# External Search Notes — EML-ONTO-CORE-07

A fresh external literature search was run immediately before drafting Paper 07.

The comparison layer uses primary/author research manuscripts when available.

## 1. Layered Monoidal Theories I

Leo Lobski, Fabio Zanasi.
`Layered Monoidal Theories I: Diagrammatic Algebra and Applications`.
arXiv:2602.19776 (2026).

Relevance:
- combines formal descriptions of systems at different abstraction levels;
- permits translations between several monoidal theories within one precise diagrammatic framework.

Use in UMF:
- recent strong precedent for modeling one scientific system through multiple typed levels plus explicit translations.
- UMF is not claimed to be a layered monoidal theory.

## 2. Layered Monoidal Theories II

Leo Lobski, Fabio Zanasi.
`Layered Monoidal Theories II: Fibrational Semantics`.
arXiv:2602.22373 (2026).

Relevance:
- gives fibrational / opfibrational / deflational semantics for layered monoidal theories;
- connects layered theories with Grothendieck fibrations and displayed categories.

Use:
- methodological support for indexed/layer-relative formal structures.

## 3. Layered Monoidal Theories

Leo Lobski.
`Layered Monoidal Theories`.
arXiv:2512.12139 (2025).

Relevance:
- larger treatment of several abstraction levels, translations, and sound/complete translations in a domain example.

Use:
- comparison for the UMF principle that integration requires explicit translations rather than untyped equality.

## 4. Displayed Categories

Benedikt Ahrens, Peter LeFanu Lumsdaine.
`Displayed Categories`.
arXiv:1705.04296 (2017).

Relevance:
- modularly builds multi-component categorical structures by adding data/properties over a base category;
- provides a basis for fibrational constructions and modular formalization.

Use:
- comparison for the UMF vertical-spine-plus-cross-cut modular architecture.

## 5. Categorical semantic abstraction

Shin-ya Katsumata, Xavier Rival, Jérémy Dubut.
`A Categorical Framework for Program Semantics and Semantic Abstraction`.
arXiv:2309.08822 (2023).

Relevance:
- treats interpretations as structured functorial objects and abstraction relations through explicit natural transformations;
- emphasizes soundness of semantic abstraction.

Use:
- comparison for explicit cross-layer translation and preservation conditions.

## 6. Institutional ontology integration

Robert E. Kent.
`The Institutional Approach`.
arXiv:1810.08074 (2018).

Relevance:
- uses categorical institution/fibration ideas to organize local logics and integrate heterogeneous ontologies.

Use:
- comparison for preserving local theory identity while enabling global semantic integration.

## 7. Decorated Cospans / Dynamical Systems and Sheaves

Brendan Fong.
`Decorated Cospans`.
arXiv:1502.00872 (2015).

Patrick Schultz, David I. Spivak, Christina Vasilakopoulou.
`Dynamical Systems and Sheaves`.
arXiv:1609.08086 (2016).

Use:
- background comparison for compositional interfaces and local/global structured systems already used in Papers 02–06.

## Boundary rule

None of these papers prove:
- the existence of a pre-formal unary ontology;
- the universality/minimality of the E/L/C triad;
- Phi_pre = Closure;
- CRL derivability from Closure;
- UMF as a physical Theory of Everything.

They are used only as technical precedents for layered, indexed, compositional, and translation-aware formalisms.