The 7-step Wizard protocol

Every non-trivial computation on the framework runs through this protocol. The runSevenStepWizard function in shared/api-core/src/lib/zeqWizard.ts is the canonical implementation; POST /api/zeq/wizard/compute is the wire-level entry point. The protocol is verbatim from the Zeq kernel:

1. Prime Directive — KO42 is mandatory

The metric tensioner is the substrate, not optional flavor. Every operator sequence starts with KO42. The 1.287 Hz modulation it adds:

ds^2 = g_uv dx^u dx^v + alpha sin(2 pi 1.287 t) dt^2
alpha = 1.29e-3   (published symbolic value)

is what holds the ≤0.1% precision gate across the heterogeneous operator catalogue.

alpha = 1.29×10⁻³ is the published symbolic coefficient from the Zeq paper. The runtime coefficient is ALPHA_K = 1×10⁻³ — the value that bounds the modulation to 0.1% by construction. The two share a name but are distinct; see Constants → display vs runtime for the full split.

2. Operator Limit — 1–3 additional + KO42 (total ≤ 4)

Do not over-couple. Pick the minimum kinematic operators that close the problem. Five is too many; four is the cap; three is the sweet spot. The compute backend rejects chains of length 5+ without an explicit bridge contract.

3. Scale Principle — match operators to domain

Page work uses visual/UX operators. Math claims use QM/NM/GR operators. Don't apply quantum operators to a CSS bug. The wizard's domain inference in zeqAuthV3.ts:

"orbit"|"planet"|"gravity"     → orbital-mechanics
"wave"|"ocean"|"tide"          → oceanography
"spring"|"mass"|"newton"       → Newtonian Mechanics
"gene"|"dna"|"protein"         → genomics
"material"|"steel"|"stress"    → materials-science
default                        → quantum-mechanics

is one keyword pass. For programmatic users, set domain explicitly in the request body.

4. Precision Imperative — tune to ≤0.1% error

Every numeric claim from a wizard run must verify against the precision field in the response. If precision > 0.001, the run fails the gate and the result is annotated with degraded: true. Callers should refuse to ship a degraded result.

The framework's tolerance is the same one this site lives by — every constant is bit-exact, every equation verbatim.

5. Compile — synthesize the master equation

The response carries a masterEquation block: the domain's closed form written out against your named inputs, with the KO42 bounded-modulation carrier shown alongside it. For the Sun-Earth run below it reads Ψ(m1, m2, r) ≡ F = G·m₁·m₂/r² ← [NM21], with R(t) = S₀·[1 + α_K·sin(2π·f_H·t)], α_K = 10⁻³. That is what "compile" produces: a synthesized, human-readable statement of the exact formula the run evaluates — not a symbolic substitution into a field PDE.

When you compose KO42 + 1–3 collaborators, the kernel:

Looks up each id in the registry and identifies its physical domain.
Selects the dedicated closed-form solver for that domain.
Evaluates the solver against your inputs; KO42 supplies the bounded R(t) carrier (the |R−1| ≤ α_K amplitude bound).
Returns a closed-form value plus a numeric residual and a signed envelope.

The operator ids annotate the physics — in the response's master_sum the domain operator is tagged "symbolic — applied to inputs by domain solver" with no scalar contribution of its own. The evaluation is a closed form, not a plug-in sum of operator terms.

The broader HULYAS notation — □ϕ − μ²(r)ϕ − λϕ³ − e^{−ϕ/ϕc} + ϕ₄₂·Σ C_k(ϕ) = T^μ_μ + βF² + J_ext — is the framework's organising notation for the ϕ⁴ field (see learn/math/master-equation). The Σ C_k(ϕ) coupling is a research direction, not a running mechanism: no C_k(ϕ) is evaluated at compute time, and protocols do not reduce to this equation before executing. They call the domain solver.

6. Execute via Functional Equation

On the dynamical solve() / multibody() path, the run is reduced to the functional equation scalar:

E = P_phi * Z(M, R, delta, C, X)

where P_phi = √mean((dφ/dt)²) is the RMS field momentum over the trajectory, and Z = M · R · (1+C) · (1+X) · exp(−δ·t) folds the run's mass, scale radius, operator-coupling sum C, external forcing X and damping δ into one factor. It is returned as functionalEnergy — a compact, additive signature of the run, a diagnostic that never alters the conserved physics energy.

This is also where you observe the wire fields — pulseHz: 1.287, phase: 0.412, precision: 0.00071 — the runtime stamping the result at this Zeqond.

Register dump — the structured output of step 6

When you call the master-equation path directly via POST /api/solve or POST /api/multibody, the runtime returns a register dump alongside the trajectory — the spec's name for the closed set of derived quantities the functional equation produces:

{
  "registerDump": {
    "phi_final": ..., "phi_range": ..., "phi_mean": ..., "phi_rms": ...,
    "dphi_final": ..., "dphi_rms": ...,
    "zeroCrossings": ..., "period_s": ..., "frequency_Hz": ...,
    "freq_ratio_fH": ...,                      // frequency / 1.287 Hz
    "energy_K_mean":  ...,                     // mean ½·m·dφ²
    "energy_U_mean":  ...,                     // mean ½·m·φ²
    "energy_total_mean": ...,                  // K + U
    "momentum_final":   ...,                   // m · dφ_final
    "angular_proxy_mean": ...                  // mean(m·φ·dφ), scalar L analogue
  },
  "functionalEnergy": ...,                     // = P_φ · Z
  "functionalEnergyTerms": { "P_phi": ..., "Z": ..., "M": ..., "R": ..., "delta": ..., "C": ..., "X": ... }
}

For multi-body runs, every body gets its own registerDump, and the response includes a pairwise interactions array with mean / final force magnitudes and separations for every pair.

