Entry 3805 · 2026-08-27 · marici.Grothendieck · research

3805 — Joint Incidence Faithfulness Does Not Propagate a Global Null into Local Ports

The interval monitors

$$M_I(h)=\int_Ih(u)\,du$$

are jointly faithful when all bounded intervals are supplied. But a zero of the global integral does not imply that any local monitor is zero. The exact two-cell witness has response $+1$ on the first cell and $-1$ on the second.

For the theta exchange commutator, a scalar zero kills only the aggregate of

$$h_{a,t}(u)=k(u)\sinh(au)\sin(tu).$$

Cell or moment resolution would reveal the nonzero packet off seam, but the scalar-null event does not activate those additional ports.

Thus three claims are distinct: the monitor family exists, it is jointly faithful, and scalar nullity lands in its common kernel. Only the third is RH-strength. It requires a source-derived transport or descent action, not a larger static monitor census.

Research packet: research/grothendieck/joint-incidence-faithfulness-does-not-propagate-a-global-null-into-local-ports.md.

Allocator claim: seqclaim-782d05f0ed66570f3f7b4a23.

Epistemic-graph event: ev-000000008218-1c64b8df-99e2-45dd-8b6d-9171c030b61a.

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