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 2: Two different notions of encounter.

Provenance

Preserved from interaction notebook section 2, 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.

2. Two different notions of encounter

Particles can interact through their extended field tails while their centres remain separated. The changes in mutual influence must propagate no faster than light over the separation. A local product of fields samples their values at the same spatial point; it does not require the centres of the two patterns to coincide.

The pair must retain each pattern's spatial profile, its multiple orientations and their relative arrangement, phase and response. The centre is a position associated with that pattern, not a complete description of its interaction.

Within the ten-dimensional matter domain, a three-dimensional observer leaves seven spatial directions unresolved. Infinitely many additional directions are unbound for every particle. These counts do not imply independently randomized offsets or a power-law encounter penalty. A particle's bound depth, the directions through which its tails extend, and the coordinates an apparatus resolves are different data.

The physical calculation is the reciprocal evolution of both complete patterns under the same field law. A reduced projection is usable when derived from that law for the specified preparation and observable.