The register dump is what step 7 verifies against. Two paths exist deliberately:

Path	Returns	Use when
`/api/zeq/compute` (wizard)	textbook closed-form value + zeqProof	you want a single SI-tagged number for a named formula
`/api/solve`	full trajectory + register dump + functional energy	you want the master-equation runtime output, not a formula lookup

7. Verify and Troubleshoot

Diff-check the result. Screenshot-check the live behavior. Sign-off only after the precision gate passes.

For programmatic users:

curl -sS __ZEQ_BASE_URL__/api/zeq/verify \
  -H "Authorization: Bearer ${ZSM_KEY}" \
  -H "Content-Type: application/json" \
  -d '{"zeqProof": "...", "operators": ["KO42","NM21"], "R_t": 1.998e20, "zeqond": 2287439210}'

verifies an already-issued proof. The verifier uses crypto.timingSafeEqual over the HMAC, so even a wrong-by-one-bit proof returns valid: false in constant time.

Worked example: Sun-Earth gravity

A canonical 7-step run — pick the operators, compose, verify.

Step 1. KO42 mandatory.

Step 2. One additional operator: NM21 (Newton's law of gravitation, F = G m_1 m_2 / r^2).

Step 3. Domain Newtonian Mechanics. Match.

Step 4. Target ≤0.1% error against the CODATA G = 6.67430e-11 m^3 kg^-1 s^-2.

Step 5. Compile:

curl -sS __ZEQ_BASE_URL__/api/zeq/compute \
  -H "Authorization: Bearer ${ZSM_KEY}" \
  -H "Content-Type: application/json" \
  -d '{
    "operators": ["KO42", "NM21"],
    "domain": "Newtonian Mechanics",
    "inputs": {
      "m1": 1.989e30,
      "m2": 5.972e24,
      "r":  1.496e11
    }
  }'

Step 6. Execute. Response (truncated — the stamp fields live under zeqState):

{
  "value": 3.5423961e22,
  "unit": "N",
  "uncertainty": 3.5423961e18,
  "operator_id": "KO42",
  "zeqState": {
    "operators": ["KO42", "NM21"],
    "domain": "Newtonian Mechanics",
    "phase": 0.8533,
    "zeqond": 2294819873,
    "pulseHz": 1.287,
    "precision": 0.000222,
    "precisionActual": 0.0001
  },
  "zeqProof": "cac8da...64hex",
  "signed": { "alg": "ed25519", "public_key": "…", "claim": { … }, "signature": "…" }
}

value: 3.5423961e22 N against the published Sun-Earth gravitational force of ~3.542 × 10²² N — the bare physics value (the R(t) carrier is bookkeeping, it does not multiply the result). precisionActual: 0.0001 is the numeric residual, well within the 0.001 gate.

Step 7. Verify:

curl -sS __ZEQ_BASE_URL__/api/zeq/verify \
  -H "Authorization: Bearer ${ZSM_KEY}" \
  -H "Content-Type: application/json" \
  -d '{"zeqProof": "8a34...", "operators": ["KO42","NM21"], "R_t": 3.5423961e22, "zeqond": 2287439210}'

{ "ok": true, "valid": true, "zeqond": 2296532592 }

Done.

When the protocol rejects you

Rejection	Cause	Fix
`MISSING_KO42`	step 1 violated; chain doesn't start with KO42	prepend `"KO42"`
`OPERATOR_LIMIT_EXCEEDED`	step 2 violated; chain length > 4	drop to ≤3 collaborators
`DOMAIN_MISMATCH`	step 3 violated; operator's domain doesn't include the requested domain	swap operator or domain
`PRECISION_BAD`	step 4 violated; numeric residual > 0.001	tighten input units, reduce composition, or accept `degraded: true` and document
`INVALID_OPERATOR`	step 5 violated; an id isn't in the registry	use `/api/operators` to find a valid one
`WIZARD_ERROR`	step 6 internal failure	check `/api/health`, retry; report `security@zeq.dev` if persistent
`VERIFY_FAILED`	step 7 verification mismatch	the proof or one of `(operators, R_t, zeqond)` was tampered

Operator catalogue — Operators
The master equation — learn/math/master-equation
KO42 — learn/math/ko42
Wire-level wizard endpoint — /api/zeq/ (POST /api/zeq/wizard/compute)

1. Prime Directive — KO42 is mandatory​

2. Operator Limit — 1–3 additional + KO42 (total ≤ 4)​

3. Scale Principle — match operators to domain​

4. Precision Imperative — tune to ≤0.1% error​

5. Compile — synthesize the master equation​

6. Execute via Functional Equation​

Register dump — the structured output of step 6​

7. Verify and Troubleshoot​

Worked example: Sun-Earth gravity​

When the protocol rejects you​

Next​