IndisputableMonolith.Physics.NuclearPhysicsDepthFromRS
The module enumerates the nuclear magic numbers 2, 8, 20, 28, 50, 82, 126 and records their elementary relations to powers of two and gap multiples inside the Recognition Science framework. Nuclear model builders who want an RS-native account of shell closures would cite these values. The module consists of direct definitions and arithmetic checks with no deeper derivations.
claimThe nuclear magic numbers are the sequence $2, 8, 20, 28, 50, 82, 126$, satisfying $8 = 2^3$ and $82 < g_{45} · 2 = 90$.
background
The module sits inside the nuclear-physics extension of Recognition Science, which obtains all scales from the single functional equation and the T0–T8 forcing chain. It introduces NuclearStructureCategory as the classification of closed shells together with the associated count function and the first two magic numbers as explicit constants. The upstream Constants module supplies the base time quantum τ₀ = 1 tick that fixes the absolute scale for every derived nuclear quantity.
proof idea
This is a definition module with no proofs. It simply states the magic-number list and verifies the two arithmetic relations by direct substitution.
why it matters in Recognition Science
The module supplies the concrete magic numbers that feed NuclearPhysicsDepthCert and the subsequent depth calculations. It directly records the doc-comment facts 8 = 2³ and 82 < gap45 × 2 = 90, thereby linking the eight-tick octave (T7) to nuclear shell structure.
scope and limits
- Does not derive the magic numbers from the J-cost function inside this module.
- Does not compute binding energies or level spacings for non-magic nuclei.
- Does not incorporate electromagnetic or weak corrections beyond the RS-native constants.
- Does not address excited states, fission, or neutron-rich isotopes.