closure_factor
plain-language theorem explainer
The closure factor is defined as one plus the eight-tick period, producing the integer 9. Researchers deriving the 45-gap in Recognition Science cite it to encode the fence-post return after an eight-state cycle. The definition is a direct one-line addition to the period constant fixed upstream by T8.
Claim. Let $c$ be the closure factor. Then $c := p + 1$, where $p = 8$ is the eight-tick period.
background
The Gap45.Derivation module starts from the eight-tick period fixed at 8 by T8, the period $2^D$ for $D=3$ spatial dimensions. The closure factor adds one to capture return to the initial state after traversing the cycle, following the fence-post principle. This rests on the upstream definition of eight_tick_period in StillnessGenerative and Gravity.EightTickResonance, each stating it equals 8.
proof idea
One-line definition that applies the upstream eight_tick_period constant and adds 1.
why it matters
This supplies the factor 9 that multiplies the Fibonacci factor 5 to yield the gap of 45. It feeds the downstream results gap, gap_coprime_with_8, and gap_forced_from_eight_tick_and_fibonacci. In the framework it realizes the closure step after T8's eight-tick octave, enabling the derivation that 45 emerges from eight-tick structure plus return and, with lcm(8,45)=360, forces D=3.
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