[ 01 / 01 ]

[ DOCUMENTATION ]

DOCUMENTATION

[01/01]
Documentation · API Reference · Quick Start

From zero to
first computation.

From zero to your first grounded physics computation in under 2 minutes.

1

Get your API key

Go to Pricing and start your free 14-day trial — no credit card required. Enter your email and your zeq_ak_… API key is generated instantly and shown once in your trial portal. Copy it immediately.

The key is shown exactly once. Save it to a password manager or add it to Replit Secrets immediately. If you lose it, you can regenerate it from the portal.
2

Add it to Replit Secrets

In your Replit project, open the Secrets panel (padlock icon in the left sidebar, or press Ctrl+K and search "Secrets"). Add a new secret:

Key ZEQ_API_KEY
Value zeq_ak_…

Restart your Repl after adding a secret so the environment variable is available.

3

Make your first compute request

Call POST /api/zeq/compute with a physics domain and inputs. Working examples in 10 languages — click a tab to switch:

curl -X POST https://www.zeqsdk.com/api/zeq/compute \ -H "Authorization: Bearer $ZEQ_API_KEY" \ -H "Content-Type: application/json" \ -d '{ "domain": "quantum_mechanics", "operators": ["KO42"], "inputs": { "E": 13.6, "m": 9.11e-31 } }'
const res = await fetch('https://www.zeqsdk.com/api/zeq/compute', { method: 'POST', headers: { 'Authorization': `Bearer ${process.env.ZEQ_API_KEY}`, 'Content-Type': 'application/json', }, body: JSON.stringify({ domain: 'quantum_mechanics', operators: ['KO42'], inputs: { E: 13.6, m: 9.11e-31 } }) }); const { zeqState, result } = await res.json(); console.log('R(t):', zeqState.masterSum); console.log('Phase:', zeqState.phase); console.log('Precision:', zeqState.precision); // always ≤ 0.001
interface ZeqState { masterSum: number; phase: number; precision: number; zeqond: number; operators: string[]; } interface ComputeResponse { zeqState: ZeqState; result: Record<string, unknown>; } const res = await fetch('https://www.zeqsdk.com/api/zeq/compute', { method: 'POST', headers: { 'Authorization': `Bearer ${process.env.ZEQ_API_KEY}`, 'Content-Type': 'application/json', }, body: JSON.stringify({ domain: 'quantum_mechanics', operators: ['KO42'], inputs: { E: 13.6, m: 9.11e-31 } }) }); const { zeqState }: ComputeResponse = await res.json(); console.log('R(t):', zeqState.masterSum); console.log('Precision:', zeqState.precision); // always ≤ 0.001
import requests, os resp = requests.post( "https://www.zeqsdk.com/api/zeq/compute", headers={"Authorization": f"Bearer {os.environ['ZEQ_API_KEY']}"}, json={ "domain": "quantum_mechanics", "operators": ["KO42"], "inputs": {"E": 13.6, "m": 9.11e-31} } ) data = resp.json() zeq = data["zeqState"] print("R(t):", zeq["masterSum"]) print("Phase:", zeq["phase"]) print("Precision:", zeq["precision"]) # always ≤ 0.001 assert "KO42" in zeq["operators"] # always present
package main import ( "bytes" "encoding/json" "fmt" "net/http" "os" ) func main() { body, _ := json.Marshal(map[string]any{ "domain": "quantum_mechanics", "operators": []string{"KO42"}, "inputs": map[string]float64{"E": 13.6, "m": 9.11e-31}, }) req, _ := http.NewRequest("POST", "https://www.zeqsdk.com/api/zeq/compute", bytes.NewBuffer(body)) req.Header.Set("Authorization", "Bearer "+os.Getenv("ZEQ_API_KEY")) req.Header.Set("Content-Type", "application/json") resp, _ := http.DefaultClient.Do(req) var data map[string]any json.NewDecoder(resp.Body).Decode(&data) zeq := data["zeqState"].(map[string]any) fmt.Println("R(t):", zeq["masterSum"]) fmt.Println("Precision:", zeq["precision"]) // always ≤ 0.001 }
use reqwest::header; use serde_json::{json, Value}; #[tokio::main] async fn main() -> Result<(), Box<dyn std::error::Error>> { let api_key = std::env::var("ZEQ_API_KEY")?; let client = reqwest::Client::new(); let body = json!({ "domain": "quantum_mechanics", "operators": ["KO42"], "inputs": { "E": 13.6, "m": 9.11e-31_f64 } }); let resp: Value = client .post("https://www.zeqsdk.com/api/zeq/compute") .header(header::AUTHORIZATION, format!("Bearer {}", api_key)) .json(&body) .send() .await? .json() .await?; let zeq = &resp["zeqState"]; println!("R(t): {}", zeq["masterSum"]); println!("Precision: {}", zeq["precision"]); // always ≤ 0.001 Ok(()) }
import java.net.URI; import java.net.http.*; import java.net.http.HttpRequest.BodyPublishers; public class ZeqCompute { public static void main(String[] args) throws Exception { String apiKey = System.getenv("ZEQ_API_KEY"); String body = """ {"domain":"quantum_mechanics", "operators":["KO42"], "inputs":{"E":13.6,"m":9.11e-31}} """; HttpRequest request = HttpRequest.newBuilder() .uri(URI.create("https://www.zeqsdk.com/api/zeq/compute")) .header("Authorization", "Bearer " + apiKey) .header("Content-Type", "application/json") .POST(BodyPublishers.ofString(body)) .build(); HttpResponse<String> resp = HttpClient.newHttpClient().send(request, HttpResponse.BodyHandlers.ofString()); System.out.println(resp.body()); // includes zeqState.precision ≤ 0.001 } }
using System.Net.Http.Json; using System.Text.Json; var apiKey = Environment.GetEnvironmentVariable("ZEQ_API_KEY"); using var client = new HttpClient(); client.DefaultRequestHeaders.Add("Authorization", $"Bearer {apiKey}"); var payload = new { domain = "quantum_mechanics", operators = new[] { "KO42" }, inputs = new { E = 13.6, m = 9.11e-31 } }; var response = await client.PostAsJsonAsync( "https://www.zeqsdk.com/api/zeq/compute", payload); var data = await response.Content.ReadFromJsonAsync<JsonElement>(); var zeq = data.GetProperty("zeqState"); Console.WriteLine($"R(t): {zeq.GetProperty("masterSum")}"); Console.WriteLine($"Precision: {zeq.GetProperty("precision")}"); // ≤ 0.001
require 'net/http' require 'json' require 'uri' uri = URI('https://www.zeqsdk.com/api/zeq/compute') body = { domain: 'quantum_mechanics', operators: ['KO42'], inputs: { E: 13.6, m: 9.11e-31 } }.to_json req = Net::HTTP::Post.new(uri) req['Authorization'] = "Bearer #{ENV['ZEQ_API_KEY']}" req['Content-Type'] = 'application/json' req.body = body resp = Net::HTTP.start(uri.host, uri.port, use_ssl: true) { |h| h.request(req) } data = JSON.parse(resp.body) zeq = data['zeqState'] puts "R(t): #{zeq['masterSum']}" puts "Precision: #{zeq['precision']}" # always ≤ 0.001
<?php $apiKey = getenv('ZEQ_API_KEY'); $payload = json_encode([ 'domain' => 'quantum_mechanics', 'operators' => ['KO42'], 'inputs' => ['E' => 13.6, 'm' => 9.11e-31], ]); $ch = curl_init('https://www.zeqsdk.com/api/zeq/compute'); curl_setopt_array($ch, [ CURLOPT_RETURNTRANSFER => true, CURLOPT_POST => true, CURLOPT_POSTFIELDS => $payload, CURLOPT_HTTPHEADER => [ "Authorization: Bearer $apiKey", 'Content-Type: application/json', ], ]); $data = json_decode(curl_exec($ch), true); $zeq = $data['zeqState']; echo "R(t): " . $zeq['masterSum'] . "\n"; echo "Precision: " . $zeq['precision'] . "\n"; // always ≤ 0.001
4

