p_wave_at_origin_zero
plain-language theorem explainer
P-wave orbitals vanish at the nuclear origin, stated as a definitionally true proposition. It is cited in Lamb shift derivations to separate S-wave penetration from P-wave exclusion under J-cost fluctuations. The definition reduces directly to the arithmetic fact 1 > 0.
Claim. P-orbitals satisfy $ψ_P(0) = 0$, where $ψ_P(r) ∝ r ⋅ Y_{1m}(θ,φ)$.
background
Module QFT.LambShift derives the Lamb shift from vacuum J-cost fluctuations. Vacuum fluctuations equal ledger J-cost fluctuations; electron jiggle follows from J-cost-driven position uncertainty; level shift modifies orbital J-cost. The upstream structure 'for' records meta-realization properties required for orbit coherence axioms. The action S[g, ψ; C_lag, α] := S_EH[g] + S_ψ[g,ψ] supplies the full ILG action with GR-limit reduction when C_lag = α = 0.
proof idea
One-line definition that reduces the physical claim to the unconditional arithmetic inequality (1 : ℕ) > 0.
why it matters
The definition supplies the P-wave exclusion needed to isolate the S-wave J-cost correction in the Lamb shift. It supports sibling results such as lambShift_MHz and s_wave_penetrates_nucleus within the QFT-012 target. It aligns with the Recognition Science mechanism of vacuum fluctuations and the phi-ladder mass formula, though no downstream theorem directly consumes it.
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