Five Protocols.
One Field.

ZFK is the foundation of the ZeqField cryptographic layer. It derives a 256-bit encryption key from the HULYAS framework constants — the HulyaPulse frequency (1.287 Hz), Zeqond interval (0.777 s), coupling constant α, and operator count — combined with the ZEQ_FIELD_KEY environment secret via PBKDF2-SHA256 at 200,000 iterations. The derived key encrypts all PII in the Zeq.dev system using AES-256-GCM authenticated encryption. Without ZEQ_FIELD_KEY, ZFK falls back to a DATABASE_URL-derived key — functional but weaker.

# Requires admin authentication cookie
curl https://www.zeqsdk.com/api/admin/zeqfield/status \
  -H "Cookie: zeq_admin_token=<token>"

ZeqPulse exposes the live state of the HulyaSync master clock. The public endpoint returns a single snapshot: the current Zeqond index τ, phase φ within the active Zeqond, and the instantaneous R(t) value. The authenticated SSE stream delivers a new pulse tick every 777 ms — one per Zeqond — allowing agents to synchronise operations, replay computations deterministically, or detect temporal drift. The Zeqond is a monotonically-increasing integer counter; two calls at the same Zeqond will return identical phase and R(t) values.

curl https://www.zeqsdk.com/api/zeq/pulse

{
  "protocol": "ZeqPulse",
  "zeqond": 2941083127,            // τ — current Zeqond index
  "phase": 0.3214,               // φ ∈ [0,1] within this Zeqond
  "R_t": 1.000412,               // HulyaPulse modulation value
  "pulseHz": 1.287,
  "zeqondSec": 0.777,
  "alpha": 0.00129,
  "precision": 0.000412,
  "timestamp": "2026-03-27T14:22:08.123Z",
  "modulation": "R(t) = [1 + α·sin(2π·f·t)]  where f=1.287 Hz, α=0.00129"
}

curl -N https://www.zeqsdk.com/api/zeq/pulse/stream \
  -H "Authorization: Bearer $ZEQ_API_KEY"

# Returns one event every 777 ms:
data: {"zeqond":2941083127,"phase":0.0012,"R_t":1.000013,"pulseHz":1.287,...}

data: {"zeqond":2941083128,"phase":0.0015,"R_t":1.000891,"pulseHz":1.287,...}

For low-latency applications requiring bidirectional communication, ZEQ exposes a WebSocket endpoint at wss://www.zeqsdk.com/api/zeq/ws. Once connected, clients send JSON compute requests and receive streamed ZeqState responses synchronised to the 1.287 Hz HulyaPulse. The connection stays open, eliminating HTTP handshake overhead on repeated calls. Authentication is sent as the first message after open — the server closes the socket with code 4401 if no valid zeq_ak_ key is received within 5 seconds.

const ws = new WebSocket('wss://www.zeqsdk.com/api/zeq/ws');

ws.addEventListener('open', () => {
  // Authenticate immediately after connection open
  ws.send(JSON.stringify({ type: 'auth', token: process.env.ZEQ_API_KEY }));
});

ws.addEventListener('message', (event) => {
  const msg = JSON.parse(event.data);
  if (msg.type === 'auth_ok') {
    // Now send a compute request
    ws.send(JSON.stringify({
      type:      'compute',
      domain:    'quantum_mechanics',
      operators: ['KO42'],
      inputs:    { E: 13.6, m: 9.11e-31 }
    }));
  }
  if (msg.type === 'result') {
    console.log('R(t):', msg.zeqState.masterSum);
    console.log('Precision:', msg.zeqState.precision); // always ≤ 0.001
  }
});

Every response from POST /api/zeq/compute now includes a zeqProof field — a 64-character hex HMAC-SHA256 digest that seals the computation result. The proof covers the operator IDs, R(t) value, Zeqond counter, and the first 8 characters of the calling user's ID. Any mutation to these values — even a single bit flip — produces a completely different HMAC, immediately detectable by calling POST /api/zeq/verify. ZeqProof provides the chain-of-custody attestation layer that makes Zeq.dev results auditable and verifiable by third parties.

