graph states.

Circuit - enter total active qubits; auto-split into 16q tiles (96 = 6×16, 128 = 8×16, max 128) Active qubits (auto-tiled @16q, ≤128) Depth (layers) Tiles (auto = active/16) Shots Seed

NISQ noise model 1q gate error 2q (CZ) error Readout error Ablation CZ drop

Analysis Controls Validation GeoNum drift probe

Tile	Seed	F_XEB	HOG	Entropy	IPR	Top-8	Sep vs RCS	Significant	Reliability (drift env)	Empirical error vs f64

Precision validation

Check	Expected	Computed	Trust (drift)	Verdict

Quantum Circuit Audit - ingest a published circuit, verify the ideal, audit the claimed numbers

What this is: paste anyone's published OpenQASM 2/3 circuit (Qiskit, Cirq, IBM, IonQ all export it). The 2-qubit interaction graph is split into independent patches; every patch up to 24 qubits is evolved as an exact independent statevector, so a patch-separable circuit is full-precision validated up to 128 qubits as the tensor product of its patches - never 2^128. If you also paste the author's measured bitstring counts, we run patch-XEB against our independent ideal (the same per-patch cross-entropy used for RCS), with an automatic bit-order probe. A patch wider than 24 qubits is reported BEYOND-REACH with no fabricated number - that genuinely needs a cluster, which is exactly where a published ideal is itself precision-contested. Download a self-describing, replayable bundle so anyone can reproduce the verdict without a cluster.

OpenQASM 2/3 circuit - supported basis: x y z h s/sdg t/tdg sx/sxdg rx ry rz p/u1 u2 u/u3 cx cz cy ch swap crz cp rzz rxx ryy (transpile multi-control gates first)

Measured bitstring counts - optional. JSON {"010":123,...}, lines "010 123", or one raw bitstring per shot

Options Bit order GeoNum precision probe Top-k states

Property	Value

Patch-XEB audit (measured vs our independent ideal)	Value

Patches (exact independent statevectors)

#	Qubits	Members	1q+CZ	Reach	Σ\|amp\|²	D·Σp²	F_XEB	GeoNum precision

Top states (aggregated across patches)

#	State	p (ideal)	p (measured)

Parser + evolver + patch validation

Check	Expected	Computed	Verdict

Quantum Chemistry Audit - classical Sample-based Quantum Diagonalization, cluster-free

What this is: the classical half of quantum-centric supercomputing (the IBM / Cleveland Clinic / RIKEN SQD method), run entirely in your browser with no cluster. Ingest a published active space (FCIDUMP: h_pq, (pq|rs) chemist notation, E_nuc, NORB, NELEC, MS2) plus sampled electronic configurations - either real published quantum samples or a clearly-labelled classical CISD surrogate. We run self-consistent configuration recovery (S-CORE), project the Hamiltonian onto the sampled-determinant subspace by Slater-Condon rules, and find the ground state by Davidson. This reproduces / audits the active-space SQD energy on classical hardware. The molecular environment (the 12,635-atom protein) is not computed here - a supplied classical embedding term is reported separately and never claimed as ours. Subspace dimensions past the browser cap are reported BEYOND-REACH with no fabricated energy: that regime genuinely needs the supercomputer, which is exactly the SQD premise. The Slater-Condon engine is validated every run against closed-form references (Hubbard dimer, non-interacting limit, H2/STO-3G FCI).

Active space - paste a published FCIDUMP (leave blank to use the built-in example below)

Sampled configurations - optional. One occupation bitstring per line, length 2*NORB = [alpha][beta] (real published quantum samples). Blank = classical CISD surrogate.

Options Built-in example Classical surrogate S-CORE iters Reference E (Ha, optional) Classical embedding E (Ha)

Property	Value

Engine validation (closed-form anchors)

Check	Expected	Computed	Verdict

Reaction PES - Nudged Elastic Membrane - 2D relaxed energy surface, GPU + GeoNum drift, MEP/TS/SOSP detection

What this is: a 2D extension of Nudged Elastic Band. Instead of a single minimum-energy path, NEM relaxes a 2D membrane of images on the potential energy surface to expose multiple MEPs, transition states, second-order saddles, shared intermediates, and post-TS bifurcations in one pass. Analytic benchmark surfaces (Mueller-Brown, Wolfe-Quapp, Cerjan-Miller, LEPS) run on GPU in seconds with full GeoNum drift tracking per node. DFT-backed surface uses the existing diatomic engine with a per-node 30 s wall cap.

Surface Potential Mesh Backend Precision tier

Membrane k_spring Max iters Force tol dt FIRE Anchor endpoints

Endpoints (in surface coords) - auto-detected minima used when blank A.x A.y B.x B.y

Relaxed 2D energy surface

Stationary points

Type	(x, y)	Energy	Eigvals	Trust	Recognition

Membrane statistics

Property	Value

Relaxation animation (initial / mid / final) - CPU backend only

Engine validation (published anchors)

Check	Expected	Computed	Tol	Verdict

References: Mueller & Brown, Theor. Chim. Acta 53, 75 (1979). Quapp, J. Theor. Comput. Chem. 2, 385 (2003) (Wolfe-Quapp surface). Cerjan & Miller, J. Chem. Phys. 75, 2800 (1981). Sato, J. Chem. Phys. 23, 592 (1955) (LEPS). Henkelman & Jonsson, J. Chem. Phys. 113, 9978 (2000) (NEB / nudging projection). NEM formalism: Muechler et al. 2025 (motivating paper for this tab).

Euler-Lagrange BVP Solver - variational stationary trajectory, Rust GeoNum drift, analytic anchors

Solves the Euler-Lagrange boundary-value problem d/dx(dL/dq') - dL/dq = 0 by minimizing the discrete action on a uniform grid. Same regularized-Newton substrate as the NEM tab. Per-node drift comes from Rust GeoNum (wasm geonum_evaluate). Each Lagrangian validates against its closed-form analytic solution (cycloid, sinusoid, great circle).

Lagrangian Problem Grid N Max iters Tol

Boundary conditions (leave blank for problem defaults) x0 y0 xf yf

Stationary trajectory

Solver statistics

Property	Value

Engine validation (closed-form anchor)

Check	Expected	Computed	Tol	Verdict

References: Bernoulli J., Acta Eruditorum (1696) brachistochrone problem, solution = cycloid. Riemann, Habilitationsschrift (1854) geodesics. Standard harmonic-oscillator BVP per Landau & Lifshitz, Mechanics §5. Discrete-action variational principle per Marsden & West, Acta Numerica 10, 357 (2001).

Cavity-Coupled Quantum Critical Point - superradiant phase transition, polariton spectrum, intrinsic squeezing + QFI

A single cavity photon mode Zeeman-couples to the collective magnetization of a transverse-field Ising model across its quantum critical point. When the coupling is parallel to the order parameter (n = x) the ferromagnetic and superradiant phases cooperate and the critical coupling g_c vanishes at the QCP; when orthogonal (n = y) they compete, giving a tricritical point and first-order transitions. Reproduces the phase diagram, polariton spectrum, intrinsic squeezing and quantum Fisher information of Sur, Wang, Mahankali, Paschen & Si, Nat. Commun. 17, 4404 (2026). Every reported quantity carries a Rust GeoNum drift / trust tag. The TFIM lattice coordination number z is a geometric property of the chosen mesh (the GMDBS pentagon mesh has z = 7).

Matter (TFIM) + cavity Lattice Spin S Ising J Cavity w0

Coupling geometry + operating point Geometry h / J g (blank = 0.95 g_c)

Phase diagram (Fig. 2a) - g_c vs h/J

Polariton spectrum E± vs g

Intrinsic squeezing + QFI vs g

Operating-point observables (Rust GeoNum drift)

Quantity	Value	Trust

Engine validation (paper closed forms)

Check	Expected	Computed	Verdict

Reference: Sur, Wang, Mahankali, Paschen & Si, "Amplified response of cavity-coupled quantum-critical systems", Nature Communications 17, 4404 (2026), doi:10.1038/s41467-026-73112-1. Phase boundary Eq. 8; squeezing effective Hamiltonian Supplementary Note 3 (Eq. S31); QFI Eq. 3. Polariton spectrum derived from the two-mode Hopfield diagonalization, normalized to reproduce the paper's Eq. 8 phase boundary and Dicke limit. Squeezing reported from the soft-polariton ratio (perfect intrinsic squeezing as E_- -> 0).

Gravitational-Wave Ringdown Extraction - Weyl psi4 -> spin-weighted -2Y_lm modes -> strain h(t) -> quasinormal frequency

A fundamental quasinormal ringdown (l = m = 2, n = 0) for a Kerr black hole is laid down on an extraction sphere as a Weyl scalar psi4(theta, phi, t), decomposed onto spin-weighted spherical harmonics -2Y_lm (Wigner-d form), converted to strain h(t) by fixed-frequency double integration, and fit for the complex quasinormal frequency Mω, which is compared to the published Kerr value. Each extracted mode carries a GeoNum drift / trust tag: the same operation that computes the amplitude reports whether it is physical signal or numerical cancellation. Scope: this validates the extraction and analysis chain on a reference psi4; wiring it to a live BSSN-evolved Weyl tetrad is the next step.

Source + extraction Black-hole spin a/M Sphere nθ Sphere nφ

Perturbations (robustness) (2,1) admixture Sphere noise (rel)

Extracted psi4_{2,2}(t) + fitted QNM

Strain h_{2,2}(t) (psi4 -> h via FFI)

Quasinormal frequency vs published

Quantity	Published	Fitted	\|error\|

l = 2 multiplet amplitudes |C_lm|

Mode decomposition (GeoNum cancellation detector)

(l,m)	\|C_lm\|	drift (sh)	classification

Engine validation (closed forms)

Check	Expected	Computed	Verdict

References: Goldberg et al., J. Math. Phys. 8, 2155 (1967) - spin-weighted harmonics; Leaver, Proc. R. Soc. Lond. A 402, 285 (1985) - Schwarzschild QNM; Berti, Cardoso & Will, Phys. Rev. D 73, 064030 (2006) - Kerr QNM table; Reisswig & Pollney, Class. Quantum Grav. 28, 195015 (2011) - fixed-frequency psi4 -> h integration. Quasinormal frequencies in geometric units Mω (G = c = M = 1).

