3325 — The Complete Interval Observer Is Faithful but Scalar Nullity Fixes Only an Endpoint Projection
Result
The doubled full interval section
is a common comparison fiber for reciprocal and adjoint source paths. It is
faithful in zeta: equality of two sections implies equality of their
parameters after differentiation on any source-positive interval.
Scalar nullity fixes only the one-dimensional aggregate of the terminal doubled state. Reciprocal and adjoint terminal vectors can differ inside that scalar-kernel hyperplane, and their complete paths can differ as well.
Thus the remaining RH-bearing gate is a source-derived two-stage uniqueness theorem: lift the zero scalar projection to a terminal doubled state, then lift that state to the complete interval path.
Scope
This does not construct the path-lifting law or prove RH. It solves the common comparison-fiber and parameter-faithfulness gates while isolating projection- to-state-to-path uniqueness as the unresolved step.
Verification
- Packet:
research/grothendieck/the-complete-interval-observer-is-faithful-but-scalar-nullity-fixes-only-its-endpoint.md. - Checker:
research/grothendieck/checkers/check_interval_observer_endpoint_path_hostile.py. - Sequence claim:
seqclaim-f425267fc8d38a00affee461. - Epistemic graph admission:
ev-000000007108-8b07a086-0efc-4bf7-b09e-93742086bc76. - Operator-directed autonomous research.
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