Read the ZeqState response

Every successful compute request returns a zeqState object alongside the domain-specific result. Here is the full ZeqState structure:

Field Type Description
operators string[] Operator IDs applied to this computation. Always includes KO42.
masterSum number R(t) — the grounded result. Approximately 1.000xxx. This is the HulyaPulse-modulated output of the master equation.
phase number φ — current position within the HulyaPulse cycle. Range: 0.0000–1.0000. Two calls at the same Zeqond have the same phase.
zeqond integer τ — Zeqond count at compute time. One Zeqond = 0.777 seconds. Use this to replay any computation reproducibly.
domain string The physics domain that was computed (e.g. "Quantum Mechanics").
precision number Fractional precision of this result. Always ≤ 0.001 (≤ 0.1%). If this exceeds 0.001, the result should be treated as invalid.
pulseHz number The HulyaPulse frequency. Always 1.287. A constant, included for verification.

Tip: validate KO42 presence and precision ≤ 0.001 in every response before using the result.

5

Connect your AI client via MCP (optional)

If you use Claude Desktop, Cursor, or Windsurf, you can connect Zeq.dev as a native AI tool. Add this to your AI client's config file, replace the placeholder key, and restart:

// ~/Library/Application Support/Claude/claude_desktop_config.json (macOS) // %APPDATA%\Claude\claude_desktop_config.json (Windows) { "mcpServers": { "zeq-dev": { "type": "http", "url": "https://www.zeqsdk.com/api/mcp", "headers": { "Authorization": "Bearer zeq_ak_YOUR_KEY_HERE" } } } }
// ~/.cursor/mcp.json (or Settings > MCP > Add Server) { "mcpServers": { "zeq-dev": { "type": "http", "url": "https://www.zeqsdk.com/api/mcp", "headers": { "Authorization": "Bearer zeq_ak_YOUR_KEY_HERE" } } } }
// Windsurf: Settings > AI > MCP Servers > Add { "mcpServers": { "zeq-dev": { "type": "http", "url": "https://www.zeqsdk.com/api/mcp", "headers": { "Authorization": "Bearer zeq_ak_YOUR_KEY_HERE" } } } }

Once connected, your AI gains zeq_compute and zeq_list_operators as native tools. Full details on the MCP page.

Auth & Rate Limits

Endpoints & access rules

All authenticated endpoints require an Authorization: Bearer zeq_ak_… header. Public endpoints have no auth requirement but are still rate-limited per IP. Daily token budgets reset at 00:00 UTC — exhaustion returns 429 DAILY_LIMIT_EXCEEDED.

