eight_tick
plain-language theorem explainer
The eight-tick period is defined as the natural number 8. Researchers deriving spatial dimensions from recognition forcing cite this constant to connect the octave cycle directly to D = 3. The definition is a direct assignment with no computation or lemmas.
Claim. The eight-tick period is the natural number $8$.
background
The RRF Foundation module states that all physical constants derive from φ via gate identities in the chain φ → E_coh → τ₀ → c → ℏ → G → α^{-1}. The tick is the fundamental RS time quantum with τ₀ = 1. In the DimensionForcing context, Dimension is an alias for ℕ while eight_tick supplies the octave period of 8 ticks. Upstream results define tick as the RS-native time quantum and note that one octave equals 8 ticks as the fundamental evolution period.
proof idea
This is a direct definition that assigns the constant value 8 to eight_tick in the natural numbers. No lemmas are applied and no tactics are used beyond the assignment.
why it matters
This definition supplies the concrete value referenced by downstream results including D3_compatible, eight_tick_forces_D3, RSCompatibleDimension, and simplicial_loop_tick_lower_bound. It realizes the eight-tick octave (T7, period 2^3) and supports forcing of D = 3 (T8) within the recognition composition law and gap-45 synchronization.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.