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 11: Next proof obligations.

Provenance

Preserved from interaction notebook section 11, 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.

11. Next proof obligations

The next pair calculation must use actual isolated field patterns at their own frequencies and evolve both through the same causal field law. Retain their extended tails, complete spatial and orientation structure, relative phases and reciprocal deformation.

Derive forces and any changes of shape from that evolution with complete energy and momentum accounting. Determine how the response depends on bound/free orientation and the detector's resolved coordinates. No centre-coincidence requirement, coordinate-mirroring constraint or independent random-offset ensemble is supplied in advance.

If a reduced current or kernel is useful, derive its maps, kinetic normalization, causal history and observable interpretation. Electromagnetic identification and any reaction rate remain outputs to calculate, rather than assumptions fixing the interaction's dimensionality.