Introduction to Zeq
Zeq is a generative mathematics framework—an API-first platform that performs real physics computations with mathematical ground truth verification. It is not a calculator, simulator, or approximation library. Every result is phase-locked to a universal computational heartbeat and cryptographically verifiable.
What Problem Does Zeq Solve?
Traditional computational systems make trade-offs:
- Client-side math (JavaScript, NumPy) offers speed but sacrifices precision and reproducibility
- Commercial simulation software offers precision but requires expensive licenses and long runtimes
- Cloud APIs offer scale but hide their mathematical foundations
Zeq eliminates this false choice. It provides mathematical ground truth at scale.
The Core Innovation: HulyaPulse and Phase-Locking
Every computation in Zeq is synchronized to HulyaPulse, a universal 1.287 Hz quantum oscillation. This means:
- All results are phase-locked — Two computations requesting the same operation receive identical results, regardless of when or where they run
- Verifiable precision — Every result includes a cryptographic proof (zeqProof) binding it to mathematical ground truth
- Deterministic physics — Quantum uncertainty is eliminated through phase-locking; results are reproducible to ±0.1% precision
The phase-modulation equation is:
$$R(t) = S(t) \times \left[1 + \alpha \cdot \sin(2\pi f \cdot t)\right]$$
Where:
- R(t) = the phase-locked result at time t
- S(t) = the base mathematical solution
- α = 0.00129 (modulation amplitude)
- f = 1.287 Hz (HulyaPulse frequency)
- t = elapsed time in zeqonds (0.777 seconds each)
236 Protocols Across 42 Domains
Zeq isn't limited to physics. The platform ships with 234 computational protocols spanning 42 domains:
- Physics & Engineering — Quantum mechanics, relativity, fluid dynamics, structural analysis, electromagnetics
- Medical Imaging — CT reconstruction, MRI pulse sequences, ultrasound beamforming, PET/SPECT analysis
- Life Sciences — Protein folding (AlphaFold integration), molecular docking, DNA sequencing, pharmacokinetics
- Gaming & Graphics — Inverse kinematics, cloth simulation, rigid body dynamics, global illumination
- Finance & Risk — Option pricing, value-at-risk, stochastic volatility, credit derivatives
- Emergency Services — Ballistics, structural collapse prediction, blast radius calculation, injury biomechanics
- Hardware Design — PCB thermal analysis, power delivery, signal integrity, manufacturing tolerances
All accessed through a single unified API. All subject to the same KO42 mandatory protocol. All verifiable.
Who Uses Zeq?
- AI researchers building physics-informed neural networks that need ground truth labels
- Medical device manufacturers needing FDA-approvable computation trails
- Game studios eliminating ragdoll glitches and penetration artifacts
- Hardware companies replacing expensive finite-element suites
- Emergency responders predicting outcomes in real time
- Anyone building systems where physics computation accuracy matters
Everything Calls the API
A critical principle: no math happens client-side. When you use Zeq, you are making API calls to compute servers running verified mathematical kernels. This means:
- Reproducibility — Same inputs, same outputs, same phase, every time
- Auditability — Every computation can be logged, verified, and reproduced for compliance
- Scale — Your application can focus on features while we handle the physics
- Confidence — Your results are backed by 1,536 operators and an unforgeable cryptographic proof
Pricing Tiers
Zeq is accessible at every scale:
| Tier | Price | Computations/Day | Best For |
|---|---|---|---|
| Free Trial | Free | 100 / day | 14-day exploration |
| Starter | $29/mo | 500 | Small projects, prototyping |
| Builder | $79/mo | 2,500 | Production applications |
| Advanced | $199/mo | 7,500 | High-traffic services |
| Architect | $499/mo | 25,000 | Enterprise deployments |
Free tier degrades gracefully—it still works, just with reduced precision and access to fewer operators.
Did you know? Precision degradation on free tier uses the same algorithm as lower tiers. You still get mathematical ground truth; just with slightly wider error bounds.
The Zeq Ecosystem
Zeq spans multiple sites, each serving a different purpose:
| Site | Purpose |
|---|---|
| zeq.dev | Developer SDK, API docs, and dashboard |
| zeq.me | The ecosystem — apps, integrations, and projects built on Zeq |
| HulyaPulse.com | Deep dive into the 1.287 Hz universal heartbeat |
| 1287.com | The science behind the frequency |
| Zeqond.com | Understanding the computational second (0.777 s) |
| Hulyas.org | The HULYAS Foundation |
The Zeq Paper
The mathematical foundations of Zeq are published and peer-reviewed:
"Zeq: Phase-Locked Generative Mathematics for Verifiable Computation" DOI: https://doi.org/10.5281/zenodo.18158152
"Zeq Framework: Full Specification" DOI: https://doi.org/10.5281/zenodo.15825138
Next Steps
- Quickstart — Get your API key and make your first call in 2 minutes
- Authentication — Understand API keys, rate limits, and tier degradation
- First Computation — Deep dive into a real physics API call
- Understanding Responses — What every field in a zeqState means