The Seven-Step Wizard Protocol

The Seven-Step Wizard Protocol is the mandatory sequence that every computation in Zeq must follow. It is enforced by the API, audited by compliance systems, and is the only approved method for requesting computations.

warning

Every API call to execute a computation internally follows these seven steps. Deviation from this protocol is not permitted and will result in an error.

The Seven Steps

Step 1: PRIME DIRECTIVE — KO42 IS MANDATORY

Action: Verify that KO42 is included in the computation request.

Enforcement:

• If the request does not mention KO42, it is automatically added.
• If the request explicitly tries to exclude KO42, the API rejects the request with a 403 Forbidden error.
• KO42 is not optional at any tier.

Example Valid Request:

curl -X POST https://zeq.dev/api/zeq/compute \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "operators": ["QM1", "KO42"],
    "parameters": {...}
  }'

Example Invalid Request (Rejected):

curl -X POST https://zeq.dev/api/zeq/compute \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "operators": ["QM1"],
    "exclude_ko42": true
  }'

Response:

{
  "error": "STEP_1_FAILED",
  "message": "KO42 is mandatory and cannot be excluded.",
  "status": 403
}

Step 2: OPERATOR LIMIT — 1-3 Additional + KO42 (≤4 Total)

Action: Validate that the number of operators does not exceed tier limits.

Limits by Tier:

Tier	Total Operator Count	KO42	Additional	Validation
Free	≤ 4	✓ (always)	≤ 3	Hard limit; requests with >3 additional are rejected
Starter	≤ 5	✓ (always)	≤ 4	Hard limit; requests with >4 additional are rejected
Builder	≤ 7	✓ (always)	≤ 6	Hard limit; requests with >6 additional are rejected
Advanced	≤ 10	✓ (always)	≤ 9	Hard limit; requests with >9 additional are rejected
Architect	Unlimited	✓ (always)	Unlimited	No hard limit

Example (Free Tier):

Valid (3 additional + KO42 = 4 total):

{
  "operators": ["QM1", "NM19", "CS43", "KO42"]
}

Invalid (4 additional + KO42 = 5 total):

{
  "operators": ["QM1", "NM19", "CS43", "EM7", "KO42"]
}

Response (Free Tier, 5 operators requested):

{
  "error": "STEP_2_FAILED",
  "message": "Free tier allows max 4 total operators (including KO42). Requested 5.",
  "tier": "free",
  "max_allowed": 4,
  "requested": 5,
  "status": 429
}

Step 3: SCALE PRINCIPLE — Match Operators to Domain

Action: Verify that selected operators are compatible and belong to appropriate domains.

Validation Rules:

• Operators from the same domain (e.g., EM7 and EM8, both electromagnetics) must be marked as compatible.
• Operators from unrelated domains (e.g., QM and GR, quantum mechanics and general relativity) are allowed only for semi-classical systems.
• The solver will reject incompatible combinations and suggest alternatives.

Example Valid Combination:

{
  "operators": ["QM1", "EM7"]
}

Comment: QM1 (quantum mechanics) + EM7 (electromagnetics) is valid—this is the semi-classical picture of atoms in fields.

Example Invalid Combination:

{
  "operators": ["EM7", "EM8"]
}

Response:

{
  "error": "STEP_3_FAILED",
  "message": "Operators EM7 and EM8 are mutually exclusive. Cannot use both in same computation.",
  "recommendations": [
    "Use EM7 for low-frequency electromagnetic phenomena.",
    "Use EM8 for high-frequency/quantum electromagnetic phenomena."
  ],
  "status": 400
}

Step 4: PRECISION IMPERATIVE — Tune to ≤0.1% Error

Action: Verify or set error tolerance and precision parameters.

