The M2 Soliton Function, First Layer Closed: Certification, Dictionary, and the A2-q Verdict for the Weak-Cloud Bag (v0.4.1, Figure-Regenerated + Cross-Library Audit)

We deliver the first complete layer of the M2 soliton-function program. In BVP units (η=σ=1), we complete the full certification chain of the two-component boundary value problem for the mother core (Higgs-ized medium compacton, 1/r³ source + B7-pinned core) and the weak cloud (Yukawa-coupled): anchor reproduction (nail-cap to nine digits, pp-mapping 4/4, joint root to six digits), reconstruction of Dictionary v2 (digit-exact reproduction of the Born-level printout), docking with the five-term family v1.0 analytic derivation, and the formal A2-q verdict |q_tot/q_eff−1| = 3.3% < 5% (PASS). Also delivered: Scale Bridge 2b(a) (3.622 keV/BVP unit, κ_min = 958 co-signed), the cloud excitation spectrum, the ν running profile (+0.12/−0.56/+0.91) and the three-generation closure (winding truncation × critical-end collapse law, confirmed by LEP N_ν = 3). All conclusions carry anchor labels and flip conditions F1–F5. v0.4.1 errata: (1) the four figures were regenerated through the certification chain (regeneration-labeled); (2) supplementary-material anchor 1 (nail-cap) carries a transcription caveat — reruns failed to reproduce −0.672922006, diagnosis: regular-core equation (φ−φ³) substituted for the mother equation (φ+φ³+1/r³); anchors 2/3 and Dictionary v2 were independently reproduced in the 20261005 session; (3) cross-library audit (C-line, 20261005): the frozen nail-cap value was independently reproduced from the mother equation at the [anchor: ρ_c = 0.5] domain, corroborating the diagnosis (executable repair of the script's Anchor-1 block pending as flip item F7); (4) v0.3 kept on record (draft-placeholder figure incident). References: [1] D.V. Shirkov, I.L. Solovtsov, PRL 79, 1209 (1997). [2] D. Hanneke, S. Fogwell, G. Gabrielse, PRL 100, 120801 (2008). [3] T. Aoyama et al., Phys. Rept. 887 (2020) 1; Fermilab Muon g-2, PRL 135, 101802 (2025). [4] Particle Data Group, PDG 2026, PTEP 2026, 083C01. [5] BES III Collaboration, arXiv:2607.20366; ICHEP 2026. Computational collaboration: Kimi (Moonshot AI); C-line co-signature (κ_min = 958, −5.2%/+4.9%).