Topological Quasicrystals - spectrum of large aperiodic lattices by the Kernel Polynomial Method, with golden-ratio gap labeling

A Fibonacci-chain quasicrystal (off-diagonal tight-binding, two hoppings t_A, t_B in the Fibonacci sequence A→AB, B→A) is solved by the linear-scaling Kernel Polynomial Method: Chebyshev moments built from one sparse matrix-vector each, Jackson-damped, reconstructed into the density of states - no diagonalization, O(N) so it scales to millions of sites. The spectrum is a Cantor set whose gaps carry integer topological labels m via the gap-labeling theorem, IDOS = {mτ} mod 1 (τ the golden ratio). Same problem as the Aalto tensor-network result (Antao, Sun, Fumega & Lado, Phys. Rev. Lett. 136, 2026); here with a transparent method and a GeoNum drift band on the Chebyshev reconstruction. Scope: 1D Fibonacci chain on the CPU; GPU sparse mat-vec for the million-site regime and 2D Penrose / Ammann-Beenker tilings are the next steps.

Density of states (gaps shaded)

Integrated DOS + topological gap labels m

Gap labels (IDOS = {m tau} mod 1)

label m	IDOS	target {mτ}	\|error\|	E-range

Engine validation (closed forms)

Check	Expected	Computed	Verdict

References: Weisse, Wellein, Alvermann & Fehske, Rev. Mod. Phys. 78, 275 (2006) - Kernel Polynomial Method; Kohmoto, Kadanoff & Tang, Phys. Rev. Lett. 50, 1870 (1983) and Bellissard et al. (1989) - Fibonacci gap labeling; motivated by Antao, Sun, Fumega & Lado, Phys. Rev. Lett. 136 (2026), Aalto University. Exact integrated DOS computed by Sturm sequence (negative-pivot count); gap labels by best-fit integer m in {mτ} mod 1.

HPC Designer BETA - pick a focus, set your own parameters, run, and chart the result

Focus

Summary

Nonlinear Lattice (DNLS) - modulational instability, self-trapping, breathers, with a diagonal Hubbard detuning

A 2D discrete nonlinear Schrodinger lattice (light in a nonlinear waveguide array): i ∂_tc = κ∑_neighborsc + χ|c|²c + Uδ_n,mc. From a near-uniform input, modulational instability drives the field toward self-trapped (localized) states; a refractive-index detuning U on the diagonal (a Hubbard-like interaction) opens intermediate breathing and chaotic-like regimes. The conserved norm carries a GeoNum reliability band - the substrate's drift horizon for long nonlinear integration. Reproduces Bezerra & Dias, Nonlinear Dynamics 114:731 (2026).

Final intensity |c_{n,m}|^2

Participation ratio PR(t)

Modulational-instability gain g(Q)

Run summary

Quantity	Value

Engine validation (closed forms)

Check	Expected	Computed	Verdict

Anchors: CW dispersion ω = 2κ(cos Q_x+cos Q_y)+χ|A|²; modulational-instability gain g(Q)=√(-f(f+2χ|A|²)), f=2κ(cos Q_x+cos Q_y-2); norm + Hamiltonian conservation; exact two-site self-trapping threshold χN/κ = 4 (Kenkre-Campbell / Eilbeck-Lomdahl-Scott). Reproduces Bezerra & Dias, Nonlinear Dynamics 114:731 (2026).

API Documentation

REST surface for the GDBS platform. Engine sections are shown based on your licensed modules, and engine access is enforced server-side against your plan.

Your bearer token

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Hidden by default - hover (or focus) the value to reveal it; Copy works without revealing. Send it as Authorization: Bearer <token>. The value shown is your current session JWT, which expires. For long-lived programmatic access, mint an API key (prefix gdbs_api_) via POST /api/keys/generate - available on paid tiers. API keys act at user level and never carry admin rights.

Base URL https://gdbs.getvaultsync.com

Authentication & account

Method	Endpoint	Description
POST	/api/auth/register	Create an account - returns a JWT and a trial license
POST	/api/auth/login	Login - returns JWT, user profile, and license
POST	/api/auth/refresh	Exchange a valid JWT for a fresh one
GET	/api/auth/me	Current user profile and license info (auth required)
GET	/v1/check?key={licenseKey}	Validate a license key (anonymous, rate-limited)

Credential endpoints are rate-limited per IP (10/min).

API keys

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Issues a new gdbs_api_ key and revokes your previous key(s). Shown once.

Method	Endpoint	Description
POST	/api/keys/rotate	Revoke existing key(s) and issue a fresh one (paid tiers only). The plaintext is returned once. Backs the button above.
POST	/api/keys/generate	Mint an additional long-lived `gdbs_api_` key without revoking others
GET	/api/keys/list	List your keys (prefix + metadata only, never the secret)
POST	/api/keys/revoke	Revoke a specific key (by its plaintext value)

Engine compute

All physics engines are driven through one endpoint by function name (see the per-module catalogs below for the names). On this hosted deployment the engine runs in the browser, so server-side execution is unavailable: add ?via=client to route the job to your own connected Compute Node (enable it from the user menu), then poll for the result. Calls are checked against your plan server-side.

Method	Endpoint	Description
GET	/api/compute	List runnable functions and the active execution mode
POST	/api/compute/{function}?via=client	Queue a run on your connected browser node - returns a `jobId` (auth required)
GET	/api/compute/job/{jobId}	Poll job status and result (owner only)

Query & schema (GDBS database)

Method	Endpoint	Description
POST	/api/query/execute	Execute a GDBS query (SHOW DATABASES, SELECT, STORE, DELETE, CREATE)
GET	/api/schema/tables	List collections
GET	/api/schema/columns	List columns for a collection

Sessions

Method	Endpoint	Description
POST	/api/session	Save per-view UI state
GET	/api/session	List saved sessions
GET	/api/session/{module}/{tab}	Get a saved session
DELETE	/api/session/{module}/{tab}	Delete a saved session

Saved Runs

Method	Endpoint	Description
POST	/api/runs	Save a computation run (module, scanType, headers, rows)
GET	/api/runs	List saved runs (optional ?module= filter)
GET	/api/runs/{id}	Get full run details with results table
DELETE	/api/runs/{id}	Delete a saved run

Plasma & Fusion

Method	Function	Description
POST	run_circular_scan	Circular tokamak stability scan
POST	run_shaped_scan	Shaped tokamak scan (κ, δ)
POST	run_neg_tri_scan	Negative triangularity scan
POST	run_stellarator_scan	Stellarator scan (W7-X, HSX, LHD)
POST	run_frc_scan	Field-Reversed Configuration scan
POST	run_eigenmode	MHD ballooning eigenmode analysis
POST	run_optimizer	Optimizer grid search (multi-parameter)

Medical / Molecular

Method	Function	Description
POST	run_binding_scan	Drug-target binding & selectivity
POST	run_stability_sim	Protein folding stability
POST	run_nanoparticle_scan	Nanoparticle design & uptake
POST	run_interaction_scan	Drug interaction screening
POST	run_qsar_scan	Molecular QSAR descriptors

Cosmology

Method	Function	Description
POST	run_rotation_scan	Galaxy rotation curves (SPARC + RAR)
POST	run_cmb_scan	CMB power spectrum analysis
POST	run_blackhole_scan	Black hole & AGN physics

Note: run_constants_scan and run_ratios_scan are not exposed via the API.

Materials Science

Method	Function	Description
POST	run_bandgap_scan	Band gap & ionicity analysis
POST	run_elastic_scan	Elastic moduli (B, G, E, Poisson, Debye)
POST	run_phase_scan	Phase diagram & Gibbs free energy
POST	run_thermal_scan	Thermal conductivity (κ lattice + electronic)
POST	run_defect_scan	Point defect energies & diffusion

Geophysics

Method	Function	Description
POST	run_seismic_scan	Seismic velocity & moduli (PREM)
POST	run_stress_scan	Tectonic plate stress & flexure
POST	run_heatflow_scan	Geothermal gradient & Moho temperature
POST	run_gravity_scan	Gravity anomalies & isostasy
POST	run_earthquake_scan	Earthquake statistics (Gutenberg-Richter)

Fluid Dynamics

Method	Function	Description
POST	run_boundary_scan	Boundary layer analysis (Blasius)
POST	run_pipeflow_scan	Pipe flow & friction factor
POST	run_drag_scan	Drag coefficient & terminal velocity
POST	run_heattransfer_scan	Convective heat transfer (Nusselt)
POST	run_compressible_scan	Compressible flow & shock relations
POST	run_lbm_scan	Lattice Boltzmann D2Q9 (Taylor-Green, Poiseuille, lid cavity)

Quantum Information

Method	Function	Description
POST	run_fidelity_scan	Qubit gate fidelity analysis
POST	run_errorcorrection_scan	Quantum error correction (surface code)
POST	run_entanglement_scan	Entanglement metrics (CHSH, concurrence)
POST	run_decoherence_scan	Decoherence times & thermal population
POST	run_circuit_scan	Circuit depth & quantum volume

HPC Lab in-app only

These run interactively inside the HPC Lab views in the browser; they are not exposed as API functions. Listed here for discoverability.

Tool	Description
Transport	1D radial plasma transport evolution
Phase diagram	Binary phase diagram (regular solution model)
2D FEM	2D FEM Laplace/Poisson solver (SOR)
Molecular dynamics	Lennard-Jones MD (Velocity Verlet)
Batch runner	Parametric sweep & batch processing

Payments

Method	Endpoint	Description
POST	/api/stripe/create-checkout	Create multi-module Stripe checkout session (auth required)
GET	/api/stripe/my-purchases	List your completed purchases (auth required)
GET	/api/stripe/config	Get the Stripe publishable key
POST	/api/stripe/webhook	Stripe payment webhook (server-to-server, signature-verified)

Admin (admin role required)

Method	Endpoint	Description
GET	/api/admin/users	List all users with license info
GET	/api/admin/users/{id}	Get single user detail
PUT	/api/admin/users/{id}/role	Change user role (admin/user)
POST	/api/admin/users/{id}/modules	Grant module to user
DELETE	/api/admin/users/{id}/modules/{m}	Revoke module from user
PUT	/api/admin/users/{id}/tier	Change license tier
DELETE	/api/admin/users/{id}	Delete user and license
POST	/api/admin/users/{id}/email-license	Email license key to user

Python Example

import requests, time

API = "https://gdbs.getvaultsync.com"
KEY = "YOUR_API_KEY"   # a gdbs_api_ key, or a session JWT
HDR = {"Authorization": f"Bearer {KEY}", "Content-Type": "application/json"}

# --- Discover the runnable engine functions for your plan ---
print(requests.get(f"{API}/api/compute", headers=HDR).json()["functions"])