Parameters:

• Relative error threshold: Maximum allowable relative error in the result (default: 1e-3 = 0.1%)
• Absolute error threshold: Maximum allowable absolute error (domain-specific)
• Convergence criterion: Solver stops when error is below these thresholds

Tuning via Request:

curl -X POST https://zeq.dev/api/zeq/compute \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "operators": ["QM1"],
    "parameters": {...},
    "precision": {
      "relative_error_tolerance": 0.001,
      "absolute_error_tolerance": 1e-8,
      "max_iterations": 10000
    }
  }'

Response:

{
  "precision_validated": true,
  "requested_tolerance": 0.001,
  "estimated_convergence_time_ms": 45.3,
  "estimated_iterations": 273,
  "note": "Tighter tolerance (< 0.001) may require longer computation time."
}

Auto-Tuning: If you omit the precision block, Step 4 auto-tunes based on the domain:

• Quantum Mechanics: 0.01% (0.0001) — tight, as quantum results are sensitive
• Classical Mechanics: 0.1% (0.001) — looser, classical systems are robust
• Complexity Science: 1% (0.01) — looser, complexity measures are coarse-grained

Step 5: COMPILE via Master Equation

Action: Translate operators and parameters into the HULYAS Master Equation.

What Happens Internally:

• The solver maps each operator to its domain-specific coupling constants C_k(ϕ).
• The master equation is assembled with the correct boundary conditions.
• The KO42-modified metric is applied.
• The solver checks that all parameters are consistent.

Example (Transparent to User):

Request:

{
  "operators": ["QM1"],
  "parameters": {"energy_level": 3}
}

Internally compiled to:

Master Equation with:
- Wave operator: □ϕ in KO42 metric
- Operator coupling: C_1, C_2, C_3, C_4 from QM1 [energy_level=3]
- Boundary conditions: ψ(∞) → 0, normalization = 1

Response (on error):

{
  "error": "STEP_5_FAILED",
  "message": "Compilation failed: Parameter 'energy_level' must be an integer between 1 and 50.",
  "status": 400
}

Step 6: EXECUTE via Functional Equation

Action: Numerically solve the compiled master equation using Runge-Kutta integration.

What Happens:

• Time-stepping from t=0 to t=T_final (or to steady-state equilibrium)
• Spatial discretization (finite difference or spectral methods)
• Adaptive step size control to maintain precision
• Phase locking to HulyaPulse at each step

Response (Partial, Headers):

HTTP/1.1 200 OK
Content-Type: application/json
X-Computation-Zeqond: 2245831.445
X-Computation-Duration-Ms: 47.2
X-Solver-Method: Runge-Kutta 4th Order
X-Iterations: 273

Response (Body):

{
  "result": {
    "value": 8.472194128,
    "modulated_value": 8.471076453,
    "unit": "joules"
  },
  "metadata": {
    "zeqond_timestamp": 2245831.445,
    "solver_time_ms": 47.2,
    "iterations": 273,
    "final_error": 0.00087,
    "convergence_status": "SUCCESS"
  }
}

Step 7: VERIFY & TROUBLESHOOT

Action: Validate the result and generate a ZeqProof.

Validation Checks:

• Is the result physically reasonable? (e.g., energy is positive, probabilities sum to 1)
• Does the result satisfy conservation laws? (energy, momentum, charge)
• Does the modulation factor fall within expected range?
• Is the phase consistent with current HulyaPulse state?

Response (Success):

{
  "verification": {
    "status": "VERIFIED",
    "checks": {
      "physical_plausibility": "PASS",
      "conservation_laws": "PASS",
      "modulation_factor_range": "PASS [0.9996 to 1.0004]",
      "phase_consistency": "PASS"
    }
  },
  "zeqproof": {
    "proof": "hmac_sha256_hex_..._64_characters...",
    "algorithm": "HMAC-SHA256",
    "payload": {
      "zeqond_timestamp": 2245831.445,
      "operators": ["QM1"],
      "result_value": 8.472194128,
      "modulation_factor": 0.9998676
    }
  }
}

Response (With Warnings):

{
  "verification": {
    "status": "VERIFIED_WITH_WARNINGS",
    "checks": {
      "physical_plausibility": "PASS",
      "conservation_laws": "WARNING: Energy conservation off by 0.15%",
      "modulation_factor_range": "PASS",
      "phase_consistency": "PASS"
    },
    "warning_message": "Energy conservation error is slightly above nominal (0.1%). Consider increasing precision tolerance or checking input parameters."
  }
}

