**Appendix C: Detailed Graph Data (Edges)** **C.2: Edges Originating from General Relativity (GR) Nodes:** | Source Node ID | Target Node ID | Type | Rationale | Conf. | Dir. | |:------------------------- |:--------------------------- |:---------------- |:-------------------------------------------------------------------------------------------------------------------------------------- |:---- |:--- | | `GR` | `CM` | `F-LIM` (Inverse) | General Relativity contains Classical Mechanics (Newtonian Gravity) as its weak-field, low-velocity limit. | H | D | | `GR` | `LCDM` | `F-BAS` | General Relativity provides the fundamental framework for gravity and spacetime dynamics used in the ΛCDM model. | H | D | | `GR` | `Math::DifferentialGeometry` | `S-FORM` | General Relativity is mathematically formulated using the language and tools of differential geometry (manifolds, tensors). | H | D | | `GR` | `Problem::QuantumGravity` | `F-REQ` | General Relativity’s incompatibility with quantum mechanics necessitates a more fundamental theory of quantum gravity. | H | D | | `GR::EquivalencePrinciple` | `GR` | `S-COMP` | The Equivalence Principle is a core conceptual component and motivation for General Relativity’s geometric interpretation. | H | D | | `GR::EquivalencePrinciple` | `CM::GravityLaw_Newton` | `F-CHL` | The Equivalence Principle motivates viewing gravity as geometry, challenging the Newtonian concept of gravity as a force. | H | D | | `GR::GeneralCovariance` | `GR` | `S-COMP` | The Principle of General Covariance is a key principle guiding the mathematical formulation of General Relativity. | H | D | | `GR::SpacetimeManifold` | `GR` | `S-COMP` | The modeling of spacetime as a pseudo-Riemannian manifold is the central mathematical structure defining GR. | H | D | | `GR::SpacetimeManifold` | `GR::MetricTensor` | `S-COMP` | The metric tensor defines the geometry of the spacetime manifold in GR. | H | D | | `GR::MetricTensor` | `GR::EFE` | `S-COMP` | The metric tensor (and its derivatives forming the Einstein tensor) is a key component of the Einstein Field Equations. | H | D | | `GR::GeodesicMotion` | `GR` | `S-COMP` | The principle that free particles follow geodesics is a core postulate describing motion within GR. | H | D | | `GR::GeodesicMotion` | `CM::Law2_Force` | `F-CHL` | Geodesic motion (path determined by geometry) offers an alternative explanation for gravitational trajectories compared to F=ma. | H | D | | `GR::EFE` | `GR` | `S-COMP` | The Einstein Field Equations are the central dynamical law of General Relativity. | H | D | | `GR::EFE` | `GR::StressEnergyTensor` | `C-NEC` | The Stress-Energy Tensor acts as the source term in the EFE, determining the spacetime curvature. | H | D | | `GR::EFE` | `GR::CosmologicalConstant` | `S-COMP` | The cosmological constant Λ is an optional term within the structure of the EFE. | H | D | | `GR::EFE` | `GR::Determinism` | `L-ENT` | The EFE are deterministic partial differential equations for the metric tensor, given source terms and initial/boundary conditions. | H | D | | `GR::EFE` | `CM::GravityLaw_Newton` | `F-LIM` (Inverse) | Einstein’s Field Equations reduce to Newton’s law of gravitation in the appropriate weak-field, low-velocity limit. | H | D | | `GR::StressEnergyTensor` | `Concept::Energy` | `F-BAS` | The Stress-Energy Tensor generalizes the concept of energy density and includes momentum density and stress. | H | D | | `GR::DynamicSpacetime` | `CM::AbsoluteSpacetime` | `L-CTR` | GR’s dynamic spacetime, which interacts with matter, contradicts CM’s fixed, absolute spacetime background. | H | S | | `GR::DynamicSpacetime` | `Phil::Physicalism` | `F-REQ` | The dynamic nature of spacetime in GR requires physicalism to clarify whether spacetime itself is a fundamental physical entity. | M | D | | `GR::ContinuumAssumption` | `Problem::PlanckScale` | `F-REQ` | GR’s assumption of a smooth spacetime continuum is expected to break down at the Planck scale, requiring a quantum gravity description. | H | D | | `GR::Determinism` | `QM::IntrinsicIndeterminism` | `L-CTR` | The deterministic evolution described by GR conflicts with the probabilistic nature of measurement outcomes in standard QM. | H | S | | `GR::Locality` | `QM::NonLocality` | `F-CHL` | GR’s description of local interactions propagating at speed c is challenged by the non-local correlations of quantum entanglement. | H | D | | `GR::Singularity` | `GR` | `F-CHL` | The prediction of singularities indicates a breakdown or limit of applicability of the GR framework itself. | H | D | | `GR::Singularity` | `Problem::GRSingularity` | `L-INST` | GR’s predictions are the primary instances defining the singularity problem in physics. | H | D | | `GR::Singularity` | `Problem::QuantumGravity` | `F-REQ` | Singularities signal the need for a quantum theory of gravity to describe physics under extreme conditions. | H | D |