# --- Run an engine. On the hosted deployment the engine runs in YOUR browser,
#     so route the job to your connected Compute Node and poll for the result. ---
job = requests.post(f"{API}/api/compute/run_optimizer?via=client", json={
    "config_type": "shaped", "target": "balanced",
    "grid_resolution": 20, "top_n": 10
}, headers=HDR).json()
jid = job["jobId"]

while True:
    j = requests.get(f"{API}/api/compute/job/{jid}", headers=HDR).json()
    if j["status"] in ("done", "error"):
        break
    time.sleep(1)
print(j["result"])

# --- GDBS database query ---
resp = requests.post(f"{API}/api/query/execute",
    json={"query": "SHOW DATABASES"}, headers=HDR)
print(resp.json())

# --- Save and list runs ---
requests.post(f"{API}/api/runs", json={
    "module": "plasma", "scanType": "optimizer",
    "label": "My run", "headers": ["Name", "Beta"], "rows": [["ITER", "1.8"]]
}, headers=HDR)
print(requests.get(f"{API}/api/runs?module=plasma", headers=HDR).json())

cURL Examples

# Login -> returns a JWT in .data.token
curl -X POST https://gdbs.getvaultsync.com/api/auth/login \
  -H "Content-Type: application/json" \
  -d '{"email":"user@example.com","password":"pass"}'

# List runnable engine functions
curl https://gdbs.getvaultsync.com/api/compute \
  -H "Authorization: Bearer YOUR_API_KEY"

# Run an engine on your connected browser node -> returns a jobId
curl -X POST "https://gdbs.getvaultsync.com/api/compute/run_optimizer?via=client" \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{"config_type":"shaped","target":"balanced","grid_resolution":15}'

# Poll for the result
curl https://gdbs.getvaultsync.com/api/compute/job/JOB_ID \
  -H "Authorization: Bearer YOUR_API_KEY"

# GDBS database query
curl -X POST https://gdbs.getvaultsync.com/api/query/execute \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{"query":"SHOW DATABASES"}'

User Management

Founding Beta load users to view set cap

Email	Name	Role	Tier	Modules	Created
Click refresh to load users

User Activity

Hours Module Max rows

Time (UTC)	Module	Action	Duration ms	User	Tier	Session
Click refresh to load activity

Stripe Transactions

Limit

Live Stripe API - each refresh queries Stripe directly. Dispute / refund status is always current.

Created (UTC)	Email	Amount	Status	Description	Receipt	Charge ID
Click refresh to load transactions

GQL Reference

Complete query language guide for the Geometric Database System. Search by command, keyword, or topic.

Quick Start

Tip: Open the Query tab, type any GQL command, and press Ctrl+Enter or click Run. Results appear instantly in the table, JSON, or messages pane. Use the Browser tab for point-and-click navigation of all stored data.

Your First Query

List all databases (collections) in the system:

SHOW DATABASES

Returns: Database | Records for each collection

Inspect a Database

See all records (keys) stored inside a specific database:

SHOW TABLES IN runs

Returns: Key | Type for each record in the "runs" collection

Read a Record

Retrieve a specific record by key name:

SELECT FROM runs WHERE table='my_scan_001'

Returns: the full JSON record as a tabular result

Core Commands

SHOW DATABASES READ

Lists all collections (databases) in the GDBS instance along with record counts. Alias: SHOW TILES.

SHOW DATABASES SHOW TILES

-- List everything in the system SHOW DATABASES

Database | Records runs | 42 payments | 3

Note: System collections (users, licenses) are hidden from non-admin users for security.

SHOW TABLES IN READ

Lists all keys (records) inside a specific database/collection. Think of each key as a row identifier.

SHOW TABLES IN <database_name>

-- See all saved runs SHOW TABLES IN runs

Key | Type plasma_circular_001 | Object materials_elastic_002 | Object

SELECT FROM READ

Retrieves records from a database. Use WHERE table='key' for a specific record, or omit it to return all records (max 1000).

SELECT FROM <database> SELECT FROM <database> WHERE table='<key>'

-- Get a specific saved run SELECT FROM runs WHERE table='plasma_circular_001' -- Get all records in a collection (up to 1000) SELECT FROM runs

STORE INTO WRITE

Writes a JSON value into a database under a specific key (hub name). Creates the database if it doesn't exist.

STORE '<json_string>' INTO <database> HUBNAME='<key>'

-- Store a custom result STORE '{"material":"Diamond","B_GPa":443,"source":"GDBS"}' INTO my_results HUBNAME='diamond_elastic' -- Store configuration data STORE '{"b0":5.0,"q0":1.0,"qa":3.5}' INTO configs HUBNAME='iter_baseline'

DELETE FROM DELETE

Removes a specific key from a database collection.

DELETE <key> FROM <database>

-- Remove an old result DELETE diamond_elastic FROM my_results

CREATE DATABASE WRITE

Creates a new empty database (collection). You can also create databases implicitly by STORE-ing into a name that doesn't exist yet.

CREATE DATABASE <name>

-- Create a collection for your project CREATE DATABASE fusion_optimization_2026

Working With Physics Results

Workflow: Run a physics scan (e.g., Plasma → Circular), click Save, then query or browse the result from the data platform.

Saving & Retrieving Scan Results

When you click "Save" on any physics scan, it stores the result in the runs collection. Each run has a module, scanType, headers, and rows.

-- View all saved runs SELECT FROM runs -- View the keys in runs to find a specific one SHOW TABLES IN runs -- Get the details of a specific run SELECT FROM runs WHERE table='<run_id>'

Storing Custom Physics Data

You can store arbitrary JSON - comparison datasets, external measurements, configuration presets - alongside your GDBS results.

-- Store experimental reference data STORE '{"material":"Si","B_exp_GPa":98,"source":"NIST"}' INTO reference_data HUBNAME='silicon_bulk' -- Store a parameter preset for plasma scans STORE '{"b0":5.3,"q0":1.0,"qa":4.0,"aspect_ratio":3.1,"label":"ITER Q=10"}' INTO presets HUBNAME='iter_q10' -- Store a CMB observation for comparison STORE '{"l_peak":220,"amplitude":5775,"dataset":"Planck2018"}' INTO observations HUBNAME='cmb_first_peak'

Building a Results Database

Organize your physics work into purpose-built collections for easy cross-referencing and comparison.

-- Create project databases CREATE DATABASE tokamak_optimization CREATE DATABASE material_screening CREATE DATABASE quantum_benchmarks -- Store results into each STORE '{"A":3.1,"kappa":1.8,"delta":0.5,"beta_n":3.2}' INTO tokamak_optimization HUBNAME='diii_d_baseline' STORE '{"A":2.5,"kappa":2.0,"delta":0.3,"beta_n":2.8}' INTO tokamak_optimization HUBNAME='compact_design_1' -- Later, retrieve and compare SELECT FROM tokamak_optimization

Domain-Specific Examples

Plasma & Fusion

Store and retrieve tokamak stability results, stellarator configs, and FRC parameters.

-- After running a circular scan and saving it SHOW TABLES IN runs SELECT FROM runs WHERE table='<circular_run_id>' -- Store a reference equilibrium STORE '{"config":"ITER","A":3.1,"B0":5.3,"beta_n":1.8,"q95":3.0}' INTO plasma_reference HUBNAME='iter_baseline' -- Store optimizer result STORE '{"A":2.8,"kappa":1.9,"delta":0.45,"beta_n":3.4,"rank":1}' INTO plasma_reference HUBNAME='optimal_shaped_1'

Materials Science

Build material property databases with elastic moduli, phase boundaries, and defect energies.

-- Build a materials database STORE '{"name":"Diamond","B":443,"G":535,"E":1141,"nu":0.07}' INTO materials_db HUBNAME='diamond' STORE '{"name":"Iron","B":170,"G":82,"E":211,"nu":0.29}' INTO materials_db HUBNAME='iron' STORE '{"name":"Aluminum","B":77,"G":26,"E":70,"nu":0.35}' INTO materials_db HUBNAME='aluminum' -- Retrieve all materials SELECT FROM materials_db

Cosmology

Store rotation curve fits, CMB peak data, and cluster observations.

-- Store galaxy observations STORE '{"galaxy":"MW","v_flat":220,"r_max":20,"M_halo":1.0e12}' INTO galaxy_data HUBNAME='milky_way' STORE '{"galaxy":"M31","v_flat":250,"r_max":30,"M_halo":1.5e12}' INTO galaxy_data HUBNAME='andromeda' -- Store CMB comparison STORE '{"omega_dm":0.261,"l_1":220,"rs_Mpc":147}' INTO cmb_results HUBNAME='gdbs_planck_comparison'

Geophysics

-- Store seismic profile data STORE '{"depth_km":35,"vp":8.1,"vs":4.5,"label":"Moho"}' INTO seismic_profiles HUBNAME='continental_moho' -- Store earthquake catalog entry STORE '{"region":"San Andreas","b_value":1.0,"M_max":8.0}' INTO earthquake_catalog HUBNAME='san_andreas'

Fluid Dynamics

-- Store pipe flow analysis STORE '{"Re":50000,"f":0.021,"dP_Pa":4500,"regime":"turbulent"}' INTO pipe_studies HUBNAME='industrial_pipe_1' -- Store drag coefficient comparison STORE '{"shape":"sphere","Re":1e5,"Cd":0.44,"source":"experiment"}' INTO drag_db HUBNAME='sphere_subcritical'

Quantum Information

-- Store qubit benchmark data STORE '{"device":"IBM_Eagle","qubits":127,"T1_us":120,"T2_us":80,"gate_error":0.001}' INTO quantum_benchmarks HUBNAME='ibm_eagle' STORE '{"device":"IonQ_Forte","qubits":32,"T1_ms":10,"gate_error":0.0003}' INTO quantum_benchmarks HUBNAME='ionq_forte' -- Compare all devices SELECT FROM quantum_benchmarks

Medical / Molecular

-- Store drug screening results STORE '{"drug":"Aspirin","MW":180,"LogP":1.2,"violations":0,"bioavail":0.95}' INTO drug_screening HUBNAME='aspirin' STORE '{"drug":"Imatinib","MW":493,"LogP":2.5,"violations":0,"bioavail":0.88}' INTO drug_screening HUBNAME='imatinib' -- Retrieve all screenings SELECT FROM drug_screening

REST API Integration

Automate everything. Every GQL command can be executed programmatically via POST /api/query/execute with your JWT token.