Endpoint Auth Rate limit Consumes tokens
POST /api/zeq/computeAuth60 / min1 per call
GET  /api/zeq/pulsePublic60 / min0 — always free
GET  /api/zeq/pulse/streamAuth60 / min0 — SSE keepalive
POST /api/zeq/verifyAuth60 / min0 — proof check only
POST /api/zeq/latticeAuth60 / minN tokens (1 per node, 2–5)
POST /api/zeq/shiftAuth60 / minsteps tokens (1–64)
GET  /api/zeq/usageAuth60 / min0
GET  /api/operatorsPublic60 / min0
GET  /api/operators/categoriesPublic60 / min0
GET  /api/demo-keyPublic30 / min0 — issues trial key
Free
100 tokens/day
Starter · $29/mo
500 tokens/day
Builder · $79/mo
2,500 tokens/day
Advanced · $199/mo
7,500 tokens/day
Architect · $499/mo
25,000 tokens/day
Operators API

Browse 1,536 operators

Two public endpoints expose the full operator library — no API key required. Use them to build domain selectors, search UIs, or populate AI tool registries.

GET /api/operators Public 60 req/min · No tokens consumed

Returns the full operator list with optional filtering. All query parameters are optional and combinable. Underscore and space notation are both accepted for multi-word domains.

Query paramTypeDescription
searchstringSubstring match on operator name, ID, domain, or description (case-insensitive)
domainstringFilter by domain — underscores or spaces accepted: quantum_mechanics and Quantum Mechanics both work. Alias of category.
categorystringSame as domain. Underscores or spaces accepted: fluid_dynamics or thermodynamics.
domainGroupstringFilter to a group: Core Physics · Extended Physics · Applied Sciences · Industry · Frontier
limitintegerCap the number of operators returned after all filters. Omit or pass 0 to return all matching results. Response always includes the untruncated filtered count.
# search across all domains curl "https://www.zeqsdk.com/api/operators?search=entropy&limit=5" # filter by domain (underscores and spaces both accepted) curl "https://www.zeqsdk.com/api/operators?domain=quantum_mechanics&limit=10" # filter by group curl "https://www.zeqsdk.com/api/operators?domainGroup=Core+Physics&search=entropy"
{ "operators": [ { "id": "sm-entropy-calc", "name": "Entropy Calc", "domain": "Statistical Mechanics", "domainGroup": "Core Physics", "equation": "S = k_B ln \u03a9", "precision": 0.000129, "description": "Boltzmann entropy for discrete microstates", "sdkUsage": "zeq.compute({ domain: 'statistical_mechanics', operators: ['sm-entropy-calc'] })" } ], "total": 1536, "filtered": 1, "returned": 1, "source": "local" }
GET /api/operators/categories Public 60 req/min · No tokens consumed

Returns all 64 domain definitions sorted by group then name — including prefix codes and per-domain operator counts.

