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Compute — the mathematics

This section opens the box. Not just what to call, but what the CPU does with it: how a request becomes a float64 number, how operators combine, exactly which categories compute their own physics and which fall back to numerical integration, and why every result is checkable. Every worked example in here is from a real call you can reproduce.

Start with the three that demystify the engine:

  • How a compute runs — the execution model — one real request traced end to end on the CPU: parse → resolve → bind → validate → the actual arithmetic → verify → stamp → sign, with the real numbers each step produced.
  • How equations combine — the ground state, the KO42 carrier, the per-term master sum, and why the physics value stays separate from the clock stamp.
  • What computes what — the coverage model — how 1,606 operators are served: dedicated closed-form solvers for the physics domains, a universal numerical engine for the rest. Every result real, deterministic, and method-disclosed. No black box.

Then the mechanics in depth:

  • The pipeline — the seven steps every query runs: SELECT → BIND → VALIDATE → COMPUTE → VERIFY → PULSE → RETURN.
  • The seven-step protocol — the same seven steps as a builder's contract: what each step guarantees you.
  • The solvers — the dedicated closed-form solvers over CODATA constants and the RK4 ODE fallback.
  • The master equation — the HULYAS field equation integrated (RK4) when no closed form exists, term by term.
  • The functional equation — the E = P_φ·Z reduction.
  • Operators — the vocabulary: the 42+ bootstrap set, the full catalogue, type safety, and composition.
  • The Kinematic Spectrum — every operator domain in one view: the periodic table of the 1,600+ operators across 65 domains.
  • The honesty contract — compute, ask, or refuse: the machine never fabricates.
  • Equation study — the hypothesis stamp: generated equations are labelled hypotheses, never dressed up as discoveries.
  • Compression — the .zeqc archive: Zstd, Zeqond-stamped, integrity-verified, with entropy forensics.
  • Operator modules — the per-operator time-driven surface.

The full operator catalogue lives in the reference.