baryonDecupletCount
Baryon decuplet count is defined as the natural number 10. Researchers reconstructing Gell-Mann's eight-fold way inside Recognition Science cite it to encode the 2 × 5 factor that matches the observed decuplet at D = 3. The declaration is a direct constant assignment with no computation or lemmas.
claimThe baryon decuplet cardinality is the natural number 10, written $N_ {decuplet} = 10$.
background
The module derives the eight-fold way from Recognition Science by mapping Gell-Mann multiplets to lattice periods fixed by the forcing chain. Octets have size 8 = 2^D with D = 3; the decuplet has size 10 = 2 × 5 where 5 equals the configuration dimension and the count of canonical hadron families. The definition sits beside mesonOctetCount to supply the second factor in the 2 × 5 relation.
proof idea
The declaration is a one-line definition that directly assigns the constant 10. No lemmas or tactics are applied.
why it matters in Recognition Science
It supplies the decuplet cardinality required by the EightFoldWayCert structure, which records mesonOctetCount = 2^3, baryonDecupletCount = 2 * 5, and five hadron families. The parent theorem decuplet_eq_2_times_5 then confirms the arithmetic identity by decision. This step embeds the RS counting 10 = 2 × configDim D into hadron classification and links the T7 eight-tick octave to observed SU(3) multiplets.
scope and limits
- Does not derive the integer 10 from the forcing-chain equations.
- Does not assign specific particles to decuplet states.
- Does not compute mass values or splitting patterns.
- Does not address flavor or spin representations beyond the count.
Lean usage
theorem decuplet_eq_2_times_5 : baryonDecupletCount = 2 * 5 := by decideformal statement (Lean)
28def baryonDecupletCount : ℕ := 10
proof body
Definition body.
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