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":{"E":13.6}}'

# Response includes zeqProof:
{
  "zeqState": { "operators": ["KO42", "QM01"], "masterSum": 1.000514, ... },
  "zeqProof": "a3f8c2e1d4b7a9f2c5e8d1b4a7f0c3e6d9b2a5f8c1e4d7b0a3f6c9e2d5b8a1f4"
}

curl -X POST https://www.zeqsdk.com/api/zeq/verify \
  -H "Authorization: Bearer $ZEQ_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "proof": "a3f8c2e1d4b7a9f2c5e8d1b4a7f0c3e6d9b2a5f8c1e4d7b0a3f6c9e2d5b8a1f4",
    "operatorIds": ["KO42", "QM01"],
    "R_t": 1.000514,
    "zeqond": 2941083127
  }'

{
  "protocol": "ZeqProof",
  "valid": true,
  "zeqond": 2941083127,
  "R_t": 1.000514,
  "operatorIds": ["KO42", "QM01"],
  "verifiedAt": "2026-03-27T14:22:09.000Z"
}

A ZeqLattice is a coherence grid of 2–5 computation nodes that share the same base Zeqond but operate at staggered HulyaPulse phases — each node offset by Δᵢ = i·τ/N from the base time. This models distributed physics computations where multiple agents must operate in phase-coordinated synchrony. The coherenceScore (0–1) measures how tightly the lattice nodes track each other: 1.0 = perfect synchronisation, 0.0 = complete phase divergence. The lattice equation describes the mean R(t) across all nodes.

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 } },
      { "domain": "thermodynamics",    "inputs": { "T": 300 } },
      { "domain": "fluid_dynamics",    "inputs": { "v": 1.5 } },
      { "domain": "electromagnetism",  "inputs": { "B": 0.5 } }
    ]
  }'

{
  "protocol": "ZeqLattice",
  "nodeCount": 4,
  "sharedZeqond": 2941083127,
  "coherenceScore": 0.999812,  // 1.0 = perfect sync
  "latticeEquation": "L(t) = (1/4) Σᵢ Rᵢ(t+Δᵢ)  Δᵢ=i·τ/4  coherence=0.9998",
  "callsConsumed": 4,
  "latticeNodes": [
    { "node": 1, "domain": "Quantum Mechanics", "zeqond": 2941083127, "phase": 0.1234, "R_t": 7.004823, "operator": "QM01" },
    { "node": 2, "domain": "Thermodynamics",    "zeqond": 2941083127, "phase": 0.3734, "R_t": 1.000312, "operator": "TH01" },
    { "node": 3, "domain": "Fluid Dynamics",    "zeqond": 2941083127, "phase": 0.6234, "R_t": 1.000379, "operator": "FD01" },
    { "node": 4, "domain": "Electromagnetism",  "zeqond": 2941083127, "phase": 0.8734, "R_t": 1.000451, "operator": "EM01" }
  ],
  "pulseHz": 1.287,
  "computedAt": "2026-03-27T14:22:10.000Z"
}

ZeqShift projects the R(t) value forward through time, one Zeqond step (0.777 s) at a time, for up to 64 steps. Because R(t) is deterministic and phase-locked to HulyaPulse, ZeqShift produces exact future values — not approximations. Each step returns the future Zeqond index, phase φ, and R_t. The summary includes min, max, and mean R_t across the full projection window. ZeqShift is the temporal forecasting layer of the Zeq.dev framework, enabling agents to predict the exact phase state of any future computation before committing to it.

curl -X POST https://www.zeqsdk.com/api/zeq/shift \
  -H "Authorization: Bearer $ZEQ_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "steps": 8,
    "domain": "thermodynamics",
    "inputs": { "temp_K": 500, "pressure_Pa": 101325 }
  }'

{
  "protocol": "ZeqShift",
  "domain": "Thermodynamics",
  "baseZeqond": 2941083127,
  "stepCount": 8,
  "callsConsumed": 8,  // equals stepCount
  "S_t": 50712.5,
  "summary": { "minRt": 50645.891, "maxRt": 50779.108, "meanRt": 50712.499 },
  "projection": [
    { "step": 0, "t": 1743084130.2, "zeqond": 2941083127, "phase": 0.3214, "R_t": 50712.500, "delta": 0 },
    { "step": 1, "t": 1743084130.977, "zeqond": 2941083128, "phase": 0.3214, "R_t": 50753.891, "delta": 41.391 },
    { "step": 2, "t": 1743084131.754, "zeqond": 2941083129, "phase": 0.3214, "R_t": 50779.108, "delta": 25.217 },
    // ... 5 more steps
  ],
  "equation": "R_t(step) = S(t) × [1 + α·sin(2π·f·(t₀ + step·τ))]",
  "computedAt": "2026-03-27T14:22:11.000Z"
}