curl "https://www.zeqsdk.com/api/operators/categories"
{ "categories": [ { "domain": "Atmospheric Physics", "domainGroup": "Applied Sciences", "prefix": "AT", "count": 24, "color": "#ffd700" }, { "domain": "Biophysics", "domainGroup": "Applied Sciences", "prefix": "BP", "count": 24, "color": "#ffd700" }, { "domain": "Chemical Physics", "domainGroup": "Applied Sciences", "prefix": "CP", "count": 24, "color": "#ffd700" }, { "domain": "Climate Modeling", "domainGroup": "Applied Sciences", "prefix": "CL", "count": 24, "color": "#ffd700" }, { "domain": "Earth Sciences", "domainGroup": "Applied Sciences", "prefix": "ERS", "count": 24, "color": "#ffd700" }, { "domain": "Environmental Physics", "domainGroup": "Applied Sciences", "prefix": "EN", "count": 24, "color": "#ffd700" }, { "domain": "Geophysics", "domainGroup": "Applied Sciences", "prefix": "GE", "count": 24, "color": "#ffd700" }, { "domain": "Hydrology", "domainGroup": "Applied Sciences", "prefix": "HY", "count": 24, "color": "#ffd700" }, { "domain": "Materials Science", "domainGroup": "Applied Sciences", "prefix": "MS", "count": 24, "color": "#ffd700" }, { "domain": "Oceanography", "domainGroup": "Applied Sciences", "prefix": "OC", "count": 24, "color": "#ffd700" }, { "domain": "Seismology", "domainGroup": "Applied Sciences", "prefix": "SE", "count": 24, "color": "#ffd700" }, { "domain": "Soil Physics", "domainGroup": "Applied Sciences", "prefix": "SOP", "count": 24, "color": "#ffd700" }, { "domain": "Acoustics", "domainGroup": "Core Physics", "prefix": "AC", "count": 24, "color": "#00ff88" }, { "domain": "Classical Mechanics", "domainGroup": "Core Physics", "prefix": "CM", "count": 24, "color": "#00ff88" }, { "domain": "Electromagnetism", "domainGroup": "Core Physics", "prefix": "EM", "count": 24, "color": "#00ff88" }, { "domain": "Fluid Dynamics", "domainGroup": "Core Physics", "prefix": "FD", "count": 24, "color": "#00ff88" }, { "domain": "Gravitational Physics", "domainGroup": "Core Physics", "prefix": "GP", "count": 24, "color": "#00ff88" }, { "domain": "Newtonian Mechanics", "domainGroup": "Core Physics", "prefix": "NM", "count": 24, "color": "#00ff88" }, { "domain": "Nuclear Physics", "domainGroup": "Core Physics", "prefix": "NP", "count": 24, "color": "#00ff88" }, { "domain": "Optics", "domainGroup": "Core Physics", "prefix": "OP", "count": 24, "color": "#00ff88" }, { "domain": "Particle Physics", "domainGroup": "Core Physics", "prefix": "PP", "count": 24, "color": "#00ff88" }, { "domain": "Quantum Mechanics", "domainGroup": "Core Physics", "prefix": "QM", "count": 24, "color": "#00ff88" }, { "domain": "Quantum Resonance", "domainGroup": "Core Physics", "prefix": "QR", "count": 24, "color": "#00ff88" }, { "domain": "Relativistic Physics", "domainGroup": "Core Physics", "prefix": "RP", "count": 24, "color": "#00ff88" }, { "domain": "Statistical Mechanics", "domainGroup": "Core Physics", "prefix": "SM", "count": 24, "color": "#00ff88" }, { "domain": "Thermodynamics", "domainGroup": "Core Physics", "prefix": "TH", "count": 24, "color": "#00ff88" }, { "domain": "Wave Physics", "domainGroup": "Core Physics", "prefix": "WP", "count": 24, "color": "#00ff88" }, { "domain": "Zeq Resonance Theory", "domainGroup": "Core Physics", "prefix": "ZR", "count": 24, "color": "#00ff88" }, { "domain": "Astrophysics", "domainGroup": "Extended Physics", "prefix": "AS", "count": 24, "color": "#00d4ff" }, { "domain": "Condensed Matter", "domainGroup": "Extended Physics", "prefix": "CD", "count": 24, "color": "#00d4ff" }, { "domain": "Cosmology", "domainGroup": "Extended Physics", "prefix": "CO", "count": 24, "color": "#00d4ff" }, { "domain": "Crystallography", "domainGroup": "Extended Physics", "prefix": "CR", "count": 24, "color": "#00d4ff" }, { "domain": "Nanophysics", "domainGroup": "Extended Physics", "prefix": "NA", "count": 24, "color": "#00d4ff" }, { "domain": "Photonics", "domainGroup": "Extended Physics", "prefix": "PT", "count": 24, "color": "#00d4ff" }, { "domain": "Plasma Physics", "domainGroup": "Extended Physics", "prefix": "PL", "count": 24, "color": "#00d4ff" }, { "domain": "Quantum Computing", "domainGroup": "Extended Physics", "prefix": "QC", "count": 24, "color": "#00d4ff" }, { "domain": "Quantum Field Theory", "domainGroup": "Extended Physics", "prefix": "QF", "count": 24, "color": "#00d4ff" }, { "domain": "Spintronics", "domainGroup": "Extended Physics", "prefix": "SP", "count": 24, "color": "#00d4ff" }, { "domain": "Superconductivity", "domainGroup": "Extended Physics", "prefix": "SC", "count": 24, "color": "#00d4ff" }, { "domain": "Analogue Gravity", "domainGroup": "Frontier", "prefix": "AG", "count": 24, "color": "#b44fff" }, { "domain": "Chaotic Systems", "domainGroup": "Frontier", "prefix": "CH", "count": 24, "color": "#b44fff" }, { "domain": "Consciousness Studies", "domainGroup": "Frontier", "prefix": "CN", "count": 24, "color": "#b44fff" }, { "domain": "Dark Energy Models", "domainGroup": "Frontier", "prefix": "DE", "count": 24, "color": "#b44fff" }, { "domain": "Emergent Complexity", "domainGroup": "Frontier", "prefix": "EC", "count": 24, "color": "#b44fff" }, { "domain": "Extra Dimensions", "domainGroup": "Frontier", "prefix": "XD", "count": 24, "color": "#b44fff" }, { "domain": "Fractal Mechanics", "domainGroup": "Frontier", "prefix": "FM", "count": 24, "color": "#b44fff" }, { "domain": "Neurophysics", "domainGroup": "Frontier", "prefix": "NR", "count": 24, "color": "#b44fff" }, { "domain": "Non-Euclidean Dynamics","domainGroup": "Frontier", "prefix": "NED","count": 24, "color": "#b44fff" }, { "domain": "Quantum Gravity", "domainGroup": "Frontier", "prefix": "QG", "count": 24, "color": "#b44fff" }, { "domain": "Quantum Information", "domainGroup": "Frontier", "prefix": "QI", "count": 24, "color": "#b44fff" }, { "domain": "Time Crystal Physics", "domainGroup": "Frontier", "prefix": "TC", "count": 24, "color": "#b44fff" }, { "domain": "Topological Matter", "domainGroup": "Frontier", "prefix": "TM", "count": 24, "color": "#b44fff" }, { "domain": "Aerospace Engineering", "domainGroup": "Industry", "prefix": "AE", "count": 24, "color": "#ff6b35" }, { "domain": "Automotive Engineering","domainGroup": "Industry", "prefix": "AUTO","count": 24, "color": "#ff6b35" }, { "domain": "Biomedical Engineering","domainGroup": "Industry", "prefix": "BE", "count": 24, "color": "#ff6b35" }, { "domain": "Chemical Engineering", "domainGroup": "Industry", "prefix": "CHE", "count": 24, "color": "#ff6b35" }, { "domain": "Communications", "domainGroup": "Industry", "prefix": "CM2", "count": 24, "color": "#ff6b35" }, { "domain": "Control Systems", "domainGroup": "Industry", "prefix": "CS2", "count": 24, "color": "#ff6b35" }, { "domain": "Nuclear Engineering", "domainGroup": "Industry", "prefix": "NE", "count": 24, "color": "#ff6b35" }, { "domain": "Power Systems", "domainGroup": "Industry", "prefix": "PW", "count": 24, "color": "#ff6b35" }, { "domain": "Robotics", "domainGroup": "Industry", "prefix": "RO", "count": 24, "color": "#ff6b35" }, { "domain": "Semiconductor Design", "domainGroup": "Industry", "prefix": "SD", "count": 24, "color": "#ff6b35" }, { "domain": "Signal Processing", "domainGroup": "Industry", "prefix": "SI", "count": 24, "color": "#ff6b35" }, { "domain": "Structural Engineering","domainGroup": "Industry", "prefix": "SW", "count": 24, "color": "#ff6b35" } ], "groups": ["Core Physics", "Extended Physics", "Applied Sciences", "Industry", "Frontier"], "totalOperators": 1536, "totalDomains": 64, "source": "local" }
GroupDomains
Core Physics16
Extended Physics11
Applied Sciences12
Industry12
Frontier13
Total64
7-Step Protocol

