The Kinematic Spectrum of Motion

Zeq OS ships with 1,576 physics operators across 64 categories. The core 42 — called the Kinematic Spectrum of Motion — form the mathematical foundation that every computation builds on.

All operators are accessible via the REST API (GET /api/zeq/operators). Unauthenticated requests return operator metadata (id, name, description, category); authenticated requests additionally include equations.

# List all operators (no auth required)
curl https://your-instance/api/zeq/operators

# Get a specific operator
curl https://your-instance/api/zeq/operators/QM1

# Execute an operator (auth required)
curl -X POST https://your-instance/api/zeq/operators/execute \
  -H "Authorization: Bearer <token>" \
  -d '{"operatorId":"QM1","params":{"hbar":1.054571817e-34}}'

---

Quantum Mechanics (QM1–QM17)

17 operators covering wave mechanics, quantum states, and particle physics.

ID	Description	Category
QM1	Time-dependent Schrödinger equation — quantum state evolution under a Hamiltonian	quantum
QM2	Time-independent Schrödinger equation — stationary quantum states and energy eigenvalues	quantum
QM3	De Broglie wavelength — matter wave relationship λ = h/p	quantum
QM4	Heisenberg uncertainty principle — ΔxΔp ≥ ℏ/2	quantum
QM5	Planck energy quantization — E = hν	quantum
QM6	Bohr hydrogen energy levels — E_n = −13.6/n² eV	quantum
QM7	Quantum tunneling probability — exponential decay through a potential barrier	quantum
QM8	Particle-in-a-box energy levels — E_n = n²π²ℏ²/2mL²	quantum
QM9	Quantum harmonic oscillator — E_n = (n + ½)ℏω	quantum
QM10	Photon energy — E = hν	quantum
QM11	Compton wavelength shift — Δλ = (h/mc)(1 − cosθ)	quantum
QM12	Spin angular momentum — S = ℏ√(s(s+1))	quantum
QM13	Probability density —	ψ
QM14	Dirac equation — relativistic quantum field equation	quantum
QM15	Path integral formulation — quantum amplitude summation	quantum
QM16	Quantum entanglement correlations — Bell inequality parameter	quantum
QM17	Wavefunction collapse — measurement postulate	quantum

---

Newtonian Mechanics (NM18–NM30)

13 operators covering classical mechanics, forces, and energy.

ID	Description	Category
NM18	Newton's second law — F = ma	newtonian
NM19	Gravitational force — F = Gm₁m₂/r²	newtonian
NM20	Kinetic energy — KE = ½mv²	newtonian
NM21	Gravitational force (extended) — full Newtonian gravity with constants	newtonian
NM22	Work-energy theorem — W = ΔKE	newtonian
NM23	Conservation of momentum — Σp = const	newtonian
NM24	Elastic collision velocities	newtonian
NM25	Spring force — F = −kx (Hooke's Law)	newtonian
NM26	Simple harmonic motion — x(t) = A cos(ωt + φ)	newtonian
NM27	Centripetal acceleration — a = v²/r	newtonian
NM28	Angular momentum — L = Iω	newtonian
NM29	Torque — τ = r × F	newtonian
NM30	Power — P = F · v	newtonian

---

General Relativity (GR31–GR41)

11 operators covering spacetime curvature, relativistic effects, and gravitational waves.

ID	Description	Category
GR31	Schwarzschild metric — spacetime geometry around a non-rotating mass	relativity
GR32	Gravitational time dilation — Δt' = Δt√(1 − 2GM/rc²)	relativity
GR33	Gravitational redshift — z = GM/rc²	relativity
GR34	Lorentz time dilation — Δt' = γΔt	relativity
GR35	Lorentz length contraction — L' = L/γ	relativity
GR36	Relativistic mass-energy — E = mc²	relativity
GR37	Schwarzschild radius — r_s = 2GM/c²	relativity
GR38	Geodesic equation — shortest path in curved spacetime	relativity
GR39	Einstein field equations — G_μν = 8πT_μν	relativity
GR40	Gravitational wave frequency — f_gw = 2f_orbital	relativity
GR41	Perihelion precession — Δφ = 6πGM/c²a(1−e²)	relativity

---

KO42 — The Master Equation

KO42 is mandatory in every computation. It is the HulyaPulse fundamental wavefunction — the universal synchronization anchor that ties all other operators to the 1.287 Hz temporal heartbeat.

ID	Description	Category
KO42	Zeq fundamental wavefunction — HulyaPulse modulation at 1.287 Hz	kinematic

Every computation passes through KO42. It modulates all results with the function:

R(t) = S(t) × [1 + α × sin(2π × 1.287 × t)]

Where:

• S(t) is the standard physics value from the domain operator
• α = 0.00129 is the modulation depth
• Averaging over one Zeqond (0.777 s) recovers the exact standard value

---

Full Registry (1,576 Operators)

The complete registry spans 64 categories from core physics to industry verticals. Access it via the API:

# All 1,576 operators (metadata only, no auth required)
GET /api/zeq/operators

# Filter by category
GET /api/zeq/operators?category=quantum

# Single operator by ID
GET /api/zeq/operators/QM1

# Execute with authenticated token
POST /api/zeq/operators/execute
Authorization: Bearer <token>
{"operatorId": "NM21", "params": {"G": 6.674e-11, "m1": 5.972e24, "m2": 7.342e22, "r": 3.844e8}}

Categories include: quantum, newtonian, relativity, kinematic, thermodynamics, electromagnetism, fluid_dynamics, optics, nuclear, signal_processing, aerospace, medical, finance, biotech, neuroscience, and 49 more.

Register at /api/users/register with your equation-based identity to unlock equation details and execution rights.