Full Protocol Example (End-to-End)

# Step 1-2 (embedded in request): KO42 mandatory, 3 operators total
# Step 3 (embedded): QM1 + NM19 compatible
# Step 4 (auto-tuned): Quantum domain -> 0.01% tolerance
# Step 5-7 (automatic): Compile, execute, verify

curl -X POST https://zeq.dev/api/zeq/compute \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "operators": ["QM1", "NM19"],
    "parameters": {
      "particle_mass": 9.109e-31,
      "potential": "harmonic_oscillator",
      "frequency": 1e15
    }
  }'

Full Response:

{
  "step_1_prime_directive": {
    "ko42_present": true,
    "status": "PASS"
  },
  "step_2_operator_limit": {
    "tier": "free",
    "max_allowed": 4,
    "requested": 2,
    "status": "PASS"
  },
  "step_3_scale_principle": {
    "operators": ["QM1", "NM19"],
    "compatibility": "COMPATIBLE",
    "status": "PASS"
  },
  "step_4_precision_imperative": {
    "relative_tolerance": 0.0001,
    "absolute_tolerance": 1e-10,
    "domain_auto_tuned": true,
    "status": "PASS"
  },
  "step_5_compile": {
    "master_equation": "□ϕ − μ²(r)ϕ − λϕ³ − e^{−ϕ/ϕ_c} + ϕ₄₂ ∑ C_k(ϕ) = RHS",
    "operators_compiled": ["QM1 (quantum harmonic oscillator)", "NM19 (Newton + force)"],
    "status": "PASS"
  },
  "step_6_execute": {
    "solver_method": "Runge-Kutta 4th Order",
    "time_integration": "0 to 1e-12 seconds",
    "iterations": 412,
    "computation_time_ms": 67.3,
    "status": "COMPLETE"
  },
  "step_7_verify": {
    "physical_plausibility": "PASS",
    "conservation_laws": "PASS",
    "modulation_consistency": "PASS",
    "zeqproof": "a8f2c9e1d5b4a7c2f9e8d1b5a4c7f0e9",
    "status": "VERIFIED"
  },
  "result": {
    "ground_state_energy": -6.81e-2,
    "unit": "eV",
    "modulated_value": -6.81089e-2,
    "zeqond_timestamp": 2245831.445
  }
}

Checking Protocol Status

To see the protocol status for an in-flight computation:

curl -X GET "https://zeq.dev/api/zeq/protocol-status/:computation_id" \
  -H "Authorization: Bearer YOUR_API_KEY"

Cross-References

• KO42: Step 1 enforces KO42 as mandatory
• Operators: Step 2 validates operator limits
• Master Equation: Step 5 compiles the equation
• ZeqProof: Step 7 generates the cryptographic proof

Visual Walkthrough: What Happens Inside

Here's what happens when you submit a computation request:

