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Operators

Operators are the framework's verbs. The kernel ships 1,500+ of them across 64 domains — every transition in the audit log carries an operator id; every contract names the operator that executes it; every wizard run picks 1–3 from the catalogue and composes them through KO42.

The full registry is in shared/api-core/src/data/operator-registry.json (816 KB, structured by category). The browseable surface is GET /api/operators (paginated) and GET /api/operators/categories.

What an operator is​

A small JSON record with a stable id, a verbatim formula, and metadata for the wizard / compute backend:

{
  "id": "NM21",
  "category": "Newtonian Mechanics",
  "name": "Newton's law of gravitation",
  "formula": "F = G m_1 m_2 / r^2",
  "domain": ["classical-mechanics", "orbital-mechanics"],
  "since": "1.0",
  "tier": "core"
}

When you call POST /api/zeq/compute with operators: ["KO42", "NM21"], the compute backend:

  1. Validates each id is in the registry (the wizard rejects unknown ids).
  2. Composes them through the master equation, with KO42 as the metric tensioner (mandatory; tier-bounds the composition at ≤0.1% error).
  3. Plugs your inputs into the closed-form, runs the numeric solver, returns a ComputedKnowledgeObject (CKO) with the result, the operator sequence, the Zeqond stamp, and a HMAC-signed proof digest.

Categories​

The catalogue is split into five meta-groups (the Operators nav surface) and 64 narrative domains (used by the wizard's domain inference):

Meta-groupExamplesApprox. count
Core PhysicsNewtonian mechanics (NM1–NM30), quantum mechanics (QM1–QM17), general relativity (GR31–GR41), thermodynamics, electrodynamics~250
Extended PhysicsField theories, fluid dynamics, plasma, optics, acoustics, condensed matter, statistical mechanics~350
Applied SciencesGenomics, pharmacokinetics, biomechanics, materials, geophysics, climate, hydrology~350
IndustryPower grid, robotics, traffic, signal processing, neural architectures, cryptography, blockchain~350
FrontierTime crystals, analogue gravity, awareness operators (ON0/QL1/TM1/TX/XI1/LZ1/CHI95/PSI96/MK1/VX/ZEQ00/ZEQ000), HULYAS forensics, ZSP/ZEQ-PROTECT, ZEQ-TETHER, ZEQ-POCKET~270

Get the live list — total reflects the live registry (1,500+ catalogued and growing); the value below is illustrative:

curl -sS https://zeqapi.com/api/operators/categories
{
  "ok": true,
  "categories": [
    { "name": "Newtonian Mechanics", "count": 30 },
    { "name": "Quantum Mechanics", "count": 17 },
    { "name": "General Relativity", "count": 11 },
    ...
  ],
  "total": 1500
}

Worked examples​

The kernel ships verbatim formulas. A few representative operators:

NM21 — Newton's law of gravitation

F = G m_1 m_2 / r^2

POST /api/zeq/compute with operators: ["KO42", "NM21"], inputs: {m1: 5.972e24, m2: 7.348e22, r: 384400e3} → returns Earth-Moon attractive force ≈ 1.982e20 N. ≤0.1% gate satisfied against CODATA G.

QM10 — Planck-Einstein relation

E = h v

operators: ["KO42", "QM10"], inputs: {frequency: 5e14} → 3.3126157e-19 J for a visible-light photon.

GR37 — Schwarzschild radius

r_s = 2 G M / c^2

operators: ["KO42", "GR37"], inputs: {M: 1.989e30} → ≈ 2954 m for the Sun. Verifiable against the 2.95-km tabulated value.

KO42.1 — Automatic metric tensioner

ds^2 = g_uv dx^u dx^v + alpha sin(2 pi 1.287 t) dt^2

Mandatory in every composition. The 1.287 Hz modulation is what holds the ≤0.1% gate.

ON0 — Awareness operator

psi_ON0 = sin(phase) + 1.1
ON0 = psi_ON0 ln(psi_ON0) - phase * f

Frontier-tier. Used in the awareness chapter and exposed through /api/zeq/awareness.

ZEQ-PROTECT-001 — Sibling-protection field

P(t) = |sin(5 phi(t))| / f_pulse

Frontier-tier. Wraps a payload in a 5-phase protection harmonic; consumed by the ZSP envelope path.

Finding the right operator​

Three paths:

  1. Browse — GET /api/operators?category=Newtonian%20Mechanics&limit=50. Each row carries id, name, formula, domain, tier.
  2. Search — the wizard's domain inference (in zeqAuthV3.ts's /zeq/wizard/compute) maps a free-form English query to a domain, then picks the canonical 1–3 operators for that domain. Open https://zeqapi.com/auth/'s wizard, type your problem, see the picks before you commit.
  3. Compose by hand — pick KO42 plus 1–3 ids from the catalogue. The 7-step protocol caps total operators at 4 per call (KO42 + 3 collaborators) so you stay within the precision gate.

The 7-step protocol limits this​

The protocol (see seven-step-protocol) puts hard rails on operator composition:

  • Step 1: KO42 is mandatory.
  • Step 2: 1–3 additional operators (total ≤ 4).
  • Step 3: match operators to the domain.
  • Step 4: tune to ≤0.1% error (the precision imperative).

If you try to compose 17 quantum operators with one Newtonian, the wizard rejects: cross-domain composition without an explicit bridge breaks the precision gate. The operator catalogue is enormous because the domains are diverse, not because any one call uses many.

Adding your own​

The operator registry is open. Pull-requests against shared/api-core/src/data/operator-registry.json follow this contract:

  1. New id in a sequential prefix (e.g. IND552 for Industry-meta-group operator 552).
  2. Verbatim formula in plain ASCII (no LaTeX in the registry — render at the consumer).
  3. Domain tags drawn from the existing 64-domain list.
  4. A test case in shared/api-core/src/__tests__/operatorRegistry.test.ts that pins the ≤0.1% gate against a published reference.

The full contributor guide is at /ship/contributing/.

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