Physical premise (IDWT): Physical spacetime has infinitely many ordinary spatial dimensions plus time. Matter occupies up to ten spatial dimensions; all remaining spatial directions are unbound for every particle. Depth counts a pattern's bound spatial involvement within that space. “Observed” and “unobserved” describe an observer's access, not different kinds of dimension. Older projective and nested-geometry calculations below retain their additional hypotheses; they do not establish a separate physical manifold or compactified direction. See spatial meaning and mathematical scope.

Summary: Research record, section 31: A useful decomposition of the electromagnetic problem.

Provenance

Preserved from interaction notebook section 31, recorded 2026-09-05 and corrected 2026-09-06. Original sequence contents. This is an exploratory research record, not an independently established V2 result. Read the related later audits before using an intermediate conclusion.

31. A useful decomposition of the electromagnetic problem

The source audit suggests separating three geometrically different objects that were previously being conflated.

31.1 Propagation depth

The photon propagating sector has spatial depth two. Its Maxwell-type kinetic operator and Green function live on the projected photon geometry.

31.2 Matter-response depth

A depth-six electron carries the pulled-back U(1)U(1) connection in its own projected Dirac operator,

P6D∞P6. P_6D_\infty P_6.

Hence electromagnetic curvature can act on six-dimensional electron-sector orbital/polarization variables.

31.3 Source-incidence depth

The explicit photon--electron vertex samples the electron through

(π62)∗Je. (\pi_{62})_*J_e.

This is what prevents the four extra electron coordinates from becoming independent coincidence requirements for ordinary electromagnetic contact.

The three concepts should therefore be kept distinct:

photon propagation depth≠electron response depth≠full electron coincidence depth. \boxed{ \text{photon propagation depth} \neq \text{electron response depth} \neq \text{full electron coincidence depth}. }

This appears to resolve the apparent tension between "electromagnetism is a connection on the full manifold" and "the electromagnetic interaction is a depth-two shared projection."

The connection may act on a high-depth matter sector after pullback while its independently propagating radiation mode remains depth two.