┌─────────────────────────────────────────────────────────────────┐
│ YOUR API REQUEST                                                │
│ POST /api/zeq/compute                                           │
│ {                                                               │
│   "operators": ["QM1", "NM19"],                                 │
│   "parameters": {...}                                           │
│ }                                                               │
└──────────────────────────┬──────────────────────────────────────┘
                           │
                           ▼
        ┌──────────────────────────────────────┐
        │ STEP 1: PRIME DIRECTIVE              │
        │ ✓ KO42 is mandatory                  │
        │ ✓ KO42 auto-added if missing         │
        │ ✓ Request rejected if tries to remove│
        └──────────────────────────┬───────────┘
                                   │
                           [KO42 verified]
                                   │
                           ▼
        ┌──────────────────────────────────────┐
        │ STEP 2: OPERATOR LIMIT               │
        │ ✓ Count operators: 2 + KO42 = 3 total│
        │ ✓ Free tier limit: 4 total ✓         │
        │ ✓ Request would fail here if over    │
        └──────────────────────────┬───────────┘
                                   │
                           [Limit verified]
                                   │
                           ▼
        ┌──────────────────────────────────────┐
        │ STEP 3: SCALE PRINCIPLE              │
        │ ✓ QM1 (Quantum) + NM19 (Classical)  │
        │ ✓ Compatible? YES (semi-classical)  │
        │ ✓ Request would fail here if invalid │
        └──────────────────────────┬───────────┘
                                   │
                           [Compatibility OK]
                                   │
                           ▼
        ┌──────────────────────────────────────┐
        │ STEP 4: PRECISION IMPERATIVE         │
        │ ✓ No explicit tolerance → auto-tune │
        │ ✓ QM domain → 0.01% (≤0.0001)       │
        │ ✓ Estimated: 47.2 ms to converge    │
        └──────────────────────────┬───────────┘
                                   │
                           [Precision set]
                                   │
                           ▼
        ┌──────────────────────────────────────┐
        │ STEP 5: COMPILE                      │
        │ ✓ Map QM1 → C₁,C₂,C₃,C₄             │
        │ ✓ Map NM19 → C₁₉,C₂₀                │
        │ ✓ Assemble master equation           │
        │ ✓ Set boundary conditions            │
        │ ✓ Apply KO42 metric                  │
        │ ✓ Check parameters are valid         │
        └──────────────────────────┬───────────┘
                                   │
                           [Equation assembled]
                                   │
                           ▼
        ┌──────────────────────────────────────┐
        │ STEP 6: EXECUTE                      │
        │ ✓ Runge-Kutta 4th order integration │
        │ ✓ 273 iterations (adaptive)          │
        │ ✓ Phase-locked at each step          │
        │ ✓ 47.2 ms elapsed                    │
        │ ✓ Convergence error: 0.00087 ✓       │
        └──────────────────────────┬───────────┘
                                   │
                           [Computation done]
                                   │
                           ▼
        ┌──────────────────────────────────────┐
        │ STEP 7: VERIFY & CERTIFY             │
        │ ✓ Physical plausibility: PASS        │
        │ ✓ Conservation laws: PASS            │
        │ ✓ Modulation factor: PASS [0.9996]  │
        │ ✓ Phase consistency: PASS            │
        │ ✓ Generate ZeqProof signature        │
        └──────────────────────────┬───────────┘
                                   │
                           [Result certified]
                                   │
                           ▼
┌──────────────────────────────────────────────────────────────────┐
│ RESPONSE TO CLIENT                                              │
│ {                                                               │
│   "result": {value: 8.472194128},                              │
│   "zeqproof": {signature: "a8f2c9e1d5b4a..."},                 │
│   "metadata": {zeqond_timestamp: 2245831.445}                  │
│ }                                                               │
└──────────────────────────────────────────────────────────────────┘

---

Common Mistakes at Each Step

Step 1: KO42 Mistakes

Mistake 1a: Trying to exclude KO42

{
  "operators": ["QM1"],
  "exclude_ko42": true   // ❌ FAILS
}

Error: STEP_1_FAILED: KO42 is mandatory and cannot be excluded. Fix: Remove the exclude_ko42 field. KO42 is added automatically.

Mistake 1b: Asking for "no modulation"

"parameters": {
  "modulation": "none"   // ❌ FAILS
}

Error: KO42 is built into the metric—you cannot turn it off at the parameter level. Fix: If you need different modulation, use KO42.2 (manual mode) with custom β.

Step 2: Operator Limit Mistakes

Mistake 2a: Exceeding tier limit

Free tier (max 4 total including KO42):

{
  "operators": ["QM1", "NM19", "CS43", "EM7", "KO42"]  // ❌ 5 total
}

Error: STEP_2_FAILED: Free tier allows max 4 total operators. Fix: Remove one operator, or upgrade your tier.

Mistake 2b: Forgetting to count KO42

Many users think: "I'm on Free tier, so I can use 3 operators" and add QM1, NM19, CS43. But:

QM1 + NM19 + CS43 + KO42 (automatic) = 4 total ✓ OK

If they add a 4th operator:

QM1 + NM19 + CS43 + EM7 + KO42 = 5 total ❌ FAILS

Fix: Remember KO42 is always included in the count.

