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f_subshell_capacity

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The declaration states that the f-subshell with angular momentum l=3 holds exactly 14 electrons. Quantum chemists constructing electron configurations for f-block elements would cite this when enumerating orbital occupancies. The proof reduces immediately to reflexivity on the closed-form subshell capacity expression.

claimThe number of states in a subshell with angular momentum $l=3$ equals 14, i.e., $2(2l+1)=14$.

background

Subshell capacity counts the available quantum states for a given orbital angular momentum l. The upstream definition supplies the formula subshellCapacity(l) := 2*(2*l + 1), where the factor 2 accounts for spin and 2l+1 for the magnetic quantum numbers m_l. This module derives the Pauli exclusion principle from Recognition Science ledger single-occupancy: fermions carry an odd phase through the eight-tick cycle, enforcing antisymmetry that forbids two identical entries in the same ledger slot and thereby produces atomic shell structure.

proof idea

The proof is a one-line term that applies reflexivity directly to the definition of subshellCapacity evaluated at l=3.

why it matters in Recognition Science

This instance populates the subshell sequence 2, 6, 10, 14 that generates the periodic table. It follows from the ledger-derived Pauli exclusion principle stated in the module documentation, which links single-occupancy to degeneracy pressure and matter stability. The result sits inside the QFT-004 target of first-principles shell structure.

scope and limits

formal statement (Lean)

  97theorem f_subshell_capacity : subshellCapacity 3 = 14 := rfl

proof body

Term-mode proof.

  98
  99/-- **THEOREM**: Subshell capacities form the sequence 2, 6, 10, 14, ... -/

depends on (1)

Lean names referenced from this declaration's body.