IndisputableMonolith.Mathematics.GraphTheoryFromRS
The module derives graph-theoretic objects from Recognition Science by encoding the relation 12 = 3 × 4 = D × 2^(D-1) for D=3. Researchers connecting the RS forcing chain to combinatorial models would cite it. The module supplies definitions for q3 vertices, edges, chromatic number, bipartiteness, and a bundled certificate.
claim$12 = 3 × 4 = D × 2^{D-1}$ realized by the q3 graph with vertex set q3Vertices, edge set q3Edges, chromatic number q3ChromaticNumber, and bipartiteness q3Bipartite.
background
The module Mathematics.GraphTheoryFromRS sits in the mathematics domain and imports only Mathlib to access graph primitives. It introduces the q3 graph whose parameters satisfy the module doc-comment relation 12 = 3 × 4 = D × 2^(D-1), directly implementing T8 of the forcing chain that forces D = 3 spatial dimensions. Sibling declarations define q3Vertices, q3Edges, q3ChromaticNumber, q3Bipartite, q3Edges_factored, and the certificate GraphTheoryCert.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the GraphTheoryCert that realizes the dimensional structure from the unified forcing chain in graph-theoretic terms. It feeds the eight-tick octave and D = 3 into downstream Recognition Science constructions that link mathematics to the phi-ladder and RCL. The certificate bundles the vertex, edge, and chromatic facts for use in higher-level derivations.
scope and limits
- Does not prove general theorems of graph theory.
- Does not derive physical constants or mass formulas.
- Does not reference the Recognition Composition Law.
- Does not connect to the phi-ladder or Berry threshold.