Summary and Positioning
GDBS (Geometric Database System) is a precision-computing substrate and delivery platform. It executes scientific and engineering computations with a number system whose error is a first-class, inspectable quantity rather than hidden machine rounding, and it delivers that capability through a browser-accessible application rather than a cluster queue.
CORA (Conversational Retrieval Agent) is a retrieval-deterministic interface built on the GMDBS geometric substrate. Every answer it returns is composed from specific corpus entries at known positions on a toroidal manifold. The same query against the same corpus returns the same answer, and every sentence is traceable to its source. CORA does not generate language probabilistically; it navigates a geometric layout.
The precision and verification platform: GeoNum arithmetic, the physics and engineering modules, and the HPC-grade validation suite.
The geometric retrieval product: GMDBS addressing plus the deterministic retrieval and composition pipeline, hosted at cora.getvaultsync.com.
The GDBS offering foregrounds precision and verification; GMDBS retrieval is kept minimal inside GDBS and is the basis of CORA as a separate product.
Core philosophy. Determinism, transparency, and verifiability. Numerical error is reported, not concealed. Retrieval answers are bounded by a corpus and auditable, not synthesised. Results are reproducible and, where the substrate permits, available without network access or accelerator hardware.
Legal entity. VaultSync Solutions Inc., a Wyoming C corporation.
GDBS - Geometric Database System
2.1 Definition and intent
GDBS computes physical and engineering quantities at HPC-grade precision with explicit uncertainty tracking, delivered in a standard browser. It is not positioned against the raw throughput of petascale or exascale clusters; it is positioned against the access model of those clusters - instant availability, no scheduling queue, transparent uncertainty, and reproducible results.
2.2 Substrate architecture
- The substrate engine is written in Rust and compiled to a self-contained WebAssembly
library (
gdbsio.wasm, acdylib). - The .NET 8 API host loads that library through Wasmtime; computation runs inside the WASM guest across a binary envelope protocol (GDBQ request / GDBR response).
- Corpus and data shards live in
App_Data/and are preopened for sandboxed WASI file access. - A compressed in-process store (
gms) provides content-addressed key-value storage with lz4 compression and 64-bit xxhash deduplication - the memory-expansion layer behind the gdbsio runtime. - The same Rust crate also compiles to a smaller browser-only WASM build for fully client-side, air-gap-capable operation.
The three-layer split is deliberate: Rust for substrate and engine code, .NET 8 for the API, HTML/JS for the frontend. Engine code is never written in the API or frontend languages.
2.3 GeoNum precision system
- Zones partition magnitude at the macro scale (the domain-configurable analogue of the IEEE 754 exponent field).
- Shades subdivide each zone into 2048 micro-precision steps.
- Drift is a first-class accumulated-error compartment on every value; it grows monotonically and is never discarded.
- A trust tier derives from drift, with a 1.0-shade quality gate. Under heavy cancellation, drift reports the entropic cost, not the error of the final result - a value can be reference-exact while drift is large.
Transparent uncertainty API. Every value reports
getUncertainty() and getRelativeUncertainty(). One GeoNum class;
domain specialisation changes only the zone-boundary configuration (Appendix D). Precision
tiers: 256 / 512 / 1024 / 2048 shades.
2.4 GMDBS geometric model
- 50 toroids organised as 5 pentagon groups of 10.
- (H, V, P) self-addressing - position on the manifold is the key.
- Lucas-gap level of detail; Poincare-disk local geometry, toroidal global wrap; three-degree per-pentagon separation.
- An ontology overlay resolves to 24 hubs, then domains and subdomains.
- Seeds carry 256-bit bloom signatures for fast candidate filtering.
Compression. Roughly 2 GB to 448 MB (about 78 percent) at a representative tier; per-record about 32 bytes to about 7 bytes; multi-node CPU speedup near 9.7x.
2.5 Web platform and product tiers
Single-physics exploratory tools, included with an authenticated account.
Coupled multi-physics, batch sweeps, optimiser and predictor, validation suites.
Full research sandbox with raw engine access and custom workflows.
Pricing is tier-based; authoritative figures are those published on the live platform (Appendix H). A WebGPU compute path with automatic CPU execution and a GPU-capable charting layer (opt-in per module) round out the platform.
