**Appendix C: Detailed Graph Data (Edges)** **C.8: Edges Originating from Information Science Nodes** | Source Node ID | Target Node ID | Type | Rationale | Conf. | Dir. | |:----------------------------- |:------------------------- |:------- |:------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |:---- |:--- | | `InfoSci::ShannonTheory` | `Math::ProbabilityTheory` | `F-BAS` | Shannon Information Theory is mathematically formulated using and relies fundamentally on probability theory. | H | D | | `InfoSci::ShannonTheory` | `Concept::Information` | `S-FORM` | Provides a specific, quantitative, syntactic definition of information as reduction of uncertainty. | H | D | | `InfoSci::ShannonEntropy` | `InfoSci::ShannonTheory` | `S-COMP` | Shannon Entropy (H) is a core concept/measure defined within Shannon Information Theory. | H | D | | `InfoSci::ShannonEntropy` | `StatMech::GibbsEntropy` | `S-FORM` | Shannon Entropy has the identical mathematical form as Gibbs Entropy. | H | S | | `InfoSci::ShannonEntropy` | `StatMech::GibbsEntropy` | `E-ANL` | The identical form suggests a deep analogy related to uncertainty/information/number of states between the two concepts. | H | S | | `InfoSci::ShannonEntropy` | `Concept::Entropy` | `L-INST` | Shannon Entropy is a specific instance of the broader concept of entropy, focused on information/uncertainty. | H | D | | `InfoSci::ChannelCapacity` | `InfoSci::ShannonTheory` | `S-COMP` | Channel Capacity (C) is a core concept/limit defined within Shannon Information Theory. | H | D | | `InfoSci::SourceCodingTheorem` | `InfoSci::ShannonTheory` | `S-COMP` | The Source Coding Theorem is a key result derived within Shannon Information Theory concerning data compression limits. | H | D | | `InfoSci::SourceCodingTheorem` | `InfoSci::ShannonEntropy` | `F-BAS` | The limit for lossless compression is determined by the Shannon Entropy of the source. | H | D | | `InfoSci::NoisyChannelTheorem` | `InfoSci::ShannonTheory` | `S-COMP` | The Noisy-Channel Coding Theorem is a key result derived within Shannon Information Theory concerning reliable communication limits. | H | D | | `InfoSci::NoisyChannelTheorem` | `InfoSci::ChannelCapacity` | `F-BAS` | The limit for reliable communication is determined by the Channel Capacity. | H | D | | `InfoSci::Information` | `InfoSci::ShannonTheory` | `S-COMP` | The specific syntactic concept of information (reduction of uncertainty) is central to Shannon Theory. | H | D | | `InfoSci::Information` | `Physics` | `E-ANL` | Connections between Shannon’s syntactic information and physical concepts like entropy or energy are often analogical or require careful interpretation (e.g., Landauer’s principle). | M | S | | `InfoSci::Information` | `Physics` | `F-REQ` | The precise relationship between abstract Shannon information and physical reality requires further explanation/unification. | M | D | | `InfoSci::Information` | `Philosophy` | `F-CHL` | Shannon’s purely syntactic definition challenges broader philosophical concepts of information involving meaning or semantics. | H | D |