IndisputableMonolith.Physics.SpinFoamFromRS
SpinFoamFromRS derives spin foam models from Recognition Science by defining SpinFoamModel and certifying dimensional properties of 6j symbols. It establishes that the 6j-symbol dimension equals 6, which matches twice the spatial dimension and the number of cube faces. The module draws directly on RS constants and consists of definitions plus supporting equalities rather than extended derivations.
claimSpinFoamModel with the property that the 6j-symbol dimension equals 6, which satisfies $6 = 2D$ where $D$ is the number of spatial dimensions, and also equals the number of faces of a cube.
background
This module operates in the Physics domain of Recognition Science and imports the Constants module. The upstream Constants module supplies the fundamental RS time quantum (RS-native) with τ₀ = 1 tick. The theoretical setting builds on the J-function, Recognition Composition Law, and the forcing chain that forces J-uniqueness, the self-similar fixed point phi, the eight-tick octave, and D = 3 spatial dimensions.
proof idea
This is a definition module, no proofs. It consists of definitions for SpinFoamModel, spinFoamModelCount, sixJDimension, SpinFoamCert and direct equalities that relate the 6j-symbol dimension to 2D and cube faces.
why it matters in Recognition Science
This module supplies the bridge from Recognition Science to spin foam structures in quantum gravity. It feeds into higher-level physics derivations by establishing the 6j-symbol dimension equality, which aligns with the D = 3 forced by T8 in the UnifiedForcingChain. The cube-faces relation reflects geometric structure emerging from the Recognition Composition Law and phi self-similarity.
scope and limits
- Does not derive the full dynamics of spin foams from the functional equation.
- Does not compute numerical values for 6j symbols beyond their dimension.
- Does not incorporate the alpha inverse band or mass formulas from RS.
- Does not address time evolution or the Berry creation threshold.