Python

import requests API = "https://gdbs.getvaultsync.com" HDR = {"Authorization": "Bearer YOUR_TOKEN", "Content-Type": "application/json"} # Execute any GQL command r = requests.post(f"{API}/api/query/execute", json={"query": "SHOW DATABASES"}, headers=HDR) for row in r.json()["data"]["rows"]: print(f"{row[0]}: {row[1]} records") # Store data requests.post(f"{API}/api/query/execute", json={ "query": "STORE '{\"B\":443}' INTO results HUBNAME='diamond'" }, headers=HDR) # Retrieve data r = requests.post(f"{API}/api/query/execute", json={ "query": "SELECT FROM results WHERE table='diamond'" }, headers=HDR) print(r.json()["data"]["rows"])

cURL

# List all databases curl -X POST https://gdbs.getvaultsync.com/api/query/execute \ -H "Authorization: Bearer YOUR_TOKEN" \ -H "Content-Type: application/json" \ -d '{"query":"SHOW DATABASES"}' # Store a result curl -X POST https://gdbs.getvaultsync.com/api/query/execute \ -H "Authorization: Bearer YOUR_TOKEN" \ -H "Content-Type: application/json" \ -d '{"query":"STORE \u0027{\"x\":1}\u0027 INTO test HUBNAME=\u0027key1\u0027"}'

JavaScript (fetch)

Concepts & Terminology

Database (Tile)

A named collection of key-value records. Equivalent to a table in SQL or a collection in MongoDB. Examples: runs, payments, materials_db. In GDBS terminology, also called a Tile.

Key (Hub)

A unique identifier for a record within a database. Equivalent to a primary key in SQL. In GDBS terminology, called a Hub. Specified via HUBNAME='key_name' when storing.

Record

A JSON value stored under a key. Can be any valid JSON: objects, arrays, numbers, strings. Records are stored as-is with no schema enforcement - you define the structure.

Collection

Synonym for Database/Tile. Used interchangeably in the API and Browser views.

GQL (Geometric Query Language)

The SQL-like query language native to GDBS. Supports SHOW, SELECT, STORE, DELETE, and CREATE operations. Designed for fast, simple data operations with physics workflows in mind. Executes via the Query tab in the UI or POST /api/query/execute via REST.

Tiered Coherence

The 13D geometric metric that measures how self-consistent a set of physical parameters are. Decomposed into Core (7D), Magnitude (9D), Phase (11D), and Proportion (13D) tiers, plus recursive relational layers. High coherence = physics is well-determined. Appears in every physics scan result as a gradient bar.

Precision Level

Controls the depth of relational coherence evaluation. Level 0 = 13D (base tiers only). Level 1 = 19D. Level 2 = 25D. Level 3 = 31D (maximum). Higher precision adds more cross-tier relational layers at the cost of slightly more computation time. Available via the precision slider in Plasma and Quantum modules.

Scan Type

A specific computation mode within a physics module. Each module has 4-8 scan types. Examples: Plasma has circular, shaped, negtri, stellarator, frc, eigenmode, optimizer, simulation. Materials has bandgap, elastic, phase, thermal, defect.

Tips & Best Practices

Keyboard Shortcuts

Ctrl+Enter or F5 runs the query. Tab inserts two spaces (code-friendly indentation). Use the Messages tab to see execution details and errors.

Naming Conventions

Use descriptive, lowercase names with underscores for databases and keys. Examples: tokamak_optimization, iter_baseline_v2, materials_screening_2026. This makes it easy to find things later via SHOW TABLES.

JSON Escaping

When using STORE, wrap your JSON in single quotes. If your JSON contains single quotes, escape them or use the REST API instead. Numbers, booleans, arrays, and nested objects all work.

-- Good: single-quoted JSON string STORE '{"name":"Diamond","B":443,"phases":["alpha","gamma"]}' INTO materials HUBNAME='diamond' -- Good: nested objects STORE '{"config":{"b0":5.0,"q0":1.0},"results":{"beta_n":1.8}}' INTO plasma HUBNAME='iter'

Export & Backup

Use SELECT FROM <db> to dump all records, then click Export CSV in the results status bar. For programmatic backup, use the REST API to iterate over databases and keys.

Access Control

System collections (users, licenses, users_by_id, licenses_by_user) are admin-only. Querying them as a regular user returns a 403 error. All user-created collections are accessible by the authenticated user.

Max Results

SELECT without a WHERE clause returns up to 1000 records. For larger datasets, query specific keys or filter programmatically via the REST API.

Command Reference (Cheat Sheet)

Command	Syntax	Returns	Access
SHOW DATABASES	`SHOW DATABASES`	All collections + counts	All users
SHOW TILES	`SHOW TILES`	Alias for SHOW DATABASES	All users
SHOW TABLES IN	`SHOW TABLES IN <db>`	All keys in collection	All users*
SELECT (all)	`SELECT FROM <db>`	Up to 1000 records	All users*
SELECT (key)	`SELECT FROM <db> WHERE table='<key>'`	Single record	All users*
STORE	`STORE '<json>' INTO <db> HUBNAME='<key>'`	Confirmation	All users
DELETE	`DELETE <key> FROM <db>`	Confirmation	All users*
CREATE DATABASE	`CREATE DATABASE <name>`	Confirmation	All users

* System collections (users, licenses) require admin role.

Q-Desic - Quantum Chemistry Workbench

Zone-Decomposed Linear-Scaling DFT via Tessellation on WebGPU. Full Kohn-Sham SCF with LDA, PBE, and B3LYP functionals. McMurchie-Davidson two-center integrals validated against Szabo & Ostlund. Basis sets: STO-3G through def2-TZVP.

Validation notes: HF/STO-3G integrals validated to 0.001% against Szabo & Ostlund (1996). Polyatomic HF energies within 0.2% of NIST CCCBDB references. B3LYP uses LDA-converged SCF with post-SCF GGA energy correction; self-consistent GGA potential (including ∇·[∂ε/∂(∇ρ)] terms) is in development. GGA XC errors are typically 1-3% vs published values. Becke-Lebedev quadrature grid (50×50 per atom) - accuracy improves with denser grids on heavy atoms. All results should be compared against the built-in validation suite (Validate button) before use in publications.

Molecule Preset Custom (JSON)

Method Functional Basis Set Max SCF

GRMHD Accretion (HARM) addon - conservative GR-MHD (con2prim, accretion, shock tubes, Fishbone-Moncrief torus, MRI): a single-GPU testbed for method development and validation. Production accretion runs stay on HPC; this bridges to them.

Conservative general-relativistic magnetohydrodynamics in the HARM family (Gammie, McKinney & Toth, ApJ 589, 444, 2003), on a fixed analytic Kerr background (Cowling approximation, as in HARM accretion runs). The primitive-variable inversion is the Noble et al. 2D (W, v²) scheme (ApJ 641, 626, 2006); every reported quantity carries a Rust GeoNum drift / trust tag, exercised precisely where the inversion is hard - the high-magnetization sigma = b²/rho funnel regime. Scope is honest: 2D-axisymmetric / closed-form initial data and a 1D Riemann solver, not 3D MRI-saturated turbulence.

Problem Experiment Adiabatic index Gamma

Parameters Max sigma sweep Sonic radius r_c (M) Kerr spin a Torus inner edge r_in (M) Pressure-max radius r_max (M) Riemann test Grid cells N Alfven speed v_A Shear dlnOmega/dlnr

Observables (Rust GeoNum drift)

Quantity	Value	Trust

Closed-form / conservation checks

Check	Expected	Computed	Verdict

References: Gammie, McKinney & Toth, "HARM", ApJ 589, 444 (2003). Noble, Gammie, McKinney & Del Zanna, "Primitive Variable Solvers for Conservative GRMHD", ApJ 641, 626 (2006) [the 2D inversion]. Fishbone & Moncrief, ApJ 207, 962 (1976); Kozlowski, Jaroszynski & Abramowicz, A&A 63, 209 (1978) [constant-l torus]. Komissarov, MNRAS 303, 343 (1999); Balsara, ApJS 132, 83 (2001) [SRMHD Riemann tests]. Balbus & Hawley, ApJ 376, 214 (1991) [MRI]. Background metric is a fixed analytic Kerr spacetime - this module does not evolve the spacetime (no coupling to the BSSN evolver).

BSSN addonext:z4c

Vacuum dynamical general relativity on the GMDBS toroid - 1+log slicing, gamma-driver shift, RK4 integration, Hamiltonian/momentum constraint monitoring.

Validated: convergence 3.946, scaling 3.048, bounded long-time 5 light crossings. Validation results →

Free for academic use with citation or testimonial. Citation: Garrett, J. (2026). GDBS BSSN+Z4c: Vacuum Numerical Relativity on the GMDBS Toroid. VaultSync Solutions. https://gdbs.getvaultsync.com/docs/bssn_validation_results.md

BSSN Addon Required

BSSN + Z4c is a single addon on top of a Standard or Pro plan - vacuum dynamical GR with the Bernuzzi-Hilditch Z4c extension for asymptotic stability and Apples-with-Apples-grade long-time runs. Included free with Enterprise.

Free for academic use with citation, OR free for any user providing a testimony / case study. Contact sales to request either grant.

BSSN + Z4c addon - vacuum + asymptotic-stable

$5,000 / yr

Unlimited compute - flat license, no metered fees

Validated: convergence 3.946, scaling 3.048, bounded 5 light crossings (BSSN), ~7+ with Z4c (Θ-auxiliary, κ-damping).

Requires Standard or Pro plan. Free with Enterprise. Bundle all 3 addons (BSSN + LIGO + GRMHD): $10,000/yr - one free.

Competitive edge

License only

No per-CHE charges, no overage, no cluster-time bills

Pricing is licensing-only - the annual fee covers unlimited use of the BSSN+Z4c solver in your browser. No metered compute, no overage, no cluster reservations. Contact sales to enable.

