The scalar part survives as an object. ∇A is now one quaternion: S∇A + V∇A. Construction does not require S = 0. Magnetic induction is read from the vector slot (B = V∇A). The scalar slot is kept and is constructible when nonzero — the case the four-equation teaching has no home for. S.∇A = 0 is a later constraint (Art. 617 uniqueness / Art. 619 “V unnecessary”), not ingest. If |S| is nonzero it raises; it does not delete the scalar. Sibling of the split form (Arts. 594–603 still speak in div/curl). The unsplit object is Arts. 618–619 under citation. It is on the open branch of PR #3, not yet merged to main: github.com/antmikinka/MAXWEL… Files to read against the original: - maxwell/math/quaternion.py - maxwell/electromagnetism/theory/quaternion_expressions.py - tests/test_art_618_nabla_potential.py Classical BVP cases remain (images, equipotentials). No general engine claimed. On verification: the 618 object itself is small and has direct tests (including nonzero S). The broader article corpus was built from @MathpixApp OCR with agent assistance and some manual checks; I still want more human page-against-code verification before treating every detail as settled. If something in the original wording is sharper than the present objects, I want that found.