Quantum Narrative Matrix Theory - Quantum Gravity Correction Extension
Completion: 30% → 50% (+20%)
Overall Progress
30%
Initial Completion
50%
Current Completion
+20%
Progress Increase
12/12
Tests Passed
550+
Lines of Code
8
New Methods
Key Parameters
Basic Parameters
Planck Length (l_P):1.0
Base Coupling Strength (alpha):1.0 (default)
l_P² Term Coefficient:α * l_P²
Higher-Order Correction Parameters
l_P⁴ Coupling Strength (beta):0.01 (default)
l_P⁶ Coupling Strength (gamma):0.001 (default)
l_P⁴ Term Formula:β l_P⁴ R²
l_P⁶ Term Formula:γ l_P⁶ R³
Discrete Spacetime Parameters
Lattice Spacing (lattice_spacing):1.0 (equals l_P)
Discrete Effects Enabled:True (default)
Numerical Stability Parameters
Finite Difference Step (epsilon):1e-6
Metric Regularization (regularization):0.01
Max Curvature Limit (max_curvature):1e6
Min Metric Eigenvalue (min_metric_eigenval):0.1
Complete Correction Formula
H_QG = H + αl_P²R + βl_P⁴R² + γl_P⁶R³ + discrete_effects where: - H: Base Hamiltonian matrix - R: Ricci scalar (obtained through complete curvature calculation) - discrete_effects: Discrete spacetime effect term
Implemented Methods
Curvature Calculation Toolchain
Method NameFunctionInputOutputderive_metric_tensor_from_hamiltonian()Derive metric tensor from HamiltonianH (n×n matrix)g_μν (n×n metric tensor)compute_christoffel_symbols()Compute Christoffel symbolsmetric (metric tensor)Γ^λ_μν (n×n×n array)compute_riemann_tensor()Compute Riemann curvature tensormetric, christoffelR^ρ_σμν (n×n×n×n array)compute_ricci_tensor()Compute Ricci tensorriemann, metricR_μν (n×n matrix)compute_ricci_scalar_from_hamiltonian()Compute Ricci scalar from HamiltonianH (n×n matrix)R (scalar)
Planck Scale Effect Methods
Method NameFunctionInputOutputapply_quantum_gravity_correction()Apply complete quantum gravity correctionH, spacetime_curvature (optional)H_QG (corrected Hamiltonian)_compute_discrete_spacetime_effects()Compute discrete spacetime effectsH (n×n matrix)discrete_correction (n×n matrix)compute_planck_scale_diagnostics()Planck scale diagnostic analysisH (n×n matrix)Diagnostics dictionary (20+ metrics)compare_with_observational_data()Compare with observational dataH, observational_params (optional)Comparison result dictionary
Test Details
Week 1-2 Test Suite
Test File: test_quantum_gravity_curvature.py
test_metric_derivation()
Test metric tensor derivation functionality
Verifies: shape, Hermitian property, positive definiteness, condition number
test_christoffel_symbols()
Test Christoffel symbols computation
Verifies: shape (n×n×n), numerical stability
test_riemann_tensor()
Test Riemann curvature tensor computation
Verifies: shape (n×n×n×n), computation completeness
test_ricci_scalar()
Test complete Ricci scalar computation
Test scales: n=5, 10, 15 | Verifies: finiteness, value range
test_quantum_gravity_correction()
Test complete quantum gravity correction
Verifies: Hermitian property, correction magnitude
test_numerical_stability()
Test numerical stability
Tests: small matrix (n=3), large matrix (n=20), near-singular matrix
Week 3-4 Test Suite
Test File: test_planck_scale_effects.py
test_higher_order_corrections()
Test higher-order corrections (l_P^4, l_P^6)
Verifies: l_P⁴ term, l_P⁶ term, superposition with base correction
test_discrete_spacetime_effects()
Test discrete spacetime effects
Verifies: Hermitian property, relative correction magnitude (~2%)
test_planck_scale_diagnostics()
Test Planck scale diagnostic tools
Verifies: 20+ diagnostic metrics, QG regime classification, dominant effect identification
test_observational_comparison()
Test observational data comparison functionality
Verifies: curvature constraints, discrete effects bounds, consistency score
test_parameter_control()
Test extended parameter control
Verifies: alpha, beta, gamma, include_higher_order, discrete_spacetime_enabled
test_integration()
Test complete integration
Test scales: n=5, 10, 15 | Verifies: all features integrated
Test SummaryResultTotal Tests12 testsPassed Tests12 (100%)Test Files2 test suitesTest CoverageAll core featuresNumerical StabilityVerified (small/large/boundary cases)
Key Achievements
Technical Implementation
CategoryContentStatusCurvature CalculationComplete differential geometry toolchain: H → g_μν → Γ → R^ρσμν → Rμν → RCompleteHigher-Order Correctionsl_P⁴ term (βl_P⁴R²) and l_P⁶ term (γl_P⁶R³)CompleteDiscrete SpacetimeLattice regularization, lattice spacing correction, quantum fluctuation effectsCompleteDiagnostic Tools20+ diagnostic metrics, QG regime classification, dominant effect identificationCompleteObservational ComparisonCurvature constraint checking, discrete effects bounds, consistency scoring systemComplete
Code Quality
MetricValueCode Errors0Test Pass Rate100%Numerical StabilityExcellentDocumentation CompletenessComplete
Completion Progress
StageCompletionMain AchievementsTest StatusInitial State30%Basic framework, simplified curvature approximationBasic testsAfter Week 1-240% (+10%)Complete curvature calculation toolchain6/6 passedAfter Week 3-450% (+10%)Planck scale effects extension6/6 passed
Deliverables
Code Files
File PathVersionLines of CodeStatus05_Core_Source_Code/quantum_gravity_correction.py0.5~550 lines addedComplete
Test Files
Test FileNumber of TestsPass RateStatus06_Data_and_Scripts/test_quantum_gravity_curvature.py6 tests100%Passed06_Data_and_Scripts/test_planck_scale_effects.py6 tests100%PassedProject: Quantum Narrative Matrix Theory - Quantum Gravity Correction Extension
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