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def definition def or abbrev high

eight_tick

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The eight-tick period is defined as the natural number 8. Researchers tracing the Recognition Science derivation of spatial dimension D=3 cite this constant when connecting ledger cycle length to 2^D. The definition is a direct constant assignment that supports reflexivity steps in compatibility theorems.

claimThe eight-tick period equals $8$.

background

The Dimension Forcing module proves D=3 is forced by the RS framework through topological linking, gap-45 synchronization, and spinor structure. The eight-tick period is the ledger coverage length 2^D specialized at D=3. Upstream results define gap as the product of closure and fibonacci factors equaling 45, with the doc-comment noting 'The 8-tick period (from ledger coverage of 2^D with D=3)'. The synchronization condition requires lcm(8,45)=360, which isolates D=3 via 2^3=8 and SO(3) periodicity.

proof idea

This is a direct definition that assigns the constant 8. Downstream proofs apply it by reflexivity, as in eight_tick_is_2_cubed, and unfold the name in eight_tick_forces_D3 to reduce the hypothesis to power_of_2_forces_D3.

why it matters in Recognition Science

This definition supplies the eight-tick octave from the T7 step of the forcing chain, enabling T8 to conclude D=3. It feeds into downstream results such as D3_compatible, which builds RSCompatibleDimension 3 using eight_tick := rfl, and eight_tick_forces_D3. The value closes the gap-45 synchronization where 45 is the cumulative phase over a closed 8-tick cycle, yielding the 360-degree periodicity.

scope and limits

Lean usage

example : eight_tick = 8 := rfl

formal statement (Lean)

 110def eight_tick : ℕ := 8

proof body

Definition body.

 111
 112/-- Gap-45: the integration gap parameter D²(D+2) at D = 3. -/

used by (30)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (7)

Lean names referenced from this declaration's body.