2.6 Module catalogue
Domain modules: Plasma, Fluids, Quantum, Materials / Geometric MD, Topology, Geophysics, Medical / Molecular, Cosmic, Theory. HPC Lab research engines: Multigrid Poisson, FDTD electromagnetics, Phase-Field (Cahn-Hilliard / Allen-Cahn), Compressible Euler (HLLC + MUSCL), DMRG quantum many-body. Substrate engines include BSSN/Z4c numerical relativity, a LIGO pipeline, three-body dynamics, manifold prediction, finance, MLE, RF compaction, multi-hypothesis voting, DFT kernels, and an arXiv parser; an HPC-IO group and the Adv multi-physics module complete the platform (full list in Appendix A).
2.7 Validation and results
- Hawking radiation: 0.27 percent relative error across ~60 orders of magnitude at 0.345 shade of drift, beating IEEE 754 on the same chain.
- QED coefficients c1-c5 reproduced against published references; first three to floating-point precision, fourth and fifth inside published bars (Appendix C).
- Numerical relativity: convergence 3.946 vs fourth order; scaling slope 3.048 vs cubic; ~23.94 us/cell/step; bounded evolution to ~5 (BSSN) and 7 (Z4c) light crossings.
- Cosmic: 14 canonical references; DSO prediction m_p / m_e = 12 x 9 x 17 = 1836, about 0.0076 percent from CODATA; g-dagger = 1.2 x 10^-10 m/s^2.
CORA - Conversational Retrieval Agent
3.1 Definition and intent
CORA is retrieval-deterministic. There is no generative model in the answer path. Every word is composed from specific corpus seeds at known positions on the toroidal manifold, so the same query against the same corpus produces the same answer with auditable provenance. When the answer is not in the corpus, CORA says so; out-of-corpus invention is structurally impossible. Answers are located, not produced - the geometric layout is itself the relevance function.
3.2 How retrieval works
- Plan-cache lookup - a hashed query may return at sub-microsecond latency from a bounded plan cache (~2048 entries).
- Depth and tier selection - adaptive performance tier from rolling stats; self-referential queries held to a higher acceptance threshold.
- Integrity gate - blocks extraction, identity manipulation, harmful requests.
- Routing - normalised content words; first routable word selects one of 24 ontology hubs and a target sub-toroid.
- Crawl and characterise - candidates scored by a weighted geometric relevance function (curated prior, Poincare geodesic distance, topic-hash, hub specificity, word overlap, bloom mass, usage reinforcement).
- Divergent retry - wider re-run if the best score is weak and budget allows.
- Linguistic rerank - content words as a hard filter; coverage and modifier rescale; code spans excluded.
- Composition - retrieved (dominant seed) or constructed (fragments weighted by retrieval score); no learned parameters.
- Fidelity gate - checked against source for entity coverage and overlap.
- Traceability verification - traceable fraction always measured.
- Assembly - response plus a footer of mode, confidence, traceability, routed hub and sub-toroid.
- Reinforcement and cache insert.
Session state (turn counter, accumulated ontology positions, interaction profile, conversation context) calibrates response style but does not introduce non-determinism into what is retrieved. Every response exposes confidence, traceability, mode, routed hub and sub-toroid in an inspectable trace panel.
3.3 Deployment modes
~413 KB binary, ~650 MB seed bundle (~2.17M seeds), ~850 MB wasm memory, 0-4 ms query, zero network after load - air-gap capable.
gdbsio driver, memory-mapped shards, 4.5M+ seeds, sub-100 ms boot, sub-millisecond cached query.
3.4 Hosting and integration
Hosted at cora.getvaultsync.com. Inside the GDBS application a thin bridge calls status and query endpoints; the element appears only after an appropriate tier is confirmed, a computation is registered, and the status endpoint responds, and is hidden silently otherwise.
3.5 Relationship to GMDBS and trajectory
CORA is the productised expression of the GMDBS substrate. The longer-term trajectory treats the system as a geometric brain in which retrieval is emergent - a structured navigable network whose deformation, not a re-ranking heuristic, changes what is recalled.
Design Decisions and Rationale
- Three-language split. Rust engine, .NET 8 API, HTML/JS frontend - deterministic memory-safe numerics, managed orchestration, zero-install client.
- WASM-embedded engine instead of native DLL P/Invoke - portability, a preopened-only sandbox, one codebase for server and air-gapped client.
- First-class drift instead of hidden rounding - an inspectable compartment with a quality gate; drift reports cancellation cost honestly.
- One GeoNum class, domain-tuned zone configurations - specialisation is data, not a code fork.
