Abstract
As part of Complementarity-First research and its Reciprocal Internal Complementarity (RIC) program, we study the smooth-core requirements of an admitted magnetic sector. A compact phase bundle can carry integral flux without selecting a nonzero sector or a dynamical particle. When its opposite-weight carrier is equipped with an identity-covering antiunitary involution of square +I, the fixed real plane is the underlying real bundle of the charged line. Its linking-sphere Euler number is the product of representation weight and magnetic degree. Complex first-Chern-class cancellation therefore does not remove the same-rank reciprocal extension obstruction. On the sphere, neutral stabilization removes only even winding; an additional odd charged real plane is the minimal direct-sum enlargement for an odd sector. A compatible complex rank-four realization admits a supplied SU(2) connection, while the original charged splitting fails at the scalar zero. The geometric result is separated from the choice of a classical action and from the observables to be recovered. A standard massless-scalar core has exact projected flux but fails relative Maxwell-only spatial-stress matching. For a separately supplied canonical adjoint-scalar model with equal scalar and vector masses, a rational core-to-tail contraction and an on-shell energy estimate give a certificate-qualified radial completion. Its reduced energy obeys 1.2376844 < Ered < 1.2377150. Complete relative exterior energy-density and spatial-stress errors are below 0.000789 for ρ ≥ 8; the transport discrepancy is at most π/700 under the stated finite path budget. The proofs and certificate conditions are given here, with machine-readable inputs and recorded outputs accompanying the manuscript. These conclusions do not select the action, coupling, physical mass scale, particle population, or dynamical stability. A local exchange-control application preserves the distinction between representation compatibility and field dynamics.
Where it sits in the release
The first paper of the magnetic trilogy. It separates the geometric extension result from the choice of a classical action and from the observables to be recovered; it does not select the action, coupling, mass scale, particle population, or dynamical stability.
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