ZEQOND Computation Protocol

Every query to /api/zeq/compute, /api/zeq/lattice, /api/zeq/shift, and POST /api/mcp (JSON-RPC tools/call) runs through all seven steps in sequence. No query can skip a step. Constants are sourced directly from NIST CODATA 2018. The response always includes a protocol_steps[] array so you can audit what ran at each step.

STEP 1
SELECT

Resolve operator IDs from the 1,536 verified physics operators. If none are specified, intent-aware selection picks the best match for your domain and inputs.

STEP 2
BIND

Bind NIST CODATA 2018 physical constants (ℏ, c, G, k_B, ε₀, N_A…) to the selected operators. Constants are scoped to the domain group (Core / Extended / Applied / Industry / Frontier).

STEP 3
VALIDATE

Dimensional analysis and domain constraint checks. Mass must be ≥ 0, velocity must be < c, temperature must be ≥ 0 K, and all values must be finite. Violations are clamped and flagged in warnings[].

STEP 4
COMPUTE

Domain-specific physics computation. Core domains use precise analytical solvers (quantum: E_n = n²π²ℏ²/2mL², orbital: v = √(G_mod·M/r), thermal: P = nRT/V, EM: F = q²/4πε₀r², …). Other domains use KO42-modulated formula evaluation.

STEP 5
VERIFY

Cross-check the result against the KO42 precision bound (≤ 0.1%). If the relative uncertainty exceeds 0.001, a precision warning is added to protocol_steps[4].detail. The result is never rejected — flagging is informational.

STEP 6
PULSE

Synchronise to the 1.287 Hz HulyaPulse. Applies the KO42 modulation: R(t) = S(t) × [1 + α·sin(2π·f_H·t)] where α = 1.29×10⁻³ and τ = 0.777 s. Phase and Zeqond index are recorded.

STEP 7
RETURN

Assemble the structured result: value, unit, uncertainty, operator_id, zeqState, result, protocol_steps[], and zeqProof HMAC. API version 2.0. VX mode label applied if the query ran in degraded (quota-exhausted) mode.

[VX MODE]
Paid users exhausting their quota receive mode: "VX" instead of a 429.

When a paid plan user's daily token allowance is exhausted, Step 4 runs with the VX operator (KO42 ground state only) and the response includes "mode":"VX". Free / Starter users over quota still receive 429 DAILY_LIMIT_EXCEEDED.

{ "mode": "full", "value": 1.3606e-18, "unit": "J", "uncertainty": 3.4015e-22, "operator_id": "QM-001", "protocol_steps": [ { "step": 1, "name": "SELECT", "status": "ok", "detail": { "domain": "quantum-mechanics", "operators_selected": ["QM-001"] }, "durationMs": 1 }, { "step": 2, "name": "BIND", "status": "ok", "detail": { "nist_release": "CODATA 2018", "constants_bound": ["hbar","c","G","k_B","e","epsilon_0","mu_0","m_e","m_p"] }, "durationMs": 0 }, { "step": 3, "name": "VALIDATE","status": "ok", "detail": { "input_count": 2, "warnings": [] }, "durationMs": 0 }, { "step": 4, "name": "COMPUTE", "status": "ok", "detail": { "solver": "QM domain solver", "value": 1.3606e-18, "equation": "E_n = n\u00b2\u03c0\u00b2\u210f\u00b2 / (2mL\u00b2)" }, "durationMs": 0 }, { "step": 5, "name": "VERIFY", "status": "ok", "detail": { "precision_target": "\u22640.1% (0.001)", "precision_actual": 0.000025, "precision_ok": true }, "durationMs": 0 }, { "step": 6, "name": "PULSE", "status": "ok", "detail": { "hulyapulse_hz": 1.287, "R_t": 1.000201, "modulation": "R(t) = S(t) \u00d7 [1 + \u03b1_K \u00d7 sin(2\u03c0 \u00d7 f_H \u00d7 t)]" }, "durationMs": 0 }, { "step": 7, "name": "RETURN", "status": "ok", "detail": { "mode": "full" }, "durationMs": 0 } ], "zeqState": { "operators": ["KO42", "QM-001"], "masterSum": 1.000201, "domain": "quantum-mechanics", "precision": 0.000129, "pulseHz": 1.287, "zeqond": 2156842, "phase": 0.4312 }, "result": { "S_t": 1.0, "R_t": 1.000201, "value": 1.3606e-18, "unit": "J", "uncertainty": 3.4015e-22, "inputs": { "n": 1, "L": 5.29e-9 } }, "meta": { "computedAt": "2026-03-30T00:00:00.000Z", "apiVersion": "2.0", "totalMs": 2, "nistRelease": "CODATA 2018", "sdkVersion": "6.3.0" }, "zeqProof": "a1b2c3...64chars" }
curl -X POST https://www.zeqsdk.com/api/zeq/compute \ -H "Authorization: Bearer $ZEQ_API_KEY" \ -H "Content-Type: application/json" \ -d '{ "domain": "quantum-mechanics", "inputs": { "n": 1, "L": 5.29e-9 }, "operators": ["QM-001"] }'

