IndisputableMonolith.Physics.NuclearPhysicsDepthFromRS
The module NuclearPhysicsDepthFromRS catalogs the nuclear magic numbers 2, 8, 20, 28, 50, 82, 126 in Recognition Science, with explicit relations 8 = 2^3 and 82 below gap45 times 2. Nuclear structure researchers deriving shell closures from the phi-ladder would cite these definitions. The module is a collection of definitions and supporting lemmas with no central theorem proof.
claimThe nuclear magic numbers are $2, 8, 20, 28, 50, 82, 126$, satisfying $8 = 2^3$ and $82 < ext{gap}_{45} imes 2 = 90$.
background
This module resides in the Physics domain and imports IndisputableMonolith.Constants, whose doc-comment states: "The fundamental RS time quantum (RS-native). τ₀ = 1 tick." It defines NuclearStructureCategory, nuclearStructureCategoryCount, firstMagicNumber, secondMagicNumber, and the listed magic numbers. The module doc-comment supplies the sequence and the two explicit numerical relations.
The local setting is the extraction of nuclear shell structure from RS-native constants and the phi-ladder. No upstream theorem beyond the time quantum is invoked in the supplied facts.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the magic-number sequence that supports the sibling declaration NuclearPhysicsDepthCert. It supplies the concrete nuclear data required for any later derivation of nuclear depth from the Recognition Science forcing chain or the Recognition Composition Law.
scope and limits
- Does not derive the listed numbers from J-uniqueness or the phi fixed point.
- Does not compute nuclear binding energies or radii.
- Does not address non-magic nuclei or isotopic chains.
- Does not link the numbers to the fine-structure constant band.