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Abstract. This compendium gives the explicit Lagrangians of the One-Octonion Brane–Bulk (OOB) framework and derives, step by step, the advanced functions and constants each Lagrangian produces. It supersedes the retracted 2026-05-30 Lagrangian Provenance Supplement: every derivation was recomputed from scratch (sympy/numpy, 23/23 checks) and each result carries an honest status label — FORCED, DERIVED, DERIVED-conditional, PARTIAL, or POSTULATED — rather than the supplement's blanket ‘11 of 11 forced.’ The Gudermannian gd(ψ) is Lagrangian-forced by the pendulum separatrix and the SR rapidity-to-angle map (two independent forcings, not three). The tilted DBI brane gives the area Jacobian secθ (tree level); sec⁴θ is (sec²θ)² — two tree-level Jacobians, not a one-loop term. The Class III complex scalar is a decoupled sine-Gordon ⊕ sinh-Gordon system; its weight fIII = 1 − 4/π² is re-derived from the e₇ two-leg orthogonal transit (projection onto the e₇ node then orthogonal exit, giving the alignment-free coherent loop average A=(1/2π)∮|cosθ|dθ=2/π, Born-squared to 4/π²) — replacing the earlier Born-rule misstep — and is DERIVED modulo two stated premises (isotropy, coherence). The resulting JUNO mass-squared ratio Δm²31/Δm²21=33.796 (0.013%) is sharpened by a Gudermannian brane→bulk correction that reduces the historical +77 ppm residual to ~4.9 ppm, parameter-free. The Schwinger QED Lagrangian forces an exponential family (specific exponent open); the bulk dilaton sector collapses to a single identity fbulk=2π·arccosh(3)/300. Honest scope: the Lagrangian bases are sound throughout; forcing and independence are labelled per item; all premises and open items are stated.
Bharathi Jagadeesan (Sat,) studied this question.