alpha_power_in_formula
plain-language theorem explainer
Recognition Science assigns the integer 5 as the leading exponent of the fine-structure constant in the Lamb shift energy formula, producing the scaling ΔE ~ α^5 mc² [ln(1/α) + corrections]. Atomic physicists and QED modelers cite this constant when matching vacuum J-cost fluctuations to the observed 1057 MHz splitting between 2S and 2P levels. The assignment is introduced by direct definition with no computation or lemma application.
Claim. The leading power of the fine-structure constant α in the Lamb shift energy correction is 5, so that ΔE ∼ α⁵ mc² [ln(1/α) + corrections].
background
The QFT.LambShift module derives the Lamb shift from vacuum fluctuations expressed as ledger J-cost fluctuations. Electron jiggle arises from J-cost-driven position uncertainty, which modifies orbital J-cost and lifts the degeneracy between 2S₁/₂ and 2P₁/₂ levels. The module states that vacuum fluctuations equal ledger J-cost fluctuations and that the level shift equals modification of orbital J-cost.
proof idea
Direct definition that assigns the natural number 5. No lemmas or tactics are applied.
why it matters
The definition supplies the α^5 scaling required by the LambShiftProofs structure, which verifies the 1057–1059 MHz range, S-wave penetration, P-wave exclusion, and six-significant-figure agreement. It aligns with the Recognition Science alpha band (137.030, 137.039) and the eight-tick octave structure. The downstream theorem alpha_fifth_power confirms the value by reflexivity.
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