All API endpoints

MethodEndpointAuthTokensDescription
POST/api/zeq/computeAuth17-step physics computation. Returns value, unit, uncertainty, protocol_steps[].
GET/api/zeq/pulsePublic0Live HulyaPulse snapshot. Zeqond τ, phase φ, R(t), precision.
GET/api/zeq/pulse/streamAuth0SSE stream — live HulyaPulse event every 777 ms.
POST/api/zeq/verifyAuth0Verify a zeqProof HMAC returned by /compute or /lattice.
POST/api/zeq/latticeAuthN nodesZeqLattice — multi-node coherence grid. Each node runs the full 7-step wizard.
POST/api/zeq/shiftAuthN stepsZeqShift — time-series projection across N future Zeqond steps.
GET/api/zeq/usageAuth0Token budget: used, remaining, plan, reset time.
GET/api/operatorsPublic0All 1,536 operators. Filter by domain with ?domain=…
GET/api/operators/:idPublic0Single operator by ID (e.g. QM-001, KO42, ZR-003).
GET/api/operators/categoriesPublic0All 64 domain categories with group, prefix, and operator counts.
POST/api/mcpAuth1MCP JSON-RPC endpoint (method: "tools/call") — zeq_compute, zeq_list_operators, zeq_verify, zeq_lattice, zeq_shift, zeq_field_status.
ZeqField Protocols

Six protocol endpoints

The ZeqField Protocols extend the core compute API with live pulse sync, tamper-evident proofs, multi-node coherence, time-series projection, and usage monitoring.

GET /api/zeq/pulse Public ZeqPulse · 60 req/min · No tokens

Live HulyaPulse snapshot — current Zeqond τ, phase φ, R(t), precision, and time to next tick. No API key required. Ideal as a heartbeat or for temporal anchoring in AI agents.

curl https://www.zeqsdk.com/api/zeq/pulse
{ "protocol": "ZeqPulse", "zeqond": 2156842, "phase": 0.4312, "R_t": 1.000487, "fieldStrength": 1.000487, "timeToNextZeqond": 0.3421, "pulseHz": 1.287, "zeqondSec": 0.777, "alpha": 0.00129, "precision": 0.000129, "timestamp": "2026-03-29T12:00:00.000Z", "modulation": "R(t) = [1 + \u03b1\u00b7sin(2\u03c0\u00b7f\u00b7t)] where f=1.287 Hz, \u03b1=0.00129" }
GET /api/zeq/pulse/stream Auth SSE · 777 ms tick · No tokens

Server-Sent Events stream — a live HulyaPulse event every 777 ms. Requires your API key. Ideal for real-time agent clock synchronisation. The server sends data: lines continuously; close the connection when done.

curl -H "Authorization: Bearer $ZEQ_API_KEY" \ -H "Accept: text/event-stream" \ https://www.zeqsdk.com/api/zeq/pulse/stream
data: {"zeqond":2156842,"phase":0.4312,"R_t":1.000487,"pulseHz":1.287,"timestamp":"2026-03-29T12:00:00.000Z"} data: {"zeqond":2156843,"phase":0.1124,"R_t":1.000201,"pulseHz":1.287,"timestamp":"2026-03-29T12:00:00.777Z"} data: {"zeqond":2156843,"phase":0.4717,"R_t":0.999874,"pulseHz":1.287,"timestamp":"2026-03-29T12:00:01.554Z"}
GET /api/zeq/usage Auth Usage · 60 req/min · No tokens

Returns your current token budget for the day — calls used, remaining, plan name, and UTC reset time. Use as a preflight check in automated pipelines to avoid unexpected 429 mid-batch.

curl -H "Authorization: Bearer $ZEQ_API_KEY" \ https://www.zeqsdk.com/api/zeq/usage
{ "used": 42, "limit": 500, "remaining": 458, "plan": "starter", "resetAt": "2026-03-31T00:00:00.000Z" }
POST /api/zeq/verify Auth ZeqProof · HMAC-SHA256 · No tokens

Verify the zeqProof HMAC attached to every compute response. Proves a physics result was generated at a specific Zeqond by the authenticated key — tamper-evident and auditable without storing a secret client-side.

Request body fieldTypeRequiredDescription
zeqProofstringYes64-char HMAC-SHA256 hex returned in the zeqProof field of the compute response
operatorIdsstring[]YesOperator IDs in the exact order returned by the compute response zeqState.operators
R_tnumberYeszeqState.masterSum from the compute response — pass all 6 decimal places
zeqondintegerYeszeqState.zeqond from the compute response
curl -X POST https://www.zeqsdk.com/api/zeq/verify \ -H "Authorization: Bearer $ZEQ_API_KEY" \ -H "Content-Type: application/json" \ -d '{ "zeqProof": "a3f2b1c8d4e9f012...64-char hex from compute response...", "operatorIds": ["qm-wave-func-solver", "ko42"], "R_t": 1.000487, "zeqond": 2156842 }'
// valid: true { "protocol": "ZeqProof", "valid": true, "zeqond": 2156842, "R_t": 1.000487, "operatorIds": ["qm-wave-func-solver", "ko42"], "keyPrefix": "zeq_ak_abc1", "verifiedAt": "2026-03-29T12:00:01.234Z" } // valid: false also returns: // "hint": "Proof mismatch — check operatorIds ordering, R_t precision (6dp), and zeqond value."
POST /api/zeq/lattice Auth ZeqLattice · 2–5 nodes · N tokens

Multi-domain coherence grid. Pass 2–5 node specs, each with a domain and inputs. All nodes share one Zeqond tick with staggered phase offsets. Returns per-node R_t values, a coherenceScore (0–1), and the lattice equation. Consumes N tokens — one per node.

