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What is Zeq

Zeq is three things in one package:

  1. A timebase. The HulyaPulse — exactly 1.287 Hz. Every computation happens on this clock. The Zeqond (0.777 s) is its period, and every operator completes within a Zeqond or is preempted. This is the one opinion the framework imposes on physics.
  2. A mathematics library. 42+ kinematic operators spanning quantum mechanics, Newtonian mechanics, general relativity, computer science, and awareness modeling. They compose through the HULYAS master equation and a single metric tensioner (KO42) bounds every composition at ≤0.1% error.
  3. A protocol registry. 235 named, versioned protocols — each a named formula — that let you compute over real-world problems without deriving the math yourself. You call sdk.run("zeq-propagation", params) and get a verified CKO back.

Why a timebase?​

Most numerical systems inherit time from whatever host they run on — Unix seconds, CPU ticks, framework loops. This is fine for simple work and fragile when you compose operators from different domains at different scales. A general-relativity operator measures proper time; a quantum-mechanics operator advances by ℏ-scaled phase; a signal-processing operator samples at some arbitrary rate. They don't agree unless you force them to.

Zeq forces them to agree on the HulyaPulse. Every operator is evaluated once per Zeqond. The temporal bridge operator ZTB1 converts between Unix and Zeqond losslessly:

ZTB1(t, from, to) = (t × conv_factor) + phase_offset
  Unix → Zeq:  conv_factor = 1 / 0.777
  Zeq → Unix:  conv_factor = 0.777

The synchronization equation:

t_Zeq = t_Unix / T_Z + phi_epoch
phi_current = ((t_Unix mod T_Z) / T_Z) × 2 pi
T_Z = 0.777 s

This is how every protocol in the registry is kept phase-locked to the kernel.

The math in one page​

The master equation:

Box phi  minus  mu^2(r) phi  minus  lambda phi^3  minus  e^(-phi/phi_c)
   plus  phi_42 × Sum_{k=1..42} C_k(phi)
   =  T^mu_mu  plus  beta F_{mu nu} F^{mu nu}  plus  J_ext

Read left-to-right: wave operator on the field, position-dependent mass, nonlinear self-interaction, decay term, direct coupling to all 42 operators. Right-hand side: stress-energy trace, electromagnetic coupling, external forcing. This is the equation every protocol reduces to before executing.

The Zeq equation (proper-time modulation):

R(t) = S(t) × [ 1 + alpha × sin(2 pi f t + phi_0) ]
  alpha approx 1.29e-3,   f = 1.287 Hz

Averaged over one Zeqond, R(t) recovers S(t) exactly. This is the compatibility proof with classical results — Zeq does not change what is true, it changes how we stabilize the computation of it.

The KO42 metric tensioner:

KO42.1 (automatic):  ds^2 = g_{mu nu} dx^mu dx^nu + alpha sin(2 pi × 1.287 t) dt^2
KO42.2 (manual):     ds^2 = g_{mu nu} dx^mu dx^nu + beta  sin(2 pi × 1.287 t) dt^2

This enforces the ≤0.1% error bound. Any composition that would break the bound is either tightened (by KO42.1) or returned with an explicit over-band marker.

The 7-step wizard protocol​

Every computation in Zeq goes through this. The SDK does it for you; the process is:

  1. Prime directive — KO42 is mandatory. Always.
  2. Operator limit — 1 to 3 operators plus KO42. Max 4 per call.
  3. Scale principle — match operators to problem domain.
  4. Precision imperative — tune to ≤0.1%.
  5. Compile via master equation.
  6. Execute via functional equation E = P_phi × Z(M, R, delta, C, X).
  7. Verify & troubleshoot — CKO output includes provenance.

Most SDK calls follow exactly this sequence. When you write sdk.run(protocol, params), steps 1 through 7 happen on the server, and the CKO you receive includes a verification signature.

Who this is for​

If you build anything that composes math from more than one domain, Zeq saves you work. Typical use cases:

  • Physics simulators — wind tunnels, fluid dynamics, thermodynamics, electromagnetism.
  • Science applications — medical imaging, pharmacokinetics, genomics analysis, forensic tools.
  • Engineering — structural analysis, seismic modeling, aerospace re-entry modeling.
  • Crypto & messaging — the ZEQ-PROTECT family and ZEQ-TETHER-003 power Zeq Message, Zeq Mail, and zeq-vault.
  • ML and signal work — signal classifiers, neural architectures, RL playgrounds.

If you're doing arithmetic on numbers that don't need phase-locked composition, Zeq is overkill — use NumPy.