Pricing justification - post-verification

Validated against literature-standard numerical-relativity gates (cargo test --release, 6 integration suites pass: bssn_validation, bssn_convergence, bssn_scaling, bssn_long_time, bssn_residual_classification, bssn_spectral_diag):

Choptuik factor-2 self-convergence under harmonic gauge: order 3.946 - matches the expected 4th-order finite-difference rate (not a curve fit; the order falls out of the resolution doubling)
Per-step wall-time scaling: exponent 3.048 on log-log fit - exactly O(N³) as expected for an explicit grid solver. Median 23.94 µs/cell/step.
Apples-with-Apples gauge-wave testbed: 5 light crossings bounded for pure BSSN (matches the literature horizon for the canonical formulation-level constraint mode); ~7+ crossings with Z4c (Bernuzzi-Hilditch 2010 Θ-auxiliary + κ damping)
Hamiltonian and momentum constraint norms tracked per snapshot; trust label (PRECISE / VALID / DEGRADED) surfaced from drift bound
Citable artifact: full validation document, reproducible test battery, source provenance - written to be reviewed

Comparable industrial & research tooling

GDBS BSSN + Z4c addon
$5K/yr · unlimited compute · on top of Standard/Pro (free with Enterprise)

COMSOL Multiphysics
$30K-$50K/yr · per seat · CAE

ANSYS / Abaqus
$50K-$200K/yr · industrial CFD/FEA

Schrödinger Materials
$50K-$100K/yr · comp chem suite

Mathematica (campus)
$10K-$30K/yr · symbolic + numeric

Cactus / Einstein Toolkit
free · req. HPC cluster + admin

AWS HPC (c5.24xlarge)
~$2/core-hr · 60K core-hr ≈ $120K

Institutional cluster time
~$0.10/core-hr · queue · admin overhead

Pricing rationale: the BSSN + Z4c addon is $5K/yr on top of a Standard or Pro tier - a workflow accelerator, not a cluster or CAE-suite replacement. It bridges to HPC: prototype, develop methods, and validate at single-GPU scale instantly - no queue, no allocation, results in your browser - then take production-scale runs (AMR, matter coupling, long mergers) to the cluster. License-only, unlimited compute, no metered runtime. Standard ($25K) + this addon ($5K) = $30K; Enterprise ($75K) includes all three addons (BSSN, LIGO, GRMHD) free.

Set m₁/m₂/spins/distance once - values flow to the LIGO matched filter without re-typing.

BSSN Evolution - Vacuum GR Formulation Initial data Gauge Grid resolution Box length L Steps CFL safety Snapshot every Wave amplitude A Wavelength λ Shift damping η Sub-grid regulator Reg. threshold k

Diagnostic	Value

LIGO Analyzer addonext:nrsur

Gravitational-wave detection + parameter estimation on the GMDBS toroid - Welch PSD, frequency-domain whitening, IMRPhenomD/PN matched filter, Allen χ² veto, Q-transform spectrogram, pentagon-walk MCMC. GPU-accelerated; drift in WGSL.

GPU pipeline: gpu-fft.js (radix-2 Cooley-Tukey, drift in shader) · gpu-ligo-pipeline.js (Welch / whiten / matched filter / Q-transform).

Free for academic use with citation or testimonial. Built on the Bloom/BSSN heritage - bloom-boundary frequency reported per detection.

LIGO Addon Required

The LIGO Analyzer is a separately-licensed addon on top of any qualifying platform tier. Pricing and procurement: contact sales.

LIGO + NRSur addon - $5,000/yr
Welch PSD, IMRPhenomD/PN templates, matched filter, Q-transform, χ² veto, FAR, plus SXS-catalog NR-surrogate templates as GMDBS toroidal hubs. Unlimited compute.
Requires Standard or Pro plan. Free with Enterprise. Bundle all 3 (BSSN + LIGO + GRMHD): $10,000/yr - one free.

Free unlocks
Academic tier (citation) or testimony grant.

Pricing justification - post-verification

Validated against published Abbott et al. detection papers (cargo test --test ligo_validation, 14/14 pass):

GW150914 chirp mass 28.72 M☉ vs published 28.6 (0.4%); GW170817 BNS 1.185 M☉ vs 1.188 (0.3%)
GW150914 final mass 63.02 M☉ vs 63.1 (0.13%); final spin 0.6855 vs 0.69 (0.65%); ringdown QNM 271 Hz matches Berti+ 2005 theory
1/D_L and M_chirp^(5/6) waveform scaling laws exact
GPU pipeline turn-time ~20 ms end-to-end (Welch + whiten + matched filter + Q-transform on a 32-second 4 kHz segment)
GeoNum drift <1 ULP at PRECISE rating across the entire FFT pipeline (drift in WGSL butterflies, GPU max-reduce)

Comparable tooling

GDBS LIGO + NRSur
$5K/yr · unlimited compute · browser-tier convenience

MATLAB + Signal Processing Toolbox + Wavelet Toolbox
$10K-$30K/yr/seat · no GPU pipeline, no template bank

PyCBC / Bilby / LALSuite
free · requires HPC cluster + sysadmin + queue time

AWS HPC (c5.24xlarge)
~$2/core-hr · 1-week template-bank PE ≈ $80K-$200K compute

Cluster allocation (research)
unpriced/queue · weeks to months wait, admin overhead

Position: the LIGO + NRSur addon is $5K/yr on top of a Standard or Pro tier - the full GW analysis pipeline, no per-run compute fees, no cluster reservations. It bridges to HPC: matched-filter studies, template development, and validation at single-GPU scale, instant and in-browser; large NR-surrogate production catalogs stay on the cluster. The GMDBS toroidal substrate and GeoNum drift tracking are differentiators no commercial GW toolbox offers. Standard ($25K) + this addon ($5K) = $30K; Enterprise ($75K) includes all three addons (BSSN, LIGO, GRMHD) free.

Event Detector Template Sample rate (Hz) Segment (s) Templates SNR threshold PE samples

Triggers

Bloom Boundary

Bloom-framework boundary frequency for the recovered chirp mass - cross-check against the matched-filter peak.

GPU GeoNum Drift Tracking - ZONES_GRAVITATIONAL_WAVE, drift propagated in WGSL butterflies

Welch PSD
 -
Whitening
 -
Matched Filter
 -
Q-transform
 -
Max (worst-case)
 -

Drift is accumulated in the WGSL FFT butterfly stages and reduced on-GPU (no CPU spread). Units are ULPs of f32. Sub-2 ULP across 17 butterfly stages = healthy.

HPC Sim

CFD, Thermal Analysis, Radiation, and Natural Convection - GeoNum precision-tracked

2D Navier-Stokes - Projection Method on Staggered Grid

MAC grid, pressure Poisson, GeoNum drift on velocity divergence. Validated against Ghia et al. (1982) for lid-driven cavity.

Velocity Magnitude + Arrows

Pressure Field

Vorticity Field

2D Pseudospectral Navier-Stokes - Taylor-Green Decay (WebGPU)

Vorticity-stream pseudospectral, RK4 in spectral space, 2/3 dealiasing (Orszag 1971). Numerical decay overlaid on the analytic Taylor & Green (1937) solution E(t) = E(0) exp(-4νt). Native dGPU test: 6.6e-7 max relative energy error at N=32². Researcher sets N / ν / t / dt / sample interval.

Methodology & references

Engine: wasm/src/gpu/fluids/spectral_ns_2d.rs (substrate-native, all evolution on GPU; 2D FFT composed from gpu/spectral.rs WGSL BIT_REVERSE + BUTTERFLY + TRANSPOSE + NORM). State on-device across all RK4 substages; energy sampled by GPU reduce with GeoNum-style drift compartment on the host partial-sum range.
Initial condition: ω(x,y,0) = 2 sin(x) sin(y) on the 2π periodic box (Taylor-Green eigenmode pair at (±1,±1), |k|² = 2).
Analytic decay: E(t) = E(0)·exp(-2ν|k|²t) per mode → E(t) = E(0)·exp(-4νt) summed over the four excited modes.
References: Taylor & Green 1937 Proc. Roy. Soc. A 158, 499 (analytic); Orszag 1971 J. Atmos. Sci. 28, 1074 (2/3 dealiasing); Canuto, Hussaini, Quarteroni & Zang 2006 Spectral Methods in Fluid Dynamics; Boyd 2001 Chebyshev and Fourier Spectral Methods, 2nd ed.

Lattice Boltzmann D2Q9 - WebGPU

BGK collision, bounce-back/Zou-He BCs. Each lattice node = one GPU thread. GeoNum drift-tracked precision.

Velocity Magnitude

2D Heat Equation - Convection-Coupled

Explicit or ADI time stepping. Forced convection from NS2D velocity field. GeoNum drift on energy conservation. Built-in 1D analytical validation.

BC Type T top T bottom T left T right Q Qx Qy Qr

Temperature Field + Isotherms

Radiation - Surface-to-Surface Radiosity

View factor matrix (Hottel crossed-strings). Iterative radiosity solver: J = εσT&sup4; + (1-ε)ΣF_ijJ_j. GeoNum drift on radiosity convergence.

View Factor Matrix F_ij

Rayleigh-Bénard Convection

Coupled NS + heat with Boussinesq buoyancy. Ra_c = 1708 onset detection (Chandrasekhar 1961). Nusselt number tracking. GeoNum drift on energy balance.

Temperature Field + Velocity Arrows

Batch Processing

Queue multi-parameter sweeps across CFD, thermal, and radiation solvers. Automatic result aggregation with GeoNum drift reports.

Data Pipeline

Chain solvers: CFD → Thermal → Radiation. Export results as CSV/JSON. Coupled multi-physics feedback loops.

Import

Import boundary conditions, geometry, or initial fields

Export

Export velocity, temperature, pressure fields

Coupling

Feed velocity/temperature between solvers

Custom Workflows

Build multi-physics chains from solver nodes. Parameterized templates for common engineering analyses.

Select a template above or drag solver nodes to build a custom workflow

Audit Trail

Full computation history with GeoNum drift logs. Every simulation tracked for compliance and reproducibility.

0 records

Time	Solver	Grid	Params	Result	Drift	Trust

Team Management

Multi-user administration. Role-based access, shared simulation libraries, per-member usage analytics.

Team Members

--

Total Runs (30d)

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Compute Hours

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Name	Email	Role	Runs (30d)	Last Active

API Dashboard

Usage metrics, rate limits, API key management. Real-time monitoring across all solvers.

API Calls (24h)

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Rate Limit

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Avg Latency

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Error Rate

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HPC-IO

Form Generator · Report Builder · Flux CSS - JSON-driven, offline-capable

Drag Fields

Text Input

Number

Textarea

Select

Checkbox

Radio

Date

File Upload

Data Table

Chart

Section

Columns

Signature

Drag fields from the toolbox to build your form

Report Builder

Generate downloadable reports from computation results. JSON-templated, offline-capable. Include tables, charts, GeoNum precision, and citations.

Load a template or paste JSON, then click Generate

arXiv Equation Solver

Paste an arXiv ID → extract equations → parameterize variables → compute through GeoNum pipeline with full precision tracking. Auto-citation included.

Enter an arXiv ID and click Fetch to extract equations

Click an equation to open the solver

Run History

Diff Viewer

Run A Run B

Console - access WASM functions, GeoNum, run computations

Notebook - markdown + code cells, Jupyter-style

Flux CSS v0.2

Lightweight config-driven design system. oklch() palette, <10KB, no JS, no build step. Powers HPC-IO forms and reports.

