magic_8_eq_2cubed
plain-language theorem explainer
The equality 8 = 2^3 identifies the eight-tick period with three spatial dimensions in Recognition Science. Nuclear physicists modeling shell closures would cite this when linking magic numbers to the phi-ladder and J-cost minima. The proof is a one-line decide tactic that verifies the arithmetic identity directly.
Claim. $8 = 2^3$, where the left side is the eight-tick period and the right side follows from the count of spatial dimensions.
background
Nuclear magic numbers arise in Recognition Science as gaps in the shell-model energy spectrum at J-cost minima on the nuclear recognition lattice. The module lists the sequence 2, 8, 20, 28, 50, 82, 126 and singles out 8 as the eight-tick period at D = 3. This supplies the direct arithmetic identification required by the forcing chain at T7-T8.
proof idea
The proof is a one-line wrapper that applies the decide tactic to the decidable equality (8 : ℕ) = 2 ^ 3.
why it matters
This theorem populates the eight_from_8tick field inside the NuclearMagicCert structure. It anchors the observed magic number 8 to the eight-tick octave (period 2^3) at D = 3, a landmark step in the T7-T8 segment of the forcing chain. The parent certificate bundles it with the full magic-number list and the containment statements for 2 and 8.
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