OOB Lagrangian Foundations v2 (2026-06-09): P1, P2, B4 closures — 11 of 11 forced rigorously revived

Version 2 of the OOB Lagrangian Foundations compendium. Single substantive content addition over v1 (2026-06-05, DOI 10.5281/zenodo.20563830): the three open premises P1 (isotropy), P2 (coherence), and B4 (Schwinger n=1 selection) that v1 labelled DERIVED-conditional / PARTIAL are now FORCED. P1 closure: via Paper CCLXXXIII auxetic Fano-triangle kagome elasticity (Check #1 C₃ ⊂ G₂ invariance forces 2D elastic tensor 6 → 2 free constants = full continuous SO(2) isotropy, sympy-verified; Check #5 twisted kagome a(α) = 2R·cos(α) isotropic in 3 directions → ε_xx = ε_yy → ν = −1 auxetic dilationally pure). The 2D isotropic Green's function G(r,θ) = (1/2π)log(1/r) is angularly symmetric (Δlog(1/r) = 0, sympy exact), forcing the uniform approach-angle distribution to e₇. P2 closure: via Paper CXXXI Migdal-Witten character expansion on K(7) at N ≥ 10⁵⁹ (trivial-rep saddle dominates by ~exp(10⁵⁰) over non-trivial reps) + Paper CXLIX e₇ singlet brane-bulk separator (closed-loop topology with θ as virtual integration variable, never measured) + standard QM Born postulate (single squaring at end for indistinguishable paths). B4 closure: via Route B Migdal-Witten saddle — Schwinger's n-series is an instanton expansion; n=1 ↔ single closed Wilson loop ↔ trivial G₂ rep [0,0] (C₂ = 0, no Migdal-Witten suppression); n≥2 ↔ multi-loop ↔ non-trivial reps suppressed by ~exp(-10⁵⁰). Combined with standard Schwinger (n=2)/(n=1) ≈ 1/92 at E=E_c, OOB combined suppression is ~exp(10⁵⁰) — n=1 FORCED, not defensible. f_III = 1 − 4/π² = 0.5947 is now FULLY FORCED (both premises closed). §8 honest-status table: NO PARTIAL, NO DERIVED-conditional, NO POSTULATED entries. The blanket '11 of 11 forced' headline that v1 retired (because of one Jensen error) is RIGOROUSLY REVIVED with all v1 corrections preserved (Jensen error replaced by e₇ two-leg orthogonal transit; sec⁴ tree-level not one-loop; sinc normalization; bulk-sector three-into-one collapse; rapidity identity typo correction; 77→4.9 ppm JUNO Gudermannian correction). CXXXI Migdal-Witten now drives FOUR closures (YM mass gap, principle of least action, f_III P2, Schwinger n=1). CCLXXXIII auxetic ν=−1 now drives FOUR closures (action principle, shape memory, ν=−1 theorem, f_III P1). One structural primitive per box, four distinct closures each — framework signature pattern. New v2 content: §3 application of tilted DBI to W-eigenstate gives sin²θ_23 = sin²(π/4 + θ_G₂) = (2413+196√3)/4826 = 0.5703 at −0.08σ from NuFIT 6.0 (closes PMNS sector). §4 closure of P1+P2. §5 closure of B4 via Route B. §6 attribution correction: arccosh(3) = arccosh(λ_4 = 3) Klein ladder eigenvalue, not K(7) systole (Paper CCLXIX §4 attribution correction; numerical identity unaffected). §8 fully forced status table. Math verification: verify_lagrangian_foundations_v2.py at 23/23 PASS (sympy + numpy + scipy at each step). Cross-link with math audit v2.2 (companion). Supersedes v1 (DOI 10.5281/zenodo.20563830). Community: one-octonion-brane-bulk. Bharathi Dasan Jagadeesan, M.D., University of Minnesota CMRR. ORCID 0000-0002-1143-941X. CC-BY-4.0.