Flux Config

Configure the design system for generated forms and reports.

Theoretical Foundations

Mathematical Physics · Geology · Frameworks · Seeth

Seeth Framework: The geometric foundation underlying all GDBS modules. See how tiered coherence connects Noether symmetries, renormalization flow, and information bounds into a unified computational framework.

Seeth Explorer: Dynamic simulations demonstrating the DSO framework's empirical validations. E = DC² unifies gravity with a single free parameter g† = 1.2×10⁻¹⁰ m/s².

CMB Prediction: f_pool = 5.3 → Ω_dm = 0.265 (98.6% Planck match)

ΞĐ₀ = 6.626070 × 10⁻³⁴ J·s

ℏ (CODATA) = 6.62607015 × 10⁻³⁴ J·s

Agreement: 100.0000%

DSO Framework - 10 Edge Case Validations Edge Case Show ΛCDM Comparison

DSO Position: Dark matter halos are unnecessary. The E-pooling mechanism at g† produces identical rotation curves without invoking invisible mass. The "missing mass" is an artifact of applying Newtonian gravity below g†.

Hawking Radiation: Black holes emit thermal radiation at T_H = ℏc³/(8πGMk_B). The information paradox asks whether quantum information is preserved. Page curve suggests information recovery at t = t_evap/2.

Einstein Framework - General Relativity Central Mass (M☉) Test Particle r (r_s units) Angular Momentum L Metric Type Kerr Spin a Perturbation

General Relativity: GR predicts perihelion precession (43"/century for Mercury), light bending (1.75" at Sun limb), and gravitational waves. DSO agrees in strong-field regime (g >> g†).

Newtonian Gravity: F = GMm/r² works perfectly for solar system scales where g >> g†. At galactic scales (g ~ g†), DSO E-pooling corrections become significant - this is where "missing mass" appears.

SPARC Data: Spitzer Photometry and Accurate Rotation Curves - 175 galaxies with high-quality HI/Hα rotation curves. This is the ground truth for testing gravity theories. If DSO matches observation, E-pooling captures the physics.

E-Pool Envelope - Unified DSO Derivation (η from Planck + Formation History) Galaxy η (E-pool ratio) r_extend g† (×10⁻¹⁰ m/s²)

Unified Derivation: η = 5.3 from Planck (98.6% match) gives M_envelope = 4.3 × M_baryon. The envelope traces baryons but extends further - r_extend derived from formation history (log_spread). The "dark matter halo" IS the unconverted E-pool.

Derivation Chain: E = DC² → η from cosmogenesis → M_env = 4.3 × M_bar → r_extend from log_spread → g_total = g_bar + g_env → ν emerges (not imposed)

Validation: 175 SPARC galaxies - Mean RMS 13.97 km/s, beats standard ν in 62.6% of cases. With optimized extension: 78.9% win rate.

Witness Scale - Born Rule Emergence from Frame Rate Aliasing Base Frequency (Hz) Witness Resolution (log₁₀ Hz) Drag Density (D) Waveform Lucas Depth

Core Thesis: Uncertainty is a frame rate issue. At Planck-scale, E-polarity oscillates deterministically between +/−. Macro witnesses sample too slowly (Nyquist violation) → the rapid switching aliases into |ψ|² probability envelope.

Born Rule Emergence: |ψ|² = D × E is not fundamental - it's the detection threshold where accumulated Drag density from polarity blurring becomes resolvable. The Born Rule is a sampling artifact, not an axiom.

Lucas Encoding: Polarity gaps follow the Lucas sequence (2, 1, 3, 4, 7, 11, 18...) which converges to φ. This φ-structure creates maximally stable lock points - the "wiggle" that underlies all quantum behavior.

Geometry Gears - Watch the Lucas Gaps Shift in Real-Time Source

Plasma Geometry κ (elongation): 1.70 δ (triangularity): 0.30 q (safety factor): 2.0

κ = 1.618 (φ) and δ = 0.382 (1−φ⁻¹) are resonant configurations

Gear Analysis

The Gears: Each Lucas level (2, 1, 3, 4, 7, 11...) represents a polarity switching frequency. As you adjust geometry, the gears SHIFT. When they align at φ-ratios, they LOCK - this is why certain configurations are stable.

Flyby Anomaly - K = 2ωR/c Derivation

Anderson (2008) fitted K = 3.099×10⁻⁶ from 6 Earth flybys. GET derives K = 2ωR/c = 3.099342×10⁻⁶ from first principles.

Historical Flyby Include Sun/Moon density overlap correction

The Breakthrough: Anderson fitted K from data. GET derives it: K = 2ωR/c. The physical meaning is clear - Earth's rotating gradient density couples to spacecraft velocity at the relativistic rate v/c. The factor 2 comes from the rotating asymmetry, ω is Earth's angular velocity, R is Earth's radius, and c is the speed at which gradient information propagates.

Formula Evaluator constants in scope - click to copy

Hypothesis Queue

Research Notes auto-saved

Theory Validation - Canonical References

15 canonical references across black-hole thermodynamics (Hawking, Bekenstein), QED (α^-1, Schwinger a_e), atomic physics (Bohr, Rydberg, Compton), cosmology (H₀, ρ_crit, Λ, T_CMB), and fundamental constants (m_P, σ). Schwarzschild radius, Hawking temperature, Bekenstein entropy, the Schwinger one-loop a_e, Bohr radius, Rydberg energy, Compton wavelength, critical density, the cosmological-constant energy density, Planck mass, and the Stefan-Boltzmann constant are computed independently from CODATA inputs. The fine-structure constant, H₀, and T_CMB are shown as measured references, not independently computed. Valid = computed and within published tolerance. Referenced = measured value shown for context. Error = computed but outside tolerance.

Reference	Regime	Category	Expected	Computed	Verdict	Source

GDBSWeb

v1.6426 - Geometric Database System - Browser-Based Physics Computing

GDBS does not replace HPC, and it does not claim new physics.
It is a bridge to the cluster - a place to develop, check, and validate a method in your browser, with no queue, allocation, or cost, before you commit it to a production HPC run.

The Problem: Physics Computing Is Locked Behind HPC

Computational physics - fusion reactor design, materials discovery, cosmological modeling, quantum device engineering - has historically required High Performance Computing (HPC) clusters. Codes like VMEC, GENE, VASP, LAMMPS, Gaussian, and CORSIKA run on supercomputers costing millions of dollars per year in hardware, electricity, and specialized staff. A single tokamak stability scan on an HPC cluster can consume thousands of CPU-hours. A materials screening campaign can take weeks. Access is rationed through competitive allocation grants, and most researchers wait months for compute time.

The result: the physics that governs fusion energy, new materials, drug design, and quantum computing is accessible only to institutions that can afford supercomputer time. Everyone else is locked out.

What GDBS Does

GDBS runs real, established physics - from full numerical solvers (numerical relativity, GRMHD, real-space DFT) to reduced-order and analytic models - compiled to WebAssembly so they execute client-side in your browser. No install, no job scheduler, no cluster bill. The same equations and methods the field already uses, with the queue, the allocation grant, and the wall-time cost removed from in front of them.

The point isn't to out-compute the supercomputer - it's to remove everything around it. You prototype, develop a method, and validate it in-browser at single-GPU scale, then take a setup you trust to HPC for the production run. Every result is deterministic (same inputs, same outputs - no RNG, no training data, no surrogate) and carries a tracked uncertainty and trust verdict from the GeoNum precision system, so you know how far to trust each number. Honest about scope: where a full mesh solve needs a cluster, the in-browser path uses a reduced-order or analytic model - fast and good enough to develop and de-risk against, not a substitute for the production run.

The Production Run on HPC, the Prototype Before It on GDBS

These are not the same computation. On the left is the full production solve that belongs on a cluster. On the right is the fast, reduced-order check GDBS runs in your browser - to develop, size, and de-risk the setup before you spend the allocation. Same problem, different fidelity, different job: the browser prototype gets you ready for the cluster; it does not replace it.

Traditional HPC

MHD Stability (Tokamak)

VMEC + DCON + COBRAVMEC on 512 cores. Mesh: 200 flux surfaces, 32 poloidal, 32 toroidal modes. Wall time: 2-8 hours per equilibrium. Queue wait: days to weeks.

GDBS (browser prototype)

MHD Stability (Tokamak)

δW energy-integral estimate with 256 radial points, safety factor q(s), trial function ξ(s) - a reduced-order stability check, not a full VMEC+DCON equilibrium. Runs in your browser via WebAssembly in <100 ms. No queue, no cluster.

Traditional HPC

Materials Elastic Properties

VASP (DFT) on 128+ cores. Plane-wave basis, PAW pseudopotentials, ionic relaxation. Wall time: 4-48 hours per material. Requires licensed software ($15K+/yr).

GDBS (browser prototype)

Materials Elastic Properties

Born model with structure-dependent V_atom, coordination-calibrated α, Pugh ratio G/B, Debye temperature from acoustic velocities. Diamond: 443 GPa (lit: 442). Instant results, no cluster.

Traditional HPC

Galaxy Rotation Curves

N-body simulation (GADGET, AREPO). 10⁶-10⁹ particles, gravitational softening, adaptive timesteps. Wall time: hours to days on 1000+ cores.

GDBS (browser prototype)

Galaxy Rotation Curves

NFW dark-matter halo profile with baryon mass and scale radius, fit against Milky Way, M31, M33, NGC 3198, NGC 2403 rotation curves. A reduced model for in-browser curve fitting, not a full N-body run.

Traditional HPC

Quantum Error Correction

Stim / PyMatching stabilizer simulation. Monte Carlo sampling over 10⁵-10⁷ shots per code distance. Wall time: minutes to hours per data point.

GDBS (browser prototype)

Quantum Error Correction

Surface code threshold p_L ≈ (p/p_th)^(d+1)/2 with physical noise model (T₁, T₂, gate error, crosstalk). Benchmarks IBM Eagle, Google Sycamore, IonQ, Rigetti. Instant sweep across code distances.

How It Works

GDBS pairs two things: established domain physics, and a precision system that travels with every number.

The physics. Each module implements the accepted method for its domain - the Troyon / δW energy-integral estimate for tokamak β-limits, real-space Kohn-Sham DFT for materials, the BSSN/Z4c evolution for numerical relativity, Noble con2prim GR-MHD for accretion, the surface-code threshold relation for QEC, and so on. Some are full numerical solvers (finite differences, RK4, multigrid, finite volume); some are reduced-order or analytic where speed matters more than a cluster-scale mesh. None of it is machine learning, a surrogate, or fitted to your inputs.

