Building Applications with Zeq OS

Zeq OS is a physics middleware framework. Any application that processes physics computations — web apps, APIs, CLI tools, dashboards — can integrate with the 1,576-operator registry, temporal synchronization via HulyaPulse, and the 7-Step Wizard Protocol. This guide covers the architecture, entry points, and requirements for building on the framework.

What Makes a Zeq OS Application

A Zeq OS application is any software that:

1. Processes physics queries through the 7-Step Wizard Protocol
2. Synchronizes with HulyaPulse at 1.287 Hz (1 Zeqond = 0.777 seconds)
3. Integrates operators from the 1,576-operator registry across 64 physics domains
4. Meets the precision guarantee of ≤0.1% mean error on all computations

Every computation is temporally anchored — the result includes a Zeqond timestamp, phase value, and KO42 metric tensioner reading that ties the calculation to a specific moment in the HulyaPulse cycle.

Architecture

┌─────────────────────────────────────────────┐
│              Your Application                │
│   (Web App, API, CLI, Dashboard, Service)    │
└──────────────────┬──────────────────────────┘
                   │
                   ▼
┌─────────────────────────────────────────────┐
│              Zeq OS SDK                      │
│   Python · JavaScript · Rust · Go · C++      │
│   TypeScript · WebAssembly                   │
├──────────────────┬──────────────────────────┤
│  ZeqProcessor    │  HulyaSync              │
│  (7-Step Wizard) │  (Temporal Layer)        │
├──────────────────┼──────────────────────────┤
│  OperatorRegistry (1,576 operators)         │
│  64 categories · O(1) lookup · full-text    │
├─────────────────────────────────────────────┤
│  HulyaPulse (1.287 Hz)                      │
│  KO42 Metric Tensioner · Phase Coherence    │
└─────────────────────────────────────────────┘

Data flows top-down: your application submits a natural-language physics query to the SDK, which selects operators, compiles them through the HULYAS Master Equation, executes, and returns a ZeqState with results, timing, and precision verification.

Entry Points

There are four ways to interact with Zeq OS from your application:

Entry Point	Protocol	Best For
SDK Direct Import	In-process function calls	Embedded computation, maximum performance
REST API	GET/POST /api/v1/*	Backend services, microservices, third-party integration
WebSocket	ws://localhost:4001/ws	Real-time dashboards, live HulyaPulse sync
CLI	zeq-cli process "query"	Scripts, automation, quick calculations

REST API (Port 4000)

The API Gateway exposes the full operator registry and computation engine over HTTP:

# Process a physics query
curl -X POST http://localhost:4000/api/v1/process \
  -H "X-API-Key: $ZEQ_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{"query": "gravitational time dilation at r=10km", "domain_hints": ["relativity"]}'

# List all operators
curl -H "X-API-Key: $ZEQ_API_KEY" http://localhost:4000/api/v1/operators/all

WebSocket (Port 4001)

The Sync Engine broadcasts HulyaPulse ticks at 1.287 Hz:

ws://localhost:4001/ws

SDK Direct Import

The fastest path — import the SDK in your language and call ZeqProcessor directly. No network overhead.

Minimal Example

Python

pip install zeq-os

from zeq_os import ZeqProcessor, HulyaSync

# Initialize
processor = ZeqProcessor()
sync = HulyaSync()

# Process a physics query through the 7-Step Protocol
result = processor.process(
    "Calculate orbital velocity at 400km altitude",
    domain_hints=["aerospace"]
)

# Inspect results
print(f"Domains:         {result.domains}")
print(f"Operators:       {result.selected_operators}")
print(f"Master Sum:      {result.master_sum:.6f}")
print(f"Phase Coherence: {result.phase_coherence:.4f}%")
print(f"Zeqond:          {result.zeqond}")
print(f"Precision Met:   {result.phase_coherence <= 0.1}")

# Temporal sync
print(f"\n{sync.daemon_tick()}")

JavaScript

npm install @zeq-os/sdk

import { ZeqProcessor, HulyaSync } from '@zeq-os/sdk';

// Initialize
const processor = new ZeqProcessor();
const sync = new HulyaSync();

// Process a physics query through the 7-Step Protocol
const result = processor.processQuery(
  "Calculate orbital velocity at 400km altitude",
  { domainHints: ["aerospace"] }
);

// Inspect results
console.log(`Domains:         ${result.domains}`);
console.log(`Operators:       ${result.selectedOperators}`);
console.log(`Master Sum:      ${result.masterSum.toFixed(6)}`);
console.log(`Phase Coherence: ${result.phaseCoherence.toFixed(4)}%`);
console.log(`Zeqond:          ${result.zeqond}`);
console.log(`Precision Met:   ${result.phaseCoherence <= 0.1}`);

// Temporal sync
console.log(`\n${sync.daemonTick()}`);

Output:

Domains:         ['aerospace']
Operators:       ['KO42', 'ORBIT_VELOCITY', 'ORBIT_ENERGY']
Master Sum:      0.998712
Phase Coherence: 0.0421%
Zeqond:          3296847201
Precision Met:   True

⏱ Zeqond 3296847201 | Phase 0.4521 | KO42 0.000891

Requirements

Every Zeq OS application must follow these rules:

KO42 is Mandatory

The KO42 Metric Tensioner is always the first operator in every computation. The SDK handles this automatically — you never need to manually include KO42, but it will always appear in selected_operators.

KO42.1 (Automatic): ds² = g_μν dx^μ dx^ν + α sin(2π·1.287t) dt²

Maximum 4 Operators per Computation (Basic Mode)

In basic mode, KO42 plus up to 3 additional operators. This constraint ensures precision stays within the ≤0.1% target. For multi-domain problems requiring more operators, use advanced or mathematical_state mode — see the 7-Step Wizard Protocol.

Mode	Operator Limit	Use Case
basic	≤4 (KO42 + 3)	Most computations
advanced	Unlimited	Multi-domain problems
mathematical_state	Unlimited + full registry	Research & analysis

Precision Target: ≤0.1% Mean Error

Derived from the modulation amplitude: α/√2 = 0.091% ≤ 0.1%. The SDK verifies this automatically and includes phase_coherence in every result. If the precision check fails, the 7-Step Protocol enters Step 7 (Verify & Troubleshoot) and iterates.

HulyaPulse Synchronization

All computations are temporally anchored to the 1.287 Hz pulse. The ZeqState result includes:

Field	Description
zeqond	Zeqond count at computation time
phase	Phase within current Zeqond [0, 1)
ko42	KO42.1 metric tensioner value at computation time
timestamp	Unix timestamp

Next Steps

• Web Applications — Build browser-based apps with JavaScript/TypeScript and WebSocket sync
• API Services — Build backend services with Python, FastAPI, and the API Gateway
• Industry Examples — Real-world examples across 6 industry domains
• API Gateway Reference — Browse all 1,576 operators by category
• 7-Step Wizard Protocol — Understand the computation pipeline
• HITE Encryption — Secure your application's data in transit