secondMagic_eq_2cubed
The second magic number equals eight. Nuclear physicists certifying structure categories within Recognition Science cite this when assembling the depth certificate. The proof is a one-line decision procedure that confirms the numerical identity from the definition.
claimThe second magic number equals $2^3$.
background
The Nuclear Physics Depth from RS module defines five nuclear structure categories (single-particle, collective, rotation, vibration, cluster) that set configDim D = 5. The second magic number is introduced directly as the natural number eight. This theorem confirms its equality to two cubed, aligning with the eight-tick octave (period $2^3$) from the T0-T8 forcing chain.
proof idea
This is a one-line wrapper that applies the decide tactic to the numerical equality between the second magic number and two cubed.
why it matters in Recognition Science
The result supplies the second_magic_cube field inside the nuclearPhysicsDepthCert definition that certifies overall nuclear physics depth. It connects to T7 of the unified forcing chain where the eight-tick octave appears as a structural period. The module reports zero sorries and zero axioms.
scope and limits
- Does not derive the second magic number from the J-cost function or Recognition Composition Law.
- Does not compute nuclear binding energies or mass formulas on the phi-ladder.
- Does not treat the first magic number or other nuclear constants.
Lean usage
have h : secondMagicNumber = 2 ^ 3 := secondMagic_eq_2cubedformal statement (Lean)
35theorem secondMagic_eq_2cubed : secondMagicNumber = 2 ^ 3 := by decide
proof body
36