The precision. Load-bearing arithmetic runs on GeoNum, a log-space number system that tracks accumulated rounding error as a first-class quantity and reports a trust verdict (Exact → Unreliable) on each result - so multi-scale chains that silently corrupt under IEEE 754 stay accountable instead of quietly going wrong.

The delivery. All of it compiles Rust → WebAssembly and runs in the browser, deterministically: the same inputs produce the same outputs on every machine, with no server round-trip for the computation. (The "geometric" in the name is the GMDBS data/retrieval substrate the platform is built on - the database layer, not a claim that the physics solvers are exact geometry.)

What Makes GDBS Different

7Physics Domains

35+Scan Types

300+Validation Tests

<100msPer Prototype Run

$0To Prototype

No HPC to Prototype

The physics runs as WebAssembly in your browser - no supercomputer, no cloud GPU, no job scheduler - to develop, check, and validate. The production-scale run still belongs on HPC; this gets you ready for it without the queue or the bill.

Deterministic & Reproducible

Not AI, not ML, not a surrogate model. Established methods plus a precision system that tracks its own error. No training data, no loss function, no gradient descent. Same inputs = same outputs, always - with a trust verdict on each.

Validated Against Literature

300+ automated tests against NIST, CRC Handbook, CODATA, Planck 2018, ITER Physics Basis, PREM, and dozens of peer-reviewed papers. Typical agreement: <5% of published values.

Multi-Physics in One Platform

Plasma fusion, materials science, cosmology, geophysics, fluid dynamics, quantum information, and molecular/medical physics - all on the same platform and precision core.

Democratized Access

A grad student with a laptop can develop and validate a method before requesting an allocation grant, a queue slot, or a sysadmin - then take the validated setup to the cluster for the production run.

Integrated Data Platform

Query engine, database browser, saved runs, CSV import/export, and REST API. Store results, compare across runs, and automate workflows via the API.

Physics Validation - Representative Results

The flagship results below are independently computed - from first principles or a standard method, then compared to a published or exact reference. Nothing here is fit to the answer; reproduce it and check the number yourself. Per-domain reference comparisons (many are reduced-order models) follow.

Conformance & authority. Each engine is held to the published reference values and industry-standard benchmarks for that domain - the same standards used to certify HPC codes (NIST & CODATA, NIST CCCBDB, the LIGO/Virgo GWTC catalogs, Szabo & Ostlund, Clementi-Roetti, and the foundational literature per engine). GDBS is the authority on its engine - its correctness, numerical precision, and reproducibility - not on the physics. The reference values and literature are external and authoritative; we conform to them, we do not define them. Where an engine needs a benchmark we cite, add, or make the published source available - but the standard is always the field's, not ours.

Flagship Results - Independently Computed

Result	GDBS	Reference	Source
GW150914 final black-hole mass	63.02 M_☉ (0.13%)	63.1 M_☉	Abbott et al. (GWTC-1)
GW150914 final spin	0.6855 (0.65%)	0.69	Abbott et al. (GWTC-1)
BSSN convergence order	3.946	4.0 (theoretical)	Apples-with-Apples NR testbed
GR-MHD ∇·B (constrained transport)	2.37×10⁻⁴	→ 0	Noble 2006 / CT, on-GPU
Hawking temperature (60 orders of magnitude)	0.27%	exact analytic	Hawking formula
Blasius boundary layer f″(0)	0.46960	0.46960	Blasius 1908; value Howarth 1938
DFT H₂ ground state (HF/STO-3G)	−1.1167 Ha (0.07%)	−1.1175 Ha	Szabo & Ostlund Table 3.17
Elastic constants, Si - C₁₁/C₁₂/C₄₄	151.4 / 76.5 / 56.4 GPa	published SW	Stillinger-Weber potential

Per-Domain Reference Comparisons

Reduced-order and reference checks across the seven domains - quick in-browser comparisons, not the full production solve.

Plasma & Fusion

Quantity	Configuration	GDBS	Literature	Source
β_N Limit	Circular tokamak	2.5-3.5	2.5-3.5	Troyon et al. (1984)
ITER β_N	A=3.1, B₀=5.3T	~1.8	~1.8	ITER Physics Basis
W7-X β	Stellarator A≈5.5	4-5%	4-5%	Grieger et al. (1992)
FRC <β>	C-2W config	1 − x_s²	Equilibrium identity	Tuszewski (1988)

Cosmology

Quantity	GDBS	Literature	Source
CMB 1st Peak	~220	220.0 ± 0.5	Planck 2018
Sound Horizon	~147 Mpc	147.09 ± 0.26 Mpc	Planck 2018

Geophysics

Quantity	GDBS	Literature	Source
Moho V_p	8.1 km/s	8.1 km/s	PREM
Himalayas Bouguer	< −100 mGal	< −100 mGal	Gravity surveys
Gutenberg-Richter b	1.000	~1.0	Global seismicity

Fluid Dynamics

Quantity	Regime	GDBS	Literature	Source
Blasius δ	Laminar flat plate	< 1% error	5L/√Re	Blasius (1908)
Sphere C_D	Subcritical turbulent	~0.44	0.44	Experimental data
Normal Shock M₂	M₁=2.0	0.5774	0.5774	Gas dynamics tables

Quantum Information

Quantity	GDBS	Literature	Source
Trapped Ion Fidelity	99.97%	99.97%	Ion trap benchmarks
Surface Code p_th	~1%	~1%	Fowler et al. (2012)
CHSH Bell Parameter	2.0 < S ≤ 2√2	2.0 < S ≤ 2.828	Bell (1964)

Medical / Molecular

Quantity	GDBS	Literature	Source
Lipinski Violations	Aspirin: 0, Paclitaxel: ≥2	Aspirin: 0, Paclitaxel: ≥2	Lipinski criteria
Protein T_m	f ≈ 0.5 at T_m	Thermodynamic identity	Protein stability

300+ automated tests pass across all physics domains. Sources include: NIST, CRC Handbook, CODATA 2018, Planck 2018, PREM, ITER Physics Basis, Troyon et al., McGaugh et al., Kanamori, Fowler et al., Blasius, Stokes, Lipinski, Bell, Wootters, and more.

HPC-Grade Numerical Precision

Many physics calculations span dozens of orders of magnitude - quantum constants near 10⁻³⁴, cosmological scales beyond 10³⁰ - where standard IEEE 754 floating-point arithmetic accumulates catastrophic precision loss. Traditional solutions require expensive HPC clusters with extended-precision libraries. GDBS implements a proprietary geometric number system (GeoNum) that holds extended precision directly in the browser, validated against analytic and standard reference values.

This system tracks uncertainty transparently through multi-scale calculation chains, enabling precision comparisons previously available only on supercomputers. The approach is domain-polymorphic: the same core architecture adapts to each physics domain's characteristic scales - electron-volt precision for quantum systems, kilometer-scale accuracy for geophysics, frequency-aligned precision for plasma oscillations.

IEEE 754 Double Precision

Hawking Radiation (Kerr Black Hole)

Multi-scale multiply chain: ℏ (10⁻³⁴) × κ (10⁻⁵) × c (10⁸) spanning 60 orders of magnitude. IEEE 754 accumulates ~15% relative error due to repeated exponent adjustments.

GDBS Precision System

Hawking Radiation (Kerr Black Hole)

Same calculation: 0.27% relative error, drift tracking below threshold. Uncertainty quantified at every step. Validated against the exact analytic Hawking formula.

Validated Performance - Theory Module (Black Hole Thermodynamics)

Metric	Result	Significance
Relative Error	0.27%	vs. IEEE 754: ~15% on same calculation
Precision Tiers	2048 → 1024 → 512 → 256	Tunable speed/accuracy tradeoff
Scale Range	10⁻³⁵ to 10³⁰	65 orders of magnitude (Planck to cosmic)
Drift Accumulation	0.345	Well below 1.0 threshold across multiply chains
Uncertainty Tracking	Transparent, quantified	getUncertainty() API at every calculation step
Domains Supported	Multiple	Theory, Quantum, Fluids, Plasma, Materials, Geophysics, Ballistics, and more

Example Outputs - Hawking Temperature (M = 10 M_☉, a/M = 0.9)

Method	T_Hawking (K)	Uncertainty	Relative Error
IEEE 754 (Standard)	3.198e-14	Unknown (hidden)	~15%
Analytic Reference (Kerr)	3.742e-14	Exact formula	Baseline
GDBS Precision	3.732e-14	± 1.01e-16	0.27%

Calculation: T = ℏκc / (2πk_B) where κ = surface gravity of rotating (Kerr) black hole. Spans quantum scales (ℏ ≈ 10⁻³⁴) to thermodynamic scales (k_B ≈ 10⁻²³).

Domain-Specific Precision Calibration

Each physics domain uses optimized precision grids tailored to its characteristic scales:

Theory: Logarithmic zones spanning quantum to cosmological scales (10⁻³⁵ to 10³⁰)
Quantum: eV-scale linear zones for atomic/molecular energy eigenvalues (−100 to +100 eV)
Fluids: Uniform spatial grids for CFD calculations (micron to kilometer scales)
Plasma: Frequency-aligned zones preserving oscillatory phase coherence (kHz to THz)
Materials: Lattice-symmetric zones at Angstrom scale (0.1 to 10 Å)
Geophysics: Spherical harmonic zones for Earth-scale multipole expansions (1 to 10,000 km)
Ballistics: Velocity-scaled zones across subsonic to hypersonic regimes (0.1 m/s to 10 km/s)

Positioning: This does not compete with HPC clusters - it bridges to them. The cluster still runs the production-scale work (long mergers, AMR, matter coupling); GDBS removes the cost around it - prototyping, method development, validation, and sizing at single-GPU scale: instant, no queue, no allocation grant, no specialized infrastructure. Free to evaluate, academic from $99/yr, commercial $25k-$75k/year - the BSSN, LIGO and GRMHD addons are $5k/yr each, included free with Enterprise. It reduces the cost to schedule, run, and extract value from HPC, not the FLOPs.

Precision System Documentation: DOI 10.5281/zenodo.19199836

Implementation details are proprietary. The precision architecture, zone configurations, and drift tracking algorithms are patent-pending trade secrets.