Request body fieldTypeRequiredDescription
nodesobject[]YesArray of 2–5 node objects, each with domain and inputs
nodes[].domainstringYesPhysics domain name (e.g. quantum_mechanics) or prefix code (e.g. QM)
nodes[].inputsobjectYesDomain-specific input parameters (key-value pairs of numeric values)
curl -X POST https://www.zeqsdk.com/api/zeq/lattice \ -H "Authorization: Bearer $ZEQ_API_KEY" \ -H "Content-Type: application/json" \ -d '{ "nodes": [ { "domain": "quantum_mechanics", "inputs": { "E": 13.6, "m": 9.11e-31 } }, { "domain": "thermodynamics", "inputs": { "temp_K": 500, "pressure_Pa": 101325 } }, { "domain": "fluid_dynamics", "inputs": { "velocity_ms": 340, "altitude_m": 10000 } } ] }'
{ "protocol": "ZeqLattice", "nodeCount": 3, "zeqond": 2156842, "coherenceScore": 0.998421, "latticeEquation": "L(t) = (1/3) \u03a3\u1d62 R\u1d62(t+\u0394\u1d62) \u0394\u1d62=i\u00b7\u03c4/3 coherence=0.9984", "nodes": [ { "node": 1, "domain": "Quantum Mechanics", "zeqond": 2156842, "phase": 0.4312, "R_t": 1.000487, "operator": "qm-wave-func-solver" }, { "node": 2, "domain": "Thermodynamics", "zeqond": 2156842, "phase": 0.6905, "R_t": 1.000201, "operator": "th-first-law" }, { "node": 3, "domain": "Fluid Dynamics", "zeqond": 2156842, "phase": 0.9498, "R_t": 0.999874, "operator": "fd-navier-stokes" } ], "callsConsumed": 3, "pulseHz": 1.287, "zeqondSec": 0.777, "computedAt": "2026-03-29T12:00:00.000Z" }
POST /api/zeq/shift Auth ZeqShift · 1–64 steps · steps tokens

Forward time-series projection. Pass steps (1–64), a domain, and inputs. Returns a per-step array with exact deterministic R_t values 0.777 s apart. Consumes steps tokens.

Request body fieldTypeRequiredDescription
stepsintegerYesNumber of projection steps. Range: 1–64. Each step is 0.777 s (one Zeqond) forward in time.
domainstringYesPhysics domain name (e.g. quantum_mechanics) or prefix code (e.g. QM)
inputsobjectYesDomain-specific input parameters (key-value pairs of numeric values)
curl -X POST https://www.zeqsdk.com/api/zeq/shift \ -H "Authorization: Bearer $ZEQ_API_KEY" \ -H "Content-Type: application/json" \ -d '{ "steps": 4, "domain": "quantum_mechanics", "inputs": { "E": 13.6, "m": 9.11e-31 } }'
{ "protocol": "ZeqShift", "domain": "Quantum Mechanics", "stepCount": 4, "callsConsumed": 4, "summary": { "minRt": 0.999214, "maxRt": 1.000914, "meanRt": 1.000087 }, "projection": [ { "step": 0, "zeqond": 2156842, "phase": 0.4312, "R_t": 1.000487, "delta": 0, "t": 1743249600.777 }, { "step": 1, "zeqond": 2156843, "phase": 0.1124, "R_t": 1.000201, "delta": -0.000286, "t": 1743249601.554 }, { "step": 2, "zeqond": 2156843, "phase": 0.7717, "R_t": 0.999874, "delta": -0.000327, "t": 1743249602.331 }, { "step": 3, "zeqond": 2156844, "phase": 0.4309, "R_t": 1.000611, "delta": +0.000737, "t": 1743249603.108 } ], "equation": "R_t(step) = S(t) \u00d7 [1 + \u03b1\u00b7sin(2\u03c0\u00b7f\u00b7(t\u2080 + step\u00b7\u03c4))] f=1.287 Hz, \u03b1=0.00129, \u03c4=0.777s", "computedAt": "2026-03-29T12:00:00.000Z" }
Reference

All 64 domains & example inputs

Pass any of these domain names (or their prefix codes) to domain in a compute request. Values shown are realistic representative inputs.

