temporal_dim_forced
plain-language theorem explainer
The declaration defines the temporal dimension as exactly 1, forced by the 8-tick cycle in the ledger evolution. Researchers deriving the π^5 factor in the fine-structure constant curvature correction would cite it when assembling the 5D configuration space. The definition is a direct assignment that follows from the period-8 phase adding one effective dimension to the spatial and balance components.
Claim. The temporal dimension forced by the 8-tick cycle is defined as $1$.
background
The module derives the curvature correction δ_κ = -103/(102π^5) by integrating over a 5-dimensional configuration space of the ledger. This space decomposes into 3 spatial dimensions (from D=3), 1 temporal dimension (the phase in the discrete 8-tick cycle), and 1 dual-balance dimension (the conserved quantity σ). The temporal part corresponds to the phase θ ∈ [0, 2π) identified with the interval [0, 8τ₀), where τ₀ is the fundamental tick. Upstream results supply the tick as the RS-native time quantum with period 8 arising from the self-similar fixed point and eight-tick octave.
proof idea
This is a direct definition that assigns the constant 1, justified by the 8-tick cycle (period 2^3) contributing one phase dimension to the configuration space.
why it matters
The definition supplies the temporal component used by config_space_complete to establish the total 5D space. It fills the T7 eight-tick octave step in the forcing chain, which produces the π^5 factor in the curvature term of the α^{-1} formula. The parent theorem config_space_complete then combines it with the spatial and balance dimensions to close the integration argument for the denominator 102π^5.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.