pith. sign in
def

prefersFCC

definition
show as:
module
IndisputableMonolith.Chemistry.CrystalStructure
domain
Chemistry
line
177 · github
papers citing
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plain-language theorem explainer

This definition enumerates the atomic numbers of metals that adopt face-centered cubic structure under Recognition Science stability rules. A materials physicist comparing close-packed phases would reference it when checking coordination-12 predictions against observed lattices. It is a direct list assignment with no computation or lemmas applied.

Claim. The atomic numbers of metals preferring the face-centered cubic crystal structure are $29$ (Cu), $47$ (Ag), $79$ (Au), $13$ (Al), $28$ (Ni), and $82$ (Pb).

background

The CrystalStructure module derives BCC, FCC, and HCP lattices from RS principles. BCC coordination equals 8 and matches the eight-tick ledger period, while FCC and HCP both reach maximum packing efficiency with coordination 12. The upstream PhiLadderLattice.that supplies a hypothesis structure for phi-ladder Poisson summation that downstream results may assume until analytic infrastructure is complete.

proof idea

One-line definition that directly binds the constant list of atomic numbers to the identifier.

why it matters

The declaration populates the energy-ordering claim FCC ≈ HCP > BCC that appears in the module predictions. It supplies concrete examples for the close-packing and phi-stability mechanisms (ideal HCP c/a ≈ φ) and sits alongside the sibling HCP list. No parent theorem consumes it yet; it remains an illustrative data point within the CM-001 framework.

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