- Geometric addressing (HVP) on a pentagon scaffold - position is the key; Poincare-local and toroidal-global with three-degree separation.
- Lucas-gap level of detail matching the substrate's natural scaling.
- Retrieval-deterministic CORA - auditability, reproducibility, corpus-bounded answers, microsecond latency, no accelerator dependency, air-gap.
- WebGPU conservative defaults - requested limits a floor not a ceiling.
- WGSL branchful modulo; per-tile transient right-hand side.
- Charting coexistence - opt-in per-module migration, reversible.
- Explicit product boundary - GDBS for precision/verification, CORA as a separate retrieval product.
- Tiered product architecture - Standard, Pro, HPC Lab.
Development History
- GeoNum core (zone/shade/drift) established; Theory Lucas zones validated first on Hawking radiation.
- Domain zone configurations defined and integrated with precision-tracking displays.
- QED cascade-closure programme: c1-c5 closed with substrate-natural denominators and a depth-2 multiple-zeta-value basis; parallel mass-mechanism probes honestly reported as failing.
- GMDBS substrate research: Goldbach orbit-class reformulation; falsification of a substrate-to-mass-ratio bridge; DSO mass-ratio predictions found independent of the substrate; pentagon attachment surfaces resolved.
- Closed-Form Validator shipped 2026-05-15; HPC Lab research engines added 2026-05-13.
- Product separation: GeoNum extracted to its own engine repository; a legacy module removed from the hub for investment focus; platform unified under "powered by GDBS".
- Charting platform built with an animated phase-space flagship; an air-gapped zero-trust codebase maintained as the reference.
Roadmap
- Numerical relativity - complete the Z4c set, damping sweeps, push toward the 1000-crossing horizon, strong-field collapse, matter coupling.
- Storage - tile-atomic drop with a key-to-tile mapper; GPU streaming slot-reuse verification.
- Materials (Adv tier) - multi-species MD, binary-alloy potentials, coupled MD+FEM feedback for industrial cases.
- Theory engine refactor; per-domain HPC validation benchmarks with dedicated UI tabs.
- Closure and tuning - GPU async batch dispatch, HVP-prescribed atoms into the closure engine, a cascade auto-tuner, a reusable geometric-closure trait.
- CORA - convergence toward the geometric-brain model: manifold-deformation retrieval and a shape-as-dispatch binding module.
- Charting - migrate remaining modules; compress the charting payload.
- SBIR Phase I - a four-task plan scoped to GeoNum precision and verification, production-port and minimal-hosting framing.
Talking Points (condensed)
Error is a first-class, inspectable quantity. HPC-grade multi-scale precision in a browser. 0.27 percent across ~60 orders of magnitude at 0.345 shade of drift.
Uncertainty queryable on every value; drift reports cancellation cost; CORA answers fully traceable.
Same input, same output. CORA says "I do not know" rather than inventing.
No queue, no scheduler, no cluster account; a browser and air-gap client.
Position is the key (HVP); pentagon scaffold, Lucas-gap tiers, ~78 percent compression.
QED c1-c5 inside published bars; convergence 3.946; cosmic calibrated to 14 references.
GDBS for precision/verification; CORA for deterministic retrieval; tiered access.
VaultSync Solutions Inc., Wyoming C corporation.
