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 29: First direct verdict on K66K_{66} from presently written V2.

Provenance

Preserved from interaction notebook section 29, 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.

29. First direct verdict on K66K_{66} from presently written V2

For the specified scalar action, the incoherent pair-density term is

H12sc=κ6J1J2, \mathcal H_{12}^{\rm sc}=\kappa_6J_1J_2,

with additional coherent terms when the two field contributions interfere. This is a local field-product expression. Extended tails can overlap and contribute to it while the pattern centres remain separated. Locality of the field product therefore supplies no general absence-of-interaction theorem before centre coincidence.

The coefficient, actual spatial fields and full reciprocal dynamics are required to determine forces or changes of orientation. A static overlap expression alone neither supplies causal time evolution nor establishes an electromagnetic identification. No assumed position lock or statistical coincidence penalty is needed as an intermediate target.