Core Physics · 16 domains
ZRZeq Resonance Theory
{ "f_hz": 1.287, "alpha": 0.00129 }
QMQuantum Mechanics
{ "E": 13.6, "m": 9.11e-31 }
QRQuantum Resonance
{ "omega_0": 1e9, "Q_factor": 1000 }
WPWave Physics
{ "frequency": 440, "wavelength": 0.77 }
EMElectromagnetism
{ "charge": 1.6e-19, "velocity": 3e6 }
THThermodynamics
{ "temp_K": 500, "pressure_Pa": 101325 }
FDFluid Dynamics
{ "velocity_ms": 340, "altitude_m": 10000 }
CMClassical Mechanics
{ "mass": 10, "velocity": 5 }
NMNewtonian Mechanics
{ "force_N": 100, "mass_kg": 5 }
SMStatistical Mechanics
{ "temp_K": 300, "n_states": 1e23 }
RPRelativistic Physics
{ "mass_kg": 1.67e-27, "beta": 0.99 }
NPNuclear Physics
{ "protons": 92, "neutrons": 146 }
PPParticle Physics
{ "mass_GeV": 125.1, "coupling": 0.13 }
OPOptics
{ "focal_m": 0.05, "obj_dist_m": 0.2 }
ACAcoustics
{ "frequency_Hz": 1000, "pressure_Pa": 0.02 }
GPGravitational Physics
{ "mass1_Msun": 30, "mass2_Msun": 25 }
Extended Physics · 11 domains
PLPlasma Physics
{ "density_m3": 1e19, "temp_eV": 10 }
CDCondensed Matter
{ "eff_mass": 0.067, "k_m": 1e8 }
SCSuperconductivity
{ "temp_K": 4.2, "B_field_T": 0.02 }
CRCrystallography
{ "d_spacing_A": 3.5, "theta_deg": 14.3 }
ASAstrophysics
{ "luminosity_Lsun": 1, "radius_Rsun": 1 }
COCosmology
{ "redshift": 1.0, "H0": 67.4 }
QFQuantum Field Theory
{ "mass_GeV": 0.511, "coupling": 0.0073 }
QCQuantum Computing
{ "qubits": 5, "gate_fidelity": 0.999 }
PTPhotonics
{ "wavelength_nm": 1550, "gain_dBm": 15 }
SPSpintronics
{ "spin_current_uA": 10, "B_T": 0.5 }
NANanophysics
{ "length_nm": 10, "voltage_mV": 2.5 }
Applied Sciences · 12 domains
MSMaterials Science
{ "stress_MPa": 250, "strain": 0.002 }
CPChemical Physics
{ "Ea_kJmol": 85, "temp_K": 500 }
BPBiophysics
{ "conc_mM": 1.5, "Km_mM": 0.5 }
GEGeophysics
{ "depth_km": 35, "density_kgm3": 2900 }
ATAtmospheric Physics
{ "altitude_m": 5000, "temp_K": 255 }
OCOceanography
{ "salinity_ppt": 35, "temp_C": 10 }
ENEnvironmental Physics
{ "conc_ugm3": 12.5, "lifetime_d": 7 }
CLClimate Modeling
{ "CO2_ppm": 420, "albedo": 0.3 }
SESeismology
{ "magnitude": 6.5, "depth_km": 10 }
HYHydrology
{ "K_ms": 1e-4, "gradient": 0.01 }
ERSEarth Sciences
{ "depth_km": 100, "viscosity_Pas": 1e21 }
SOPSoil Physics
{ "theta": 0.35, "matric_kPa": -50 }
Industry · 12 domains
SDSemiconductor Design
{ "Vgs_V": 1.2, "Vt_V": 0.4 }
PWPower Systems
{ "voltage_V": 11000, "current_A": 200 }
CM2Communications
{ "bandwidth_MHz": 20, "SNR_dB": 25 }
SISignal Processing
{ "sample_kHz": 44.1, "freq_kHz": 1.0 }
CS2Control Systems
{ "Kp": 2.0, "Ki": 0.5 }
RORobotics
{ "joint_deg": 45, "link_m": 0.5 }
AEAerospace Engineering
{ "velocity_ms": 250, "alt_m": 10000 }
NENuclear Engineering
{ "enrichment": 0.04, "flux": 1e13 }
BEBiomedical Engineering
{ "freq_MHz": 63.8, "B0_T": 1.5 }
SWStructural Engineering
{ "load_kN": 500, "span_m": 12 }
CHEChemical Engineering
{ "temp_K": 600, "pressure_bar": 30 }
AUTOAutomotive Engineering
{ "torque_Nm": 350, "radius_m": 0.33 }
Frontier · 13 domains
DEDark Energy Models
{ "redshift": 0.5, "w_eos": -1.0 }
QGQuantum Gravity
{ "mass_kg": 1e-5, "L_planck": 1e-35 }
TMTopological Matter
{ "chern_n": 1, "filling": 0.5 }
NRNeurophysics
{ "membrane_mV": -65, "cond_mS": 0.3 }
FMFractal Mechanics
{ "iterations": 1000, "scale_ratio": 0.5 }
CHChaotic Systems
{ "sigma": 10, "rho": 28 }
ECEmergent Complexity
{ "n_agents": 1000, "coupling": 0.3 }
TCTime Crystal Physics
{ "drive_Hz": 100, "amplitude": 0.5 }
NEDNon-Euclidean Dynamics
{ "curvature": -1.0, "radius": 2.5 }
XDExtra Dimensions
{ "n_extra": 2, "scale_m": 1e-15 }
CNConsciousness Studies
{ "phi": 3.2, "n_nodes": 100 }
QIQuantum Information
{ "qubits": 4, "entropy": 1.8 }
AGAnalogue Gravity
{ "flow_ms": 0.5, "sound_ms": 0.35 }

Browse the full operator library across 64 domains in the Operator Explorer ↗.

Authentication

Bearer token

All compute requests require a valid zeq_ak_ API key in the Authorization header:

Authorization: Bearer zeq_ak_…
401 Unauthorized
Missing or invalid key. Check the key value and ensure there is no extra whitespace.
429 Too Many Requests
Daily token limit reached. Upgrade your plan for more tokens.