o4_channel_closure_certificate
plain-language theorem explainer
The O4 channel closure certificate shows that the refined shift in the lepton mass chain decomposes as a base term 2W plus ledger fraction plus the explicit alpha-squared and alpha-cubed radiative corrections, while the electron-muon step matches the passive energy plus inverse-four-pi term minus second-order correction and the muon-tau step equals the D-cube face count minus 37/2 alpha. Researchers tracing the Recognition Science mass ladder would cite this result to lock the perturbative coefficients in the one-parameter lepton families. The
Claim. The refined shift equals $2W +$ ledger fraction plus $alpha^2 + 12 alpha^3$, the electron-muon generation step equals $E_{passive} + 1/(4 pi)$ minus the order-2 correction, and the muon-tau generation step equals the number of faces of the $D$-cube minus $(37/2) alpha$.
background
The module supplies the J-cost perturbation bridge that upstreams O4 closure into the Masses namespace. It certifies the Jcost(1+alpha) perturbative channel form together with the explicit alpha-squared plus twelve alpha-cubed radiative decomposition that appears inside refined_shift. Local conventions treat alpha as the fine-structure constant 1/alphaInv, cube_faces(D) as the integer 2D, and the canonical arithmetic objects as the initial Peano surface supplied by the logic realization. Upstream results include the definition of alpha, the geometric count cube_faces(D) = 2D, and the canonical arithmetic object that supplies the integer and rational slots used in the coefficient families.
proof idea
The tactic proof opens with refine to split the conjunction, then applies the channel-split lemma refined_shift_channel_form followed by simp on base_shift to reach the target base term. The second conjunct is discharged by the lemma step_e_mu_channel_split. The third conjunct applies step_mu_tau_channel_split and reduces the face count via norm_num on the definition cube_faces(D) = 2D.
why it matters
This theorem supplies the Lean closure package for O4 coefficient forcing inside the lepton chain and thereby certifies the canonical integer/rational slots required by the sibling mass-topology counts. It directly fills the channel-level form demanded by the J-cost perturbation bridge and aligns with the T5 J-uniqueness and T8 D=3 landmarks of the forcing chain. No downstream theorems yet consume it, leaving open the question of how the certified coefficients propagate into the full phi-ladder mass formula.
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