Generative Mathematics Framework

Compute physics.
Prove it mathematically.

42+ kinematic operators. One master equation. Every computation cryptographically verified, phase-stamped at 1.287 Hz, and sealed with ZeqProof. From quantum mechanics to general relativity — in a single API call.

Explore the SDK Visit zeq.dev
QM1  iℏ ∂ψ/∂t = −ℏ²/2m ∂²ψ/∂x² + Vψ  ·  NM19  F = ma  ·  GR33  G_μν + Λg_μν = 8πG/c⁴ T_μν  ·  CS47  E = −∑ p(x) log p(x)
QM12  (iγ^μ∂_μ − m)ψ = 0  ·  NM21  F = Gm₁m₂/r²  ·  GR37  r_s = 2GM/c²  ·  QM10  E = hν
NM25  KE + PE = const  ·  GR40  (ȧ/a)² = 8πG/3 ρ − kc²/a² + Λc²/3  ·  QM9  λ = h/p  ·  NM30  F = −kx
QM1  iℏ ∂ψ/∂t = −ℏ²/2m ∂²ψ/∂x² + Vψ  ·  NM19  F = ma  ·  GR33  G_μν + Λg_μν = 8πG/c⁴ T_μν  ·  CS47  E = −∑ p(x) log p(x)
QM12  (iγ^μ∂_μ − m)ψ = 0  ·  NM21  F = Gm₁m₂/r²  ·  GR37  r_s = 2GM/c²  ·  QM10  E = hν
NM25  KE + PE = const  ·  GR40  (ȧ/a)² = 8πG/3 ρ − kc²/a² + Λc²/3  ·  QM9  λ = h/p  ·  NM30  F = −kx
The Framework

One equation to rule them all

Zeq is a generative mathematics framework that compiles any physical problem — quantum, classical, or relativistic — into operator weights on a single master equation, solves it, and returns a cryptographically sealed result.

□φ − μ²(r)φ − λφ³ − e−φ/φc + φ42 ∑k=142 Ck(φ) = Tμμ + β Fμν Fμν + Jext
The HULYAS Master Equation
COMPUTE

42+ Kinematic Operators

Quantum mechanics, Newtonian mechanics, general relativity, and computer science — all accessible through a single unified API. Select operators, compile, execute.

PROVE

ZeqProof Verification

Every result is signed with HMAC-SHA256, binding the computation to its Zeqond timestamp, operator chain, and precision metrics. Tamper-evident and independently verifiable.

SECURE

ZSP Triple Encryption

Kspectral × Ktemporal × Kchaos — three mathematically independent key layers derived from the framework's own equations. Not bolted on; built in.

STATE

State Machine Engine

Proof-verified state transitions with JSON contracts, a Zeqond audit clock ticking at 1.287 Hz, and air-gapped enterprise deployment. Not a blockchain — proved by math.

COMPRESS

HZC Compression

Lossless (ZeqCompress) and lossy (TurboZEQ) codecs integrated with the KO42 metric tensioner. IEEE 754 f64 throughout. Phase-coherent with the Zeqond clock.

CLOCK

HulyaPulse 1.287 Hz

The deterministic oscillator at the heart of everything. Defines the Zeqond (0.777s), drives the KO42 metric tensioner, timestamps every computation, powers the audit chain.

Operator Spectrum

Four domains. One solver.

Every operator maps to a real equation of physics or computer science. The SDK gives you access to all of them through a single endpoint.

17
Quantum Mechanics
QM1 – QM17
13
Newtonian Mechanics
NM18 – NM30
11
General Relativity
GR31 – GR41
7+
Computer Science
CS43 – CS87
The Protocol

Seven steps. Every time.

Every computation follows the same deterministic protocol — from operator selection to cryptographic verification.

01

KO42 Metric Tensioner — Mandatory

The HulyaPulse oscillation is injected into the spacetime metric. Every computation is phase-aware from the start.

02

Select Operators (1–3 + KO42)

Choose up to 3 kinematic operators from the catalogue. Each one activates coupling terms in the master equation.

03

Match Scale to Domain

Quantum operators for atomic scale, Newtonian for human scale, relativistic for astrophysical. Cross-scale is permitted.

04

Tune to ≤ 0.1% Error

Solver parameters adapt to hit the precision target. Step size, tolerance, and iteration limits auto-calibrate.

05

Compile via Master Equation

Operators become coupling weights Ck(φ). The HULYAS Master Equation is parameterised with problem-specific values.

06

Execute via RK4 Integration

Fourth-order Runge-Kutta solves the compiled equation. The Functional and Spectral-Topological equations extract observables.

07

Verify & Seal with ZeqProof

Result is modulated by R(t), signed with HMAC-SHA256, and stamped with its Zeqond number. Independently verifiable forever.

Quick Start

Three lines to compute physics

POST an operator and parameters. Get a verified result with cryptographic proof.

// Compute gravitational force between Earth and Moon curl -X POST https://zeq.dev/api/zeq/compute \ -H "Authorization: Bearer YOUR_API_KEY" \ -H "Content-Type: application/json" \ -d '{ "operators": ["NM21"], "parameters": { "mass1": 5.972e24, "mass2": 7.342e22, "distance": 384400000 } }' // Response includes: // result.value → 1.98 × 10²⁰ N // result.zeqond → Zeqond timestamp // zeqproof.signature → HMAC-SHA256 seal // metadata.precision → ≤ 0.1% error

Start computing

Full documentation, API reference, operator guides, and code examples in Python, JavaScript, Go, Rust, and curl.

Open the SDK Visit zeq.dev