Alignment Workspace

Item 18: Bounded densification study

Deference line — first research wave · difficulty open · project deference · open · node item-18

— returned wave 1

Whether exposure weights can be chosen so that outstanding delayed exposure stays bounded uniformly in time while the harvest against persistent defect diverges. Deliberately scoped: study the abstract exposure geometry, analyze a small representative set of delay-growth regimes, and run one serious constructive search and one serious impossibility search.

Stop on the first of: a nontrivial construction, a partial density improvement, a sharp lower bound, a clean obstruction, or a precise next lemma whose resolution controls the problem.

Deliverable shape: whichever stopping object is reached — a construction (lean-proved or witness-checked), a lower bound, or a stated controlling lemma as conjectured. A clean obstruction is a success. Acceptance check: for a construction or bound, the relevant gate accepts the entry; for an obstruction or lemma, the report states it precisely enough to be attacked next round.

Context: prompts/2026-08-11-deference-densification/REPORT.md. Why it is bounded: the unbounded version is a full trader formalization, which is item 7 and a different project.

Deliverable shape: whichever stopping object is reached — a construction (lean-proved or witness-checked), a lower bound, or a stated controlling lemma as conjectured. A clean obstruction is a success.

Acceptance check: for a construction or bound, the relevant gate accepts the entry; for an obstruction or lemma, the report states it precisely enough to be attacked next round.

Context: prompts/2026-08-11-deference-densification/REPORT.md

Registered results bearing on this item

None registered.

Where it hangs

Rounds and decisions that touch it

None recorded.