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

Abstract

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) proportional to B and the first-channel RMS amplitude as A_(n=1) proportional to 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 and 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 from the framework's geometric-mean mechanism and an anchored coefficient, k = 3.89 keV, the 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 vacuum birefringence, pending source-specific eta_obs inputs. No new prediction is registered. Contingent on the established OOB framework (G2 = Aut(O) reduction, e7 separator node, Paper CCIII magnetar sector); full proofs in the BraneBulk Omnibus, concept DOI 10.5281/zenodo.19185171 (edition 0-CCCL, version DOI 10.5281/zenodo.21971669). Files: PDF, verification script with output, figure script and figure.