The Z Framework is a unified mathematical model bridging physical and discrete domains through the empirical invariance of the speed of light. It leverages the universal form Z = A(B/c) to analyze prime number distributions using geometric constraints and curvature-based geodesics.

Always reference these instructions first and fallback to search or bash commands only when you encounter unexpected information that does not match the info here.

• Install Python dependencies:
  • pip3 install numpy pandas matplotlib mpmath sympy scikit-learn statsmodels scipy seaborn plotly
  • Takes: ~45-50 seconds. NEVER CANCEL. Set timeout to 300+ seconds.
• Set Python path for imports (required when working outside repository root):
  • export PYTHONPATH=/home/runner/work/unified-framework/unified-framework
  • OR prefix commands: PYTHONPATH=/home/runner/work/unified-framework/unified-framework python3 script.py
  • Note: PYTHONPATH is only required when working from directories other than the repository root

• Test basic framework:
  • python3 -c "from core.axioms import universal_invariance; print('Test:', universal_invariance(1.0, 3e8))"
  • Takes: ~0.1 seconds
• Test discrete zeta shift computations:
  • python3 -c "from core.domain import DiscreteZetaShift; dz = DiscreteZetaShift(10); print('Works')"
  • Takes: ~1.1 seconds (includes high-precision mpmath initialization)

• Run prime curvature proof analysis:
  • python3 number-theory/prime-curve/proof.py
  • Takes: ~2 seconds. NEVER CANCEL. Set timeout to 30+ seconds.
  • Computes optimal curvature exponent k* ≈ 0.3 with 15% prime density enhancement (CI [14.6%, 15.4%])
• Run hologram visualizations:
  • python3 number-theory/prime-curve/hologram.py
  • Takes: ~1.3 seconds
• Run golden curve analysis:
  • PYTHONPATH=/home/runner/work/unified-framework/unified-framework python3 experiments/lab/golden-curve/brute_force.py
  • Takes: ~0.8 seconds. Tests Bell inequality violation in prime distributions.
• Run comprehensive data generation:
  • PYTHONPATH=/home/runner/work/unified-framework/unified-framework python3 test-finding/scripts/test.py
  • Takes: ~143 seconds (2 minutes 23 seconds). NEVER CANCEL. Set timeout to 1800+ seconds (30+ minutes) for larger datasets.

• 100 DiscreteZetaShift instances: ~0.01 seconds
• 1000 DiscreteZetaShift instances with full computation: ~2 seconds
• Large-scale analysis (test-finding/scripts/test.py): ~143 seconds (2 minutes 23 seconds)
• Prime hologram bootstrap (1000 primes): ~0.3 seconds

• axioms.py - Universal invariance functions, curvature calculations, golden ratio transformations
• domain.py - DiscreteZetaShift class with 5D helical embeddings and zeta shift computations
• orbital.py - Orbital mechanics and geometric projections

• vortex_filter.py - Vortex filtering system
• wave-crispr-signal.py and wave-crispr-signal-2.py - CRISPR signal analysis tools
• z_embeddings_csv.py - Z framework CSV embedding utilities
• Prime Density Curve/ - Prime density curve analysis tools
• Various visualization and encryption tools

• test.py - Main comprehensive test suite (143 seconds runtime)
• /lab/golden-curve/ - Golden ratio curvature analysis
• /lab/light_primes/ - Prime hologram and density analysis
• /lab/universal_frame_shift_transformer/ - Frame shift computations
• /lab/wave-crispr-signal/ - Spectral analysis tools

• /prime-curve/ - Prime curvature analysis and proof scripts
• /prime-number-geometry/ - Geometric prime analysis tools

Always test these core mathematical scenarios after making changes:

• Test universal invariance calculation: from core.axioms import universal_invariance; assert abs(universal_invariance(1.0, 3e8) - 3.33e-09) < 1e-10
• Test DiscreteZetaShift instantiation: Create instances for n=1 to 100 and verify no exceptions
• Verify high-precision computations work: Check mpmath precision is set to 50 decimal places

• Run prime curvature proof: Verify k* ≈ 0.3 and enhancement = 15% (CI [14.6%, 15.4%])
• Test golden ratio transformations: Verify φ ≈ 1.618 calculations
• Validate Mersenne prime generation in proof.py output
• Test Bell inequality violation: Run golden-curve/brute_force.py and verify quantum entanglement detection

• Benchmark DiscreteZetaShift: 1000 instances should complete in <3 seconds
• Test visualization generation: hologram.py should complete in <2 seconds
• Verify memory usage remains reasonable for large computations
• Test comprehensive analysis: test-finding/scripts/test.py should complete in ~143 seconds

• **NEV