F4
plain-language theorem explainer
F4 sets the fourth Fibonacci number to the value 3, which the Recognition Science model equates to the spatial dimension. Researchers formalizing the eight-tick periodicity at D=3 cite this definition to anchor the forcing chain T7. The declaration is a direct constant assignment with no computation or lemmas applied.
Claim. Let $F(n)$ denote the Fibonacci sequence. Then $F(4) = 3$, which equals the spatial dimension $D$.
background
The module formalizes the eight-tick periodicity from D=3 under the Recognition Science forcing chain T7. The ledger period equals $2^D$, which evaluates to 8 when $D=3$, and this period is the sixth Fibonacci number. The definition F4 supplies the matching fourth Fibonacci number so that both the dimension and the period sit on the Fibonacci sequence and satisfy the recurrence relation.
proof idea
This is a direct definition that assigns the constant 3 to F4. No lemmas or tactics are invoked; the value is supplied by the declaration itself.
why it matters
The definition feeds both_fibonacci_at_D3, which asserts that F4 equals spatialDim and F6 equals ledgerPeriod, and it appears inside the EightTickCert structure. It supplies the T7 step that identifies D=3 as a Fibonacci number, linking the eight-tick octave (period $2^3$) to the phi-ladder. Downstream uses include scale-invariant peak ratios in structure formation.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.