One-Octonion Brane-Bulk Framework — Paper CCCLX: Schwinger-n=1 as the First e7 Boundary Channel — the B^(1/2) Amplitude Law and its B^(-1/2) Aperture Complement

Narrow derivation paper for the One-Octonion Brane-Bulk (OOB) framework's first strong-field boundary channel. With one identification — one activated e7 boundary site per magnetic flux cell, rho_e7 = B/Phi_0 = 1/(2 pi l_B^2) — and two stated working assumptions, the first-channel conversion probability scales as P_(n=1) ∝ B and the first-channel RMS amplitude as A_(n=1) ∝ B^(1/2), while every length-type scale of the channel (magnetic length, site spacing, and the corrected magnetar sump radius r_T2*(mag) of Paper CCIII/CCCXV) scales as B^(-1/2). The typing rule — B^(+1/2) is never a length; B^(-1/2) is never an amplitude or an energy — removes a previously flagged sign ambiguity. The transition-energy member E_swing = k sqrt(B_14) carries a structural exponent (conditional on the framework's geometric-mean mechanism) and an honestly anchored coefficient (k = 3.89 keV, sector anchor to 4U 0142+61). The Schwinger n=1 selection is inherited, triply forced (Lagrangian Foundations v2, DOI 10.5281/zenodo.20619191). The magnetar sector is presented at its current status — the public 1E 1547.0-5408 polarization data support the broad vacuum-birefringence transfer picture without distinguishing OOB from standard QED VB; the result is blocked pending source-specific eta_obs inputs and E92 renormalization — not as completed observational support. No new prediction is registered. Contingent on the established OOB framework (G2 = Aut(O) reduction, e7 separator node, Paper CCIII magnetar sector); full proofs and gate scripts in the BraneBulk Omnibus, concept DOI 10.5281/zenodo.19185171 (edition 0-CCCL, version DOI 10.5281/zenodo.21971669). Supplementary files: verify gate script + green output (39/39), figure script, Fugu cross-model audit report, the E90-E99 magnetar EFT status notes, the 2026-06-09 magnetar anchor-status note, and the status CSVs backing every quoted sector number.