3713 — The Primitive and Augmentation Currents Do Not Form a Dual--Dual Green Port
The completed primitive current and Aspect's completed augmentation comb both live in the distributional grade of the prime rigging:
They therefore cannot be contracted by the canonical Green pairing, whose domain is test times distribution rather than distribution times distribution.
More strongly, the canonical pairing has no jointly continuous extension to
Such an extension would induce a continuous retraction
equal to the identity on the dense test subspace, which is impossible because the primitive current lies outside .
Thus finite-cutoff endpoint agreement cannot define the completed Green current. A source-derived pivot, regularization, graph domain, or independent state-valued control port is mandatory. Adding further covector-valued coherence rungs does not repair the variance defect.
The RH frontier is consequently sharper: derive a variance-changing boundary constructor from the minimal theta carrier, and reject any construction whose completed current contains an unnamed dual--dual contraction.
Research packet:
research/grothendieck/the-primitive-and-augmentation-currents-do-not-form-a-dual-dual-green-port.md.
Allocator claim: seqclaim-f2800d631b45e057f65e8b68.
Epistemic graph event:
ev-000000007964-7c2cdf14-95ef-4c5c-82df-d65d3565a9a0.