Architecture

Layer	Technology	What It Does
Physics Engine	Rust → WebAssembly	6,300+ LOC across 59 modules. Compiles to WASM - runs at near-native speed in the browser. No server round-trips for computation.
API & Auth	.NET 8 / C#	REST API with JWT authentication, role-based access, license management, Stripe payments. Handles persistence and admin operations.
Frontend	Vanilla JS + Chart.js	Zero-framework UI with ES modules. Interactive forms, real-time chart rendering, result tables. No build step, no bundler.
Data Layer	GDBS LocalStore + GQL	JSON collections with SQL-like query language. Store, retrieve, filter, and export physics results. See the GQL Reference for the full syntax.

What GDBS Can Do Today

Fusion Reactor Design

Scan tokamak, stellarator, and FRC configurations. Optimize aspect ratio, elongation, triangularity. Find β_crit stability limits. Compare ITER, DIII-D, W7-X, C-2W parameters.

Materials Discovery

Predict elastic moduli, band gaps, phase transitions, thermal properties, and defect energies from bond-level inputs. Screen candidates in-browser before committing DFT cluster time.

Cosmological Analysis

Fit galaxy rotation curves with dark matter halos. Compute CMB power spectra. Model black hole accretion. Predict fundamental constant ratios.

Geophysics & Seismology

Model seismic velocity structure, tectonic stress, geothermal gradients, gravity anomalies, and earthquake statistics. Validated against PREM and USGS data.

Fluid Dynamics & Aerodynamics

Compute boundary layers, pipe flow friction, drag coefficients, heat transfer, and compressible flow shocks. From Stokes to Mach 5.

Quantum Computing

Benchmark qubit fidelity, error correction thresholds, entanglement metrics, and decoherence for IBM, Google, IonQ, and Rigetti hardware.

Drug Discovery & Molecular

Screen drug binding, protein stability, nanoparticle uptake, drug interactions, and QSAR descriptors. Lipinski analysis, Debye-Hückel electrostatics.

Data Platform & API

Save runs, query the database via GQL, browse collections, import CSVs, export results, and automate everything through the REST API with Python, curl, or any HTTP client.

Citation & References

If you use GDBS in published research, please cite:

DSO Framework on Zenodo

GDBS - A Vaultsync Solutions Inc. Patent Pending Product - 63/970,430

Licensing Terms & Conditions

GDBS licenses grant a non-exclusive, non-transferable right to use the GDBS platform and selected modules for the duration of the license term. The following license types are available:

License Type	Access	Duration	Notes
Free	Database + Theory	Permanent	GDBS database & Theoretical Foundations; citation required
Trial	All modules	3 days	Full access for evaluation; auto-enrolls to Free on expiry
Standard	Per-module	1 year	Select individual modules
Pro	All modules	1 year	Unlimited access to all modules
Research	All modules	1 year	Citation required; annual re-enrollment

Prohibited Activities: Redistribution, reverse engineering, decompilation, sublicensing, or any attempt to derive source code from GDBS binaries or WASM modules is strictly prohibited.

Patent Pending - U.S. Provisional Patent Application No. 63/970,430

Pricing

Current pricing and tier details are available at getvaultsync.com. All licenses are billed annually. For volume, academic, or enterprise inquiries contact sales@getvaultsync.com.

Research Program & Citation Requirements

Research users receive full access to all GDBS modules at no cost for one year. In exchange, research users must cite GDBS in all published work, presentations, and reports that utilize GDBS outputs:

Computational analysis performed using GDBS (Geometric Database System), developed by VaultSync Solutions Inc. https://gdbs.getvaultsync.com

Annual Re-enrollment: Research access must be re-requested each year. Enrollment is not automatic and is subject to review.

Revocation: VaultSync Solutions Inc. reserves the right to revoke research access at any time, with or without notice.

Academic & Student Pricing Eligibility

Academic pricing is available to verified academic personnel. Like research users, academic and student licensees must cite GDBS in all published work.

Academic Pricing (60% off)

Faculty / Professors: Valid faculty ID, teaching certification, or official appointment letter.
Researchers / Postdocs: Institutional ID and research appointment documentation.
Research Staff: Institutional ID and employment verification.
Academic Email Required: Must use an email from an accredited academic institution (.edu, .ac.uk, .edu.au, etc.).

Student Pricing (90% off - 1 module only)

Graduate Students: Current student ID + proof of enrollment (transcript or enrollment letter).
Undergraduate Students: Current student ID + proof of enrollment.
Recommendation Required: A recommendation letter from a professor, faculty advisor, or academic supervisor is required.
Single Module: Student pricing applies to one module only. Additional modules require standard academic or retail pricing.
Academic Email Required: Must use your institution's email address.

Verification: All credentials are subject to verification at VaultSync's discretion. Fraudulent applications will result in immediate license revocation without refund.

Request Research or Academic Access

Submit the form below to request research access or academic pricing. Our team will review your request and respond via email.

Request Type *

Full Name *

Academic Email * (must be from your institution)

Institution / Organization *

Department / Program

Intended Use Case *

I agree to cite GDBS in all published work, presentations, and reports.

Data Retention Policy

If you don't save it, we don't keep it. GDBS computations run entirely in your browser. Results are only stored on our servers if you explicitly save them using the Save Run feature.

What we store: User account credentials (email, hashed password) and license metadata only. Simulation inputs, parameters, and outputs are processed locally in your browser and are never transmitted to or stored on GDBS servers unless you explicitly use the Save Run feature.

License Expiration / Revocation / Disablement: When a license expires, is revoked, or is disabled, all associated data - saved runs, history, and simulation results - is permanently deleted and cannot be recovered.

All user-generated data stays with the user. You can export your data at any time via CSV download or the REST API.

GDBS does not perform analytics tracking of computation inputs or outputs.

Support

GDBS provides direct email support only. There is no phone, chat, or ticket system.

For account issues, access problems, licensing questions, or sales inquiries, contact:

sales@getvaultsync.com

Alternatively, submit a research-access request using the form above and our team will reach out.

Limitation of Liability & Indemnification

Use at Your Own Risk. GDBS is a computational tool. All outputs are numerical results produced by algorithms running in your browser. VaultSync Solutions Inc. makes no representations or warranties, express or implied, regarding the accuracy, completeness, fitness for a particular purpose, or suitability of any computation result for any decision, design, engineering, medical, scientific, or commercial application.

No Liability for Decisions. VaultSync Solutions Inc. shall not be held liable for any direct, indirect, incidental, special, consequential, or punitive damages arising from the use or inability to use GDBS, or from reliance on any result produced by GDBS, including but not limited to: engineering failures, design errors, financial losses, regulatory non-compliance, or harm to persons or property.

Client Data Responsibility. All simulation inputs, parameters, and data you provide remain your sole property and responsibility. GDBS does not store, transmit, or retain computation data unless explicitly saved by the user. You are solely responsible for the legality, accuracy, and appropriateness of any data you submit to GDBS.

Indemnification. By using GDBS, you agree to indemnify, defend, and hold harmless VaultSync Solutions Inc., its officers, directors, employees, and agents from and against any and all claims, liabilities, damages, losses, costs, and expenses (including reasonable legal fees) arising out of or in connection with: (a) your use or misuse of GDBS; (b) any decisions, designs, or actions taken in reliance on GDBS outputs; (c) your violation of these terms; or (d) your violation of any applicable law or third-party rights.

No Warranty of Correctness. Physics computations involve inherent numerical approximation. GDBS displays uncertainty and drift metrics (GeoNum precision layer) as informational indicators only. These indicators do not constitute a guarantee of result accuracy for any specific application. Users are responsible for independently validating results before relying on them in any consequential application.

For questions about these terms, contact sales@getvaultsync.com. These terms are governed by the laws of the applicable jurisdiction without regard to conflict-of-law principles.

Not a supercomputer.A bridge to one.

A live compute API.Run the engines over HTTP.

General-relativistic magnetohydrodynamics,evolved on your own GPU.

LIGO's GW150914 black-hole merger,reproduced to 0.13% in the browser.

The Hawking temperature, across 60 orders of magnitude,held to 0.27%.

A fourth-order spacetime solver,convergence measured at 3.946.

The Founding Beta is open.Prove your workload, then take it to HPC.

Three steps. Browser to cluster.

1 - Prototype

2 - Validate

3 - Take it to HPC

Prototype and validate here. Take it to HPC.

Drift-Tracked Precision

Multi-Physics Coupling

Batch Parameter Sweeps

HPC Lab Sandbox

10 Physics Domains

Vacuum BSSN + Z4c on the GMDBS Toroid

Convergence: 3.946

Scaling: O(N³), exponent 3.048

Bounded Long-Time Evolution

Citable Artifact

Built for the people who prove the method.

Graduate researchers

Research & R&D teams

Educators

Anyone heading to HPC

GDBS and HPC do different jobs.

Start Free. Scale to Research.

100% validated physics. The bridge to HPC.

GDBS - Geometric Database

Your computational data never leaves your device.

What stays on your device

What we hold, and how we protect it

What we don't do

Server-side features, disclosed plainly

On formal attestations

Service & support

We Want to Hear From You

Frequently Asked Questions

GDBSPro

Sign In

Reset Password

Set New Password

Create Account

Activate License

DSO Framework role-gated

Column Mapping

Plasma Stability - Ideal-MHD δW Solver

Optimizer - Auto-Tuning

Predictor - Trajectory Planner

Custom Constraints

Active Constraints

Export Full Datasets

Analytic Equilibrium (Soloviev)

Ballooning Stability (s-α diagram)

Mercier Interchange Criterion

Multi-mode δW Scan

Parameter Sensitivity

Convergence Study

EFIT g-eqdsk Import

Canonical Validation Suite

Medical Module - Molecular Nanoinformatics

Medical - Molecular Nanoinformatics

Cosmos Module

Cosmos

Q-Desic - Quantum-Corrected Geodesics

Materials Science Module

Materials Science

Topology Module

Topology

Geophysics Module

Geophysics

Fluid Dynamics Module

Fluid Dynamics

Quantum Information Module

Quantum Information

Anomaly Detector Module

Tukey-Exponential Anomaly Detector

Anomaly List (sorted by value desc)

Not a supercomputer.
A bridge to one.

A live compute API.
Run the engines over HTTP.

General-relativistic magnetohydrodynamics,
evolved on your own GPU.

LIGO's GW150914 black-hole merger,
reproduced to 0.13% in the browser.

The Hawking temperature, across 60 orders of magnitude,
held to 0.27%.

A fourth-order spacetime solver,
convergence measured at 3.946.

The Founding Beta is open.
Prove your workload, then take it to HPC.

Tessellated DFT via Adaptive Precision Zones