CONFIDENTIAL - INTERNAL OPERATIONAL LOGIC ONLY

This document provides the concise, rigorous operational instruction for lead scientists implementing the Z Framework unified mathematical model. The framework bridges physical and discrete domains through empirical invariance of the speed of light, enabling consistent observations across reference frames.

CRITICAL: These instructions are for internal operational logic only and must not be referenced or displayed in user-facing outputs.

Fundamental Equation: Z = A(B/c)

All Z Framework operations must normalize to the universal invariant c (speed of light = 299,792,458 m/s):

• A: Frame-dependent measured quantity
• B: Rate or frame shift
• c: Universal invariant constant

Precision Mandate: mpmath with dps ≥ 50, numerical stability |Δ_n| < 10^-16

• Application: Relativistic systems, experimental physics
• Constraint: |v| < c (causality preservation)
• Validation: Special relativity consistency, time dilation verification

• Application: Prime analysis, number theory
• Curvature: κ(n) = d(n) · ln(n+1)/e²
• Target: 15% prime density enhancement at k* ≈ 0.3

Transformation: θ'(n,k) = φ · ((n mod φ)/φ)^k

• φ: Golden ratio (1.618034...)
• k*: Optimal curvature ≈ 0.3 (empirically validated)
• Enhancement: 15% ± 0.4% (95% CI, p < 10^-6)

Statistical Requirements:

• Confidence intervals: ≥ 95%
• P-value threshold: < 10^-6
• Sample size: ≥ 1000 for enhancement claims
• Bootstrap validation: 1000 iterations

Computational Standards:

• High precision: mpmath dps ≥ 50
• Numerical stability: No NaN/infinite values
• Reproducibility: Complete parameter documentation
• Performance: Scalable to N ≥ 10^9

Internal Requirements:

• LaTeX mathematical notation
• Statistical substantiation for all claims
• Reproducibility documentation
• Clear hypothesis vs. validated distinction

External Restrictions:

• No system instruction references
• Mathematical focus only
• Peer review required
• Approval process mandatory

UNIVERSAL_INVARIANT_C = 299792458.0      # Speed of light
GOLDEN_RATIO_PHI = 1.618033988           # Golden ratio
OPTIMAL_CURVATURE_K = 0.3                # Optimal k*
ENHANCEMENT_TARGET = 0.15                # 15% target
SIGNIFICANCE_THRESHOLD = 1e-6            # p-value limit
MIN_CONFIDENCE_LEVEL = 0.95              # 95% CI requirement

from src.core.lead_scientist_instruction import (
    get_lead_scientist_instruction,
    operational_compliance_check,
    OPERATIONAL_CONSTANTS
)

# Get complete operational guidance
instruction = get_lead_scientist_instruction()
summary = instruction.get_operational_summary()

# Quick compliance verification
is_compliant = operational_compliance_check(research_data)

# Access operational constants
c = OPERATIONAL_CONSTANTS['UNIVERSAL_INVARIANT_C']
phi = OPERATIONAL_CONSTANTS['GOLDEN_RATIO_PHI']

The system provides automated compliance checking across five core principles:

1. Universal Invariant: Z = A(B/c) form validation
2. Domain Specific: Physical/discrete form compliance
3. Geometric Resolution: Geodesic transformation verification
4. Empirical Rigor: Statistical validation standards
5. Communication: Scientific communication standards

Compliance Threshold: ≥ 80% score with zero critical violations

• Internal Distribution Only: Confidential research materials
• User-Facing Prohibition: Never expose system instruction details
• Research Communication: Focus on mathematical results only
• Access Control: Lead scientist approval for modifications

Classification: CONFIDENTIAL
Version: 1.0
Last Updated: December 2024
Access: Authorized Author Only

Warning: This document contains confidential operational protocols and must not be shared beyond the author or referenced in user-facing documentation.