closure_number
plain-language theorem explainer
The definition introduces the closure number as one greater than the eight-tick period. A physicist deriving the 45-tick synchronization from the dimension-forcing chain would cite it to encode the fence-post counting that closes an 8-tick cycle. It is introduced by direct arithmetic extension of the imported eight-tick constant.
Claim. The closure number is defined by $n_c := 8 + 1$, where 8 is the eight-tick period forced by three spatial dimensions.
background
In the Recognition Science framework the eight-tick period is the ledger coverage of $2^D$ at $D=3$. The module supplies physical motivation for the number 45 by treating it as cumulative phase over a closed cycle. The closure number supplies the fence-post count: eight sections require nine posts to return to the initial phase state, as stated in the module documentation.
proof idea
The definition is a one-line arithmetic extension that adds one to the eight-tick constant imported from DimensionForcing and RecognitionThermodynamics.
why it matters
This definition supplies the integer 9 that feeds the equivalence theorems showing $T(9)=45=9×5$. It closes the step from the eight-tick cycle (T7 in the forcing chain) to the triangular accumulation that yields the 45-tick period. The parent results are the derivations_equivalent theorem and the PhysicalDerivationCert structure that list the complete chain from dimension to synchronization.
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