 226  native_decide
 227
 228/-- Block electron counts: s=2, p=6, d=10, f=14. -/
 229def blockElectronCount : Block → ℕ
 230  | Block.s => 2
 231  | Block.p => 6
 232  | Block.d => 10
 233  | Block.f => 14
 234
 235/-- Block counts follow 2(2l+1) for angular momentum quantum number l. -/
 236theorem block_count_formula (b : Block) :
 237    blockElectronCount b = match b with
 238      | Block.s => 2 * (2 * 0 + 1)  -- l=0
 239      | Block.p => 2 * (2 * 1 + 1)  -- l=1
 240      | Block.d => 2 * (2 * 2 + 1)  -- l=2
 241      | Block.f => 2 * (2 * 3 + 1)  -- l=3
 242    := by
 243  cases b <;> rfl
 244
 245/-! ## Minimal indexing scaffold -/
 246
 247structure Index where
 248  rail  : ℤ
 249  block : Block
 250  deriving Repr
 251
 252/- Placeholder indexer from atomic number (deterministic, no tuning). -/
 253def indexOf (Z : ℕ) : Index :=
 254  let period : ℕ := (Z - 1) / 8
 255  let pos    : ℕ := (Z - 1) % 8
 256  let b : Block :=
 257    match pos with
 258    | 0 | 1      => Block.s
 259    | 2 | 3 | 4  => Block.p

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.