# Fresh external search notes — 2026-08-16

Fresh search was performed immediately before drafting EML-RKD-03.

The mathematical existence results below are established external mathematics. EML-RKD-03 does not claim to have invented inverse limits, Mittag–Leffler systems, compactness, König-type branch arguments, or final coalgebras. Its contribution is the typed epistemic interpretation and the separation of existence levels.

## Sources

1. The Stacks Project, Section 10.86, *Mittag-Leffler systems*, Lemma 10.86.3 (Tag 0597).
   - For a countable directed inverse system of nonempty sets satisfying the Mittag-Leffler condition, the inverse limit is nonempty.
   - The proof reduces to a sequence with surjective transition maps and uses a choice principle.

2. The Stacks Project, Section 10.86 (Tag 0594).
   - Defines/studies Mittag-Leffler stabilization of images and its role in inverse systems.

3. The Stacks Project, Lemma 4.21.7 (Tag 086J).
   - A directed inverse system of finite nonempty sets has nonempty inverse limit.

4. Miklós Pintér (2008), *Every hierarchy of beliefs is a type*, arXiv:0805.4007.
   - In a purely measurable type-space framework, higher-order belief hierarchies receive a complete universal representation.
   - Used only as a formal precedent for infinite epistemic-like hierarchies.

5. Iztok Banič, Goran Erceg & Judy Kennedy (2021), *Mapping and fixed point property theorems for inverse limits with set-valued bonding functions*, arXiv:2112.06834.
   - Studies inverse limits of compact metric spaces with upper-semicontinuous set-valued bonding functions.
   - Used as a precedent for relation/set-valued generalization.

6. Luigi Santocanale (2004), *Logical Construction of Final Coalgebras*, arXiv:math/0403227.
   - Proves final-coalgebra existence for specified finitary polynomial endofunctors under explicit categorical hypotheses.
   - Used to justify the caution that final coalgebra existence is conditional and should not be inferred from an arbitrary inverse tower.

## Search discipline
- Technical sources were primary mathematical papers or the primary Stacks Project reference.
- No secondary news/blog sources were used.