Glossary
Reference Tables
Appendix A. Module catalogue
| Module | What it computes |
|---|---|
| Plasma | Ideal-MHD stability, equilibrium, figures of merit for tokamaks, stellarators, FRCs |
| Fluids | Reynolds, boundary layer, compressible flow, lattice-Boltzmann, FDTD, heat transfer |
| Quantum | Ground-state DFT, multi-electron atoms, molecular benchmarks, circuit tools |
| Materials / Geometric MD | Molecular dynamics, elastic and thermal properties, phase diagrams, ablation |
| Topology | Faddeev-Skyrme hopfions, 1D chaos, SU(2) structure from the QED cascade |
| Geophysics | Gravitational fields, seismic propagation, stress, heat flow, earthquakes |
| Medical / Molecular | Binding, protein stability, nanoparticle design, QSAR, SASA, virtual PCR |
| Cosmic | Matter power spectrum, halo mass function, weak lensing, CMB, galaxy rotation |
| Theory | Physical and cosmological constants, black-hole thermodynamics, DSO framework |
| HPC Lab engines | Multigrid Poisson, FDTD, Phase-Field, Compressible Euler (HLLC+MUSCL), DMRG |
| Substrate engines | BSSN/Z4c, LIGO pipeline, three-body, manifold prediction, finance, MLE, RF compaction, multi-hypothesis voting, DFT, arXiv parser |
| HPC-IO / Adv | Form generator, report builder, arXiv solver, CSS design system; multi-physics coupling and batch sweeps |
Appendix B. Validation results
| Result | Observed | Reference / target |
|---|---|---|
| Hawking radiation relative error | 0.27 % | analytical |
| Hawking radiation drift | 0.345 shade | < 1.0 shade gate |
| BSSN factor-2 self-convergence | 3.946 | 4.0 (fourth order) |
| BSSN wall-time scaling slope | 3.048 | 3.0 (cubic) |
| BSSN billing calibration | ~23.94 us/cell/step | meter calibration |
| Bounded evolution (pure BSSN) | ~5 light crossings | formulation limit |
| Bounded evolution (Z4c) | 7 light crossings | next-phase: 1000 |
| DSO m_p / m_e prediction | 1836 | 0.0076 % from CODATA |
| Cosmic calibration references | 14 canonical | published values |
Appendix C. QED cascade coefficients
| Coefficient | Reference | Residual vs reference | Acceptance |
|---|---|---|---|
| c1 | Schwinger 1948 (1/2 exact) | ~5.6e-17 | floating-point |
| c2 | Petermann 1957 / Sommerfield 1958 | ~1.3e-14 | floating-point |
| c3 | Laporta-Remiddi 1996 | ~8.5e-13 | floating-point |
| c4 | Aoyama et al. (4-loop) | ~4.0e-11 | inside published bar |
| c5 | Kinoshita 2017 (5-loop) | ~5.7e-10 | inside published bar |
Transcendental basis: zeta(2), zeta(3) by Apery series; zeta(5,7,9) by Euler-Maclaurin; depth-2 multiple zeta values; genus-1 Eisenstein lattice sums. Reproduced via the release test suite.
Appendix D. GeoNum zone configurations
| Configuration | Boundary style | Range |
|---|---|---|
| Theory | Lucas-sequence logarithmic | 10^-35 to 10^30 |
| Quantum | Tight eV-scale | ~10^-2 to 10^2 eV |
| Fluids | Uniform grid | grid-dependent |
| Plasma | Plasma-frequency aligned | 10^3 to 10^12 Hz |
| Materials | Lattice-symmetric | 10^-10 to 10^-8 m |
| Geophysics | Spherical-harmonic aligned | 10^3 to 10^7 m |
| Ballistics | Mach-number scaled | 10^-1 to 10^4 m/s |
| Wide uniform | 1-unit log spacing | ~10^-110 to 10^110 |
Precision tiers (shade count): 256 exploration, 512 single-domain production, 1024 multi-scale, 2048 cross-decade and publication.
Appendix E. Technology stack
- Engine: Rust, WebAssembly
cdylib(gdbsio.wasm) plus a browser build of the same crate. - API host: .NET 8 + Wasmtime; GDBQ/GDBR envelopes;
App_Data/shards with preopened WASI access. - Storage:
gms(lz4 + 64-bit xxhash deduplication). - Frontend: HTML/JS; WebGPU with automatic CPU execution; GPU-capable charting layer.
- GeoNum maintained as a standalone engine repository.
Appendix F. Product boundary and SBIR scope
GDBS and CORA are separate products on a shared substrate. GDBS scope is GeoNum precision and verification plus the physics/engineering modules; GMDBS retrieval is minimal inside GDBS. CORA is the GMDBS geometric-retrieval product. SBIR Phase I is scoped to the GDBS side (four tasks, production-port and minimal-hosting framing); CORA's retrieval substrate is not foregrounded in the GDBS SBIR scope.
Appendix G. Key constants
- g-dagger (DSO threshold): 1.2 x 10^-10 m/s^2.
- Shade count (full tier): 2048 (2 to the 11th power).
- Drift quality gate: 1.0 shade.
- DSO mass-ratio prediction: m_p / m_e = 12 x 9 x 17 = 1836.
Appendix H. Pricing and tier note
Pricing is structured by tier: Standard (included with an authenticated account), Pro / Advanced multi-physics, and HPC Lab. Published source documents and prior internal guidance differ on specific dollar figures; this briefing states the tier structure and defers exact pricing to the live platform. Quote the tier name and confirm the current amount from the live site rather than a fixed number from memory or older documents.