Step 3: Scale Principle Mistakes

Mistake 3a: Incompatible operators

{
  "operators": ["EM7", "EM8"]  // ❌ Mutually exclusive
}

Error: STEP_3_FAILED: EM7 and EM8 cannot be used together. Fix: Check the API documentation for compatibility. Use only one of EM7 or EM8.

Mistake 3b: Mismatched domains

{
  "operators": ["CS43", "QM1"]  // ❌ Complexity + quantum mixing
}

Error: STEP_3_FAILED: Complexity science operators cannot be mixed with physics operators. Fix: Choose operators from compatible domains (e.g., QM1 + EM7 for quantum electromagnetism, or CS43 + OD5 for complexity of algorithm analysis).

Step 4: Precision Imperative Mistakes

Mistake 4a: Impossible tolerance

{
  "precision": {
    "relative_error_tolerance": 1e-20  // ❌ Numerically impossible
  }
}

Error: STEP_4_FAILED: Requested tolerance (1e-20) is below floating-point precision (1e-16). Fix: Use reasonable tolerances. For most domains, 1e-4 (0.01%) is excellent. For quantum, 1e-5 is tight but possible.

Mistake 4b: Timeout due to excessive precision

{
  "precision": {
    "relative_error_tolerance": 1e-10  // ✓ Valid but very tight
  }
}

Response (not an error, but a warning):

{
  "warning": "Step 4 validation suggests this may take 5+ seconds.",
  "recommendation": "Consider relaxing tolerance to 1e-6 (0.0001%) or upgrading to Advanced tier for faster hardware."
}

Step 5: Compilation Mistakes

Mistake 5a: Invalid parameter

{
  "operators": ["QM1"],
  "parameters": {
    "energy_level": 1000  // ❌ Out of bounds
  }
}

Error: STEP_5_FAILED: Parameter 'energy_level' must be between 1 and 50. Fix: Consult the operator documentation for valid ranges.

Mistake 5b: Missing required parameter

{
  "operators": ["QM1"]
  // Missing "hamiltonian" parameter
}

Error: STEP_5_FAILED: Required parameter 'hamiltonian' is missing for operator QM1. Fix: Provide all required inputs. Check the operator spec for mandatory parameters.

Step 6: Execution Mistakes

Mistake 6a: Divergence (computation blows up)

{
  "convergence_status": "DIVERGED",
  "final_value": "inf",
  "error": "Solver diverged after 10000 iterations."
}

Why: Parameters might be physically unreasonable (e.g., coupling constant too large), or the equation is unstable in your regime. Fix:

• Check input parameters for typos
• Reduce coupling strengths
• Use KO42.2 with smaller β
• Contact support if the operator should handle this regime

Mistake 6b: Timeout (too slow)

Computation exceeded 120 second timeout.

Why: Too many operators, too tight precision, or ill-conditioned problem. Fix:

• Remove one operator if possible
• Relax precision tolerance
• Upgrade to Advanced/Architect tier (dedicated hardware)

Step 7: Verification Mistakes

Mistake 7a: Physical implausibility

{
  "verification": {
    "physical_plausibility": "FAIL",
    "reason": "Energy is negative for a harmonic oscillator ground state."
  }
}

Why: Operator returned a physically impossible result (sign of a bug or parameter error). Fix:

• Double-check input parameters
• Verify you're using the right operator for your domain
• Contact support if the operator is faulty

Mistake 7b: Conservation law violation

{
  "verification": {
    "conservation_laws": "WARNING",
    "violation": "Energy conservation error: 2.3%"
  }
}

Why: Numerical error accumulated more than expected. Fix:

• Increase precision tolerance (reduce relative_error_tolerance)
• Use KO42.2 with tighter β
• Upgrade to higher tier for better numerics

---

See Also

• HULYAS Master Equation: The equation the protocol compiles
• ZeqProof: The cryptographic certificate generated in Step 7