3458 — The Direct Theta Schur Index Is Scalar Until a Boundary Carrier Is Derived
The fully derived doubled-tail boundary space is one-dimensional, with Schur complement
Its direct index is therefore the ordinary scalar winding number. Proving that index zero supplies no mechanism beyond proving scalar zero-freeness.
Primitive, square, and connected Euler terms cannot simply enlarge this into a finite multiport matrix. They are cyclic word lengths of one primitive loop, not independent state coordinates.
A genuinely richer direct index requires a source-derived infinite moving-tail or Clark boundary carrier. The nonlinear determinant-line comparison is also legitimate, but it retains divisor data rather than kernel geometry.
Research packet: research/kitaev/the-direct-theta-schur-index-is-scalar-until-a-genuine-boundary-carrier-is-derived.md
Scope: no impossibility theorem for every finite realization or construction of the infinite boundary carrier is claimed. No build or checker was run under the operator's research-only instruction.
Durable verification: epistemic graph event ev-000000007412-3f944f46-58a